, MSCI Barra fundamental factor model, Barclay Group Inc. bond factor model. In addition, the factor models developed by Haugen and Baker (1996a), and Chen and Zhang (2010) are also proven improvements on the CAPM-inspired single-index market model in explaining the cross-section of expected stock returns. R

Table 1.9 Annual firm numbers that have available data of OP andInv (2004-2014) Table 1.14 Time-series regressions of six value-weighted Size-B/P portfolios, Size-OP portfolios and Size-Inv portfolios on FF5F Model, Chinese A-share stock market (July

Introduction gé né rale

Les modè les de facteurs ont é té les modè les dominants dans le domaine de prix de l'actif depuis des dé cennies depuis l'apparition du 'Capital Asset Pricing Model' (CAPM) de [START_REF] Sharpe | Capital asset prices: A theory of market equilibrium under conditions of risk[END_REF], [START_REF] Lintner | The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[END_REF] et [START_REF] Black | Capital market equilibrium with restricted borrowing[END_REF]. Le CAPM d'origine peut ê tre considé ré comme le modè le de facteur à indice unique et facile à effectué et à interpré ter; cependant, il est critiqué pour ses hypothè ses et le manque du pouvoir explicatif des anomalies du marché boursier. D'innombrables chercheurs se sont consacré s à dé velopper un modè le qui remé die aux dé fauts de CAPM. Les adversaires de CAPM qui voient son manquement du pouvoir explicatif affirment qu'il doit y avoir d'autres facteurs en dehors de la rentabilité excé dentaires du marché qui dé rivent la rentabilité de l'actif. Les modèles d'évaluation des actifs qui ont plus d'un facteur sont appelés modèles multifactoriels.

L'un des modè les multifactoriels fondamentaux est 'Arbitrage Pricing Theory' (APT) introduite par [START_REF] Ross | The arbitrage theory of capital asset pricing[END_REF]. Dans cette thé orie, la plupart des hypothè ses sous-jacentes au CAPM sont assouplies. L'APT suppose qu'il y a n facteurs qui causer la rentabilité de l'actif s'é cartent systé matiquement de leurs valeurs espé ré es, mais la thé orie ne pré cise pas à quel point le nombre n, ni identifie les facteurs. [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] dé duit un modè le empirique purement à trois facteurs qui inclut un facteur lié à la taille de l'entreprise (SMB) et un facteur lié au ratio book-to-market (HML) de l'entreprise, en plus de bê ta du marché de CAPM, c'est le Modè le à Trois Facteurs de Fama-French (FF3F) cé lè bre. Ils fournissent de fortes preuves empiriques que le modè le à trois facteurs capture la plupart des variations la rentabilité de l'actif en coupe dans le marché d'action des États-Unis. En outre, la source ouverte sur le site de Kenneth R. French facilite é galement les recherches. Il est é galement inté ressant de noter que le modè le de Fama-French (FF) est l'une des principales raisons pour lesquelles le Professeur Fama reç oit le Prix Nobel de Economie 2013. Depuis l'apparition du Modè le FF3F, une é norme quantité de travail a é té effectué selon le Modè le FF3F, par exemple, chercher de nouveaux xviii facteurs ou examiner comment le Modè le FF3F fait sur marché s des actions diffé rents partout dans le monde. Actuellement, plus de chercheurs se tournent vers la recherche de la fondation é conomique en arriè re les facteurs ou les applications en pratique.

Les modè les de facteurs, en particulier le CAPM et le Modè le FF3F, occupent pas seulement un rôle pivot dans le dé veloppement de la thé orie d'é valuation des actifs, mais contribuent é galement à la pratique du marché et à l'analyse des investissements. Ils sont largement utilisé s par les gestionnaires de portefeuille, les investisseurs institutionnels, les gestionnaires financiers et les investisseurs individuels, à tel que la pré diction de la rentabilité d'actif, la sé lection de titres, la construction de portefeuille et contrôle du risque, quantifier l'exposition au risque d'un portefeuille par rapport à un indice de ré fé rence, mesurer la performance, et l'é valuation du gestionnaire de portefeuille.

L'utilisation des modè les de facteurs comme une base pour les recherches est devenue standard dans la litté rature financiè re. La preuve que les facteurs FF sont largement utilisé s peut ê tre trouvé e dans les journaux principaux dans le domaine financier, 'The Journal of Finance' et 'Journal of Financial Economics'. Ces deux journaux de premier ordre sont classé s dans les revues A-é toile (l'évaluation le plus é levé e). Ils sont habituellement classé s dans les deux ou trois revues financiè res les plus importantes du monde. Plus ré cemment, Fama et French (2015a) proposent un modè le à cinq facteurs visant à capturer la taille, la valeur, la rentabilité et l'investissement dans le rendement d'action sur le marché boursier amé ricain dans le 'Journal of Financial Economics'; et fournir le test international du modè le à cinq facteurs [START_REF] Fama | International tests of a five-factor asset pricing model[END_REF].

En outre, plus preuves empiriques ou pratiques que les modè les de facteurs sont largement utilisés peuvent être trouvés dans 'The Journal of Portfolio Management' (JPM), qui est une des revues qui propose des recherches en pointe sur l'allocation d'actifs, la mesure de la performance, les tendances du marché, la gestion des risques, l'optimisation de portefeuille, etc. Les articles publié s par JPM proviennent pas seulement des chercheurs les plus renommé s, mais aussi des praticiens renommé s. En particulier, JPM a publié un numé ro spé cial de 2017 pour cé lé brer ses 40 ans, qui contient les recherches les plus ré centes relatives aux facteurs de risque ou aux modè les des facteurs. Trois articles [START_REF] Bass | Total Portfolio Factor, Not Just Asset, Allocation[END_REF][START_REF] Cocoma | Facts about Factors[END_REF][START_REF] Bender | Quality Assurance: Demystifying the Quality Factor in Equities and Bonds[END_REF] prend l'objet d'allocation de portefeuille fondé e sur des facteurs. Quatre articles sont basé s sur l'investissement fondé sur les facteurs. Deux autres articles sont sur les mé thodologies pour construire les portefeuilles de facteurs: [START_REF] Amenc | Accounting for Cross-Factor Interactions in Multifactor Portfolios without Sacrificing Diversification and Risk Control[END_REF] fournissent deux mé thodes de construction de portefeuilles multifactoriels, tandis que [START_REF] Liu | Pure Quintile Portfolios[END_REF] propose un portefeuille de quintile avec un nouveau cadre de construction de facteurs.

Nous é numé rons ci-dessous plusieurs applications de modè les de facteurs en pratique:

Ré sumé de la thè se en franç ais xix -Gestion de portefeuille Le pouvoir d'un modè le multi-facteurs est que compte tenu des facteurs des risques et des sensibilité s aux facteurs des risques, le profil d'exposition au risque d'un portefeuille peut ê tre quantifié et contrôlé . Un gestionnaire de portefeuille peut é galement analyser son risque actuel et comprendre la taille et l'emplacement de ses paris. D'autre part, les modè les de facteurs peuvent ê tre utilisé s pour dé composer le risque du portefeuille en fonction de l'exposition aux facteurs communs, et pour é valuer la part de la rentabilité d'un portefeuille attribuable à chaque exposition aux facteurs communs. En utilisant un modè le de multifactoriel et un modè le d'optimisation, on peut construire un portefeuille pré sentant le minimum de risque actif par rapport à son indice de ré fé rence pour un nombre donné d'actifs dé tenus. Similairement, un gestionnaire de portefeuille peut construire un portefeuille qui s'incline vers un facteur spé cifié et ce portefeuille n'a aucune exposition active maté rielle à aucun autre facteur. En plus, les modè les multifactoriel de risque permettent à un gestionnaire et à un client d'é valuer les performances potentielles d'un portefeuille ou d'une straté gie de né gociation par rapport à un indice de ré fé rence.

-Estimation de rentabilité exigé et é valuation de l'é quité Les modè les de facteurs sont largement utilisé s pour estimer le taux de rentabilité du capital exigé , compte tenu du risque pertinent. Si les investisseurs s'attendent à une rentabilité d'action particulier supé rieur à une rentabilité exigé , l'action est sous-é valué ; en revanche, si la rentabilité espé ré e est infé rieur au taux de rentabilité exigé , l'action est suré valué . Le taux de rentabilité exigé est une composante dans plusieurs des mé triques et des calculs utilisé s dans finance d'entreprise et é valuation de l'é quité .

L'évaluation de l'é quité est une partie centrale dans des nombreuses activité s, telles que la sélection des titres, l'analyse des actions, en dé duisant des attentes du marché, l'évaluation des événements d'entreprise et l'é valuation des entreprises privé es. Les gestionnaires des actifs effectuent les é valuations parce que leur objectif principal est identifier les titres mal coté s (sous-é valué s ou surévalués). Les banques d'investissement qui jouent un rôle intermédiaire dans l'événements d'entreprise, par exemple dans les fusions et acquisitions, procèdent également à l'évaluation de l'entreprise cible. Un analyste d'action é value les actions qu'elle (ou il) suite (suit) pour donner des recommandations (acheter, tenir, vendre). Les analystes ou les chercheurs utilisent souvent des modèles d'é valuation pour extraire les attentes du marché . Par exemple, un analyste peut inscrire le prix du marché et le taux d'intérêt, le dividende et d'autres facteurs dans un modèle d'évaluation de l'é quité afin de dé terminer quel taux de croissance le marché implique.

-La pratique de la finance d'entreprise et le coût de l'estimation de l'é quité

Ré sumé de la thè se en franç ais xx Le coût du capital est la rentabilité exigé né cessaire pour ré aliser un projet de budgé tisation en capital. Il comprend le coût de la dette et le coût de l'é quité . Les modè les de facteurs sont gé né ralement utilisé s pour mesurer le coût de l'é quité (COE). COE est la rentabilité que les actionnaires ont besoin pour leur investissement dans une entreprise. Le COE d'une entreprise repré sente la compensation que la demande du marché en é change de possé der l'actif et portant le risque de proprié té . Les actionnaires s'attendent à obtenir une certain rentabilité sur leurs participations dans une entreprise, le taux de rentabilité exigé par les actionnaires est un coût au point de vue de l'entreprise. Le coût de l'é quité est essentiellement ce qu'il coûte à l'entreprise de maintenir un prix d'action qui est thé oriquement satisfaisant pour les investisseurs. Sur cette base, la mé thode le plus couramment accepté e pour calculer le coût de l'é quité provient du CAPM et le Modè le FF3F.

-Investissement à base de facteur Investissement à base de facteur est devenu une partie largement discuté e du canon d'investissement d'aujourd'hui. Les chercheurs d'investissement utilisent des modè les multifactoriels des risques pour exé cuter des back-tests contrôlé s sur les straté gies d'investissement futures. Pour cela, leurs besoins sont semblables à ceux des gestionnaires de portefeuille. Ils doivent mettre en oeuvre des stratégies optimales sur les donné es historiques et comprendre la performance ulté rieure de ces straté gies. Les chercheurs peuvent utiliser des back-tests pour amé liorer leurs straté gies. Ils peuvent é galement utiliser l'analyse de performance et la caracté risation des risques de portefeuille pour amé liorer leur compré hension des paris qu'ils testent. La preuve que l'investissement factoriel est en vogue peut é galement ê tre trouvé e dans le dernier numé ro spé cial (2017) de Journal of Portfolio Management. Deux articles [START_REF] Dimson | Factor-Based Investing: The Long-Term Evidence[END_REF][START_REF] Kim | Robust Factor-Based Investing[END_REF] se concentrer sur l'investissement basé sur les facteurs, et deux articles [START_REF] Podkaminer | Smart Beta is the Gateway Drug to Risk Factor Investing[END_REF][START_REF] Alford | Implementing a Smart Beta Index: The Implications of a Dual Performance Objective and Limited Liquidity[END_REF] sur la bê ta intelligente qui est une straté gie d'investissement factorielle populaire actuellement. Par exemple, MSCI a cré é une famille d'indices de facteurs (index bê ta intelligents) qui permettent d'accé der à six facteurs solides: valeur, taille faible, volatilité faible, rendement é levé , qualité et é lan.

Une dé bauche de recherches et l'utilisation pratique largement des modè les de facteurs sont les deux motivations de cette thè se. En plus, la croissance d'économique significative en Chine au cours des derniè res dé cennies a é té universellement reconnue, la Chine a maintenant la deuxiè me grande é conomie au monde, et elle est le plus grand pays en dé veloppement. Le marché boursier chinois, cré é en 1990, est un repré sentant des marché s é mergents avec une histoire relativement courte. Son dé veloppement ainsi que son immaturité ont attiré l'attention des chercheurs, et ont apporté s la question si les modè les d'é valuation des actifs tels que le modè le de FF s'appliquent é galement à ses marché s

Ré sumé de la thè se en franç ais xxi domestiques. Par consé quent, la popularité des modè les de facteurs et le marché boursier é mergent stimulent l'intention pour l'é tude des modè les factoriels sur le marché boursier chinois. On peut dire que ceci encore une autre é tude des modè les de facteurs sur la base du Modè le FF3F, mais ce que nous voulons souligner, c'est que le modè le FF3F est devenu la pierre angulaire des é tudes des facteurs, la recherche sur les modè les de facteurs a é té un sujet de recherche chaud pendant des dé cennies, et il continuera d'être un thème clé du domaine d'évaluation des actifs à l'avenir.

Le travail pré senté dans cette thè se contient trois chapitres, explorant principalement les facteurs de risque sur le marché boursier chinois sur la base du Modè le FF3F. Le succè s du Modè le FF3F sur le marché boursier des États-Unis stimule les é tudes sur l'applicabilité dans d'autres marché s dé veloppé s ou é mergents partout dans le monde, l'applicabilité du Modè le FF3F sur le marché boursier chinois a é galement é té un sujet d'actualité depuis des anné es. Cette thè se commence par un nouveau test du Modè le FF3F à l'aide des donné es du marché boursier chinois A-share, afin de ré pondre à la question si le Modè le FF3F s'applique au marché boursier chinois A-share. Les travaux suivants se dé roulent à partir de Modè le FF3F.

Le chapitre 1 ré -enquê te sur le Modè le FF3F et explore le dernier Modè le à Cinq Facteurs de sur le marché boursier chinois A-share, vise à examiner l'applicabilité des deux modè les en Chine. En outre, nous comparons les ré sultats de ré gression des deux modè les pour vé rifier si Modè le FF5F fonctionne mieux que le Modè le FF3F pour capturer la variation des rentabilité s des actions. Il est important de noter que nous prenons en compte plusieurs caracté ristiques particuliè res du marché boursier chinois qui ne sont pas né gligeables pour bé né ficier de ré sultats de recherche plus fiables.

Pour mettre en oeuvre l'enquê te, nous construisons les cinq facteurs: rentabilité s excé dentaire du marché , facteur de taille SMB, facteur de valeur HML, facteur de rentabilité RMW et facteur d'investissement CMA en utilisant des donné es du marché boursier chinois A-share. L'approche à deux étapes de Fama-MacBeth (1973) est appliqué pour les ré gressions sé ries chronologiques et les ré gressions transversales. Étant donné que l'approche à deux é tapes de Fama-MacBeth (FM ci-dessous) a causé le problè me d'erreurs sur les variables (EIV), la procé dure de correction proposé e par [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] est appliqué e.

Bien que la grande ré ussite du modè le de facteur FF, c'est aussi l'un des modèles d' é valuation des actifs qui sont les plus controversé s, principalement pour ses considé rations purement empiriques et le manque de fondements thé oriques. Le succè s du Modè le FF3F stimule la poursuite des bases é conomiques des facteurs FF. Au chapitre 2, nous procé dons à la recherche conformé ment à l'une des explications dominantes, basé e sur des xxii opportunité s d'investissement variant dans le temps dans le cadre de l'ICAPM. Nous examinons si les facteurs FF sont proxys des innovations de variables d'é tat sé lectionné es qui dé crivent les opportunité s d'investissement futures sur le marché boursier chinois Ashare. Nous choisissons quatre variables é conomiques selon [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF]: rendement en dividende agré gé e, taux de T-bonds en un mois, l'é cart de terme et l'é cart de dé faut, afin de modé liser deux aspects de l'opportunité d'investissement set-la courbe de rendement et la distribution conditionnelle des rentabilité s des actifs.

Pour extraire les termes de l'innovation, le processus de Vecteur Autoregressif (VAR) a é té utilisé . Et comme [START_REF] Campbell | Understanding Risk and Return[END_REF] souligne que'il est difficile d'interpré ter les ré sultats d'estimation pour un modè le de facteur VAR, sauf si les facteurs soient orthogonalisé s et mis à l'é chelle d'une certaine maniè re", nous orthogonalisons les innovations des variables d'état sur la rentabilité excé dentaire du marché , qui est le premier é lé ment du vecteur dans le processus VAR. L'approche à deux é tapes de Fama-MacBeth est ensuite mise en place pour les ré gressions sé ries chronologiques et les ré gressions transversales, et les ré sultats de la ré gression transversale sont ajusté s pour le problè me de l'EIV.

Dans le chapitre 3, nous choisissons le facteur de risque dé tresse comme facteur augmenté du Modè le FF3F original parmi les facteurs de risque qui ont é té dé couverts. Étant donné que le risque dé tresse de l'entreprise est un indicateur important de la performance d'une entreprise, et est é galement l'une des caracté ristiques les plus concerné es par les investisseurs et les entreprises. De plus, le risque de dé tresse financiè re a é té prouvé lié aux rentabilité s des actions é troitement et le point de vue de l'effet de la valeur est considé ré comme l'effet du risque de dé tresse proposé par la litté rature sé ries chronologique.

L'objectif principal est de tester si les facteurs FF sont des procurations pour le risque de dé tresse sur le marché boursier chinois pendant la pé riode de juillet 2005 à mai 2015. Sinon, si le modè le à quatre facteurs augmenté explique la rentabilité d'action mieux que le Modè le FF3F. En particulier, nous appliquons le modè le à base de comptabilité (O-score d 'Ohlson) et le modè le de marché (DLI des Vassalou et Xing) pour mesurer la dé tresse financiè re, afin d'identifier si les mé thodes diffé rentes qui pré disent du risque de dé tresse sont importantes pour les ré sultats empiriques. En outre, la relation entre la rentabilité d'action et le risque de détresse, et si l'effet de taille et l'effet de valeur sont lié s au risque de détresse ont é galement é té examiné s sur le marché boursier chinois.

Ré sumé de la thè se en franç ais xxiii Chapitre 1

Modè le à Cinq-Facteurs de Fama-French versus Modè le à Trois-Facteurs de Fama-French en Chine Contexte et objectif [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] proposent le Modè le FF3F et dé montrent que le facteur de taille et le facteur de valeur ont effectué ré ussi à expliquer les rentabilité s des actions en plus du bê ta du marché . Dernier, Fama et French (2015a) proposent un modè le à cinq facteurs incluant le facteur rentabilité et le facteur d'investissement en plus des trois facteurs original de FF, et ce modè le se comportent mieux que le Modè le FF3F.

Le Modè le FF3F et le Modè le FF5F sont:

i ,t f i i M ,t f i i i ,t R R a b ( R R ) s SMB h HML e        (1) i ,t f i i M ,t f i i i i i ,t R R a b ( R R ) s SMB h HML r RMW c CMA e          (2)
Il est é vident que le modè le à cinq facteurs comporte deux autres facteurs que le modè le à trois facteurs, RMW et CMA. RMW est le facteur lié à la rentabilité de l'entreprise, ce qui correspond à la diffé rence de rentabilité entre les portefeuilles qui ont les rentabilité s robustes et les rentabilité faible. Le CMA est lié e à l'investissement, lequel est la diffé rence de rentabilité entre les portefeuilles qui ont les investissements conservatifs et les portefeuilles qui ont les investissements agressifs.

Ce chapitre ré -examine l'applicabilité du Modè le FF3F en construisant des facteurs FF sur le marché boursier chinois A-share (sé ries chronologique et transversales), compte tenu de plusieurs caracté ristiques spé ciales du marché boursier chinois. De plus, ce chapitre é tudie é galement le dernier Modè le FF5F en utilisant les donné es du marché boursier chinois, afin d'examiner si les facteurs de rentabilité et d'investissement ont un pouvoir explicatif supplé mentaire. En outre, nous comparons deux modè les pour voir si le Modè le FF5F fonctionne mieux que le Modè le FF3F sur le marché boursier chinois A-share. Les comparaisons des ré sultats empiriques entre le marché boursier chinois et le marché boursier amé ricain sont é galement exé cuté s.

Caracté ristiques spé cials du marché boursier chinois

Ré sumé de la thè se en franç ais xxiv Les litté ratures empiriques suggè rent que le marché chinois pré sente des caracté ristiques spé cials, et il est iné vitable de considé rer ces caracté ristiques spé cials si les chercheurs veulent avoir des ré sultats plus pré cis en Chine. Dans notre é tude, nous ré sumons trois caracté ristiques principales qui sont é galement les plus fré quemment employé es par les litté ratures: (1) utiliser des actions né gociables, pas toutes les actions (y compris les actions né gociables et non-né gociables) pour pondé rer la rentabilité d'action en valeur, (2) inclure les entreprises de 'Petit Moyen Enterprise Planche' et 'Croissance Enterprise Planche' pour dé terminer les points de ruptures pour le facteur de taille, et (3) calculer le ratio book-toprice (B/P) au lieu du ratio book-to-market (B/M) puisque la segmentation du marché boursier chinois .

Donné es et mé thodologie

Nous incluons toutes les entreprises sur le marché boursier chinois A-share (marché boursier A-share de Shanghai et marché boursier A-share de Shenzhen), à l'exclusion des entreprises financiè res et des entreprises ayant des valeurs des B/P né gatives; en plus, une entreprise est é liminé e si les informations pertinentes manquent dans un mois ou une pé riode donné . La pé riode de recherche pour le Modè le FF3F est de juillet 2004 à mai 2015 (131 mois), et le Modè le FF5F est de juillet 2010 à mai 2015 (59 mois).

L'approche en deux é tapes de Fama-MacBeth (FM) est appliqué e pour les ré gressions, la premiè re é tape est la sé rie chronologique en utilisant l'OLS. La deuxiè me é tape est la ré gression transversale telle qu'indiqué e dans l'équation (1), où ils utilisent les bê tas estimé es obtenues de la premiè re é tape des ré gressions chronologiques, comme les variables indé pendantes dans les ré gressions transversales. Et ré glez les rentabilité s des mê mes portefeuilles (que dans la premiè re é tape) sur ces bê tas estimé es pour une pé riode de temps fixe pour dé terminer la prime de risque pour chaque facteur.

i ,t f i M i SMB i HML i i ,t ˆR R b s h            (3)
Étant donné que l'approche en deux é tapes de FM cause le problè me d'erreurs sur les variables (EIV) classiques, la procé dure de correction proposé e par [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] est ensuite appliqué e aux é carts types des estimateurs de ré gression transversale.

Construction de portefeuilles et de facteurs

À la fin de juin de chaque anné e t, tous les actions sont trié s en deux groupes de taille, Petit et Grand, le point de rupture est la mé diane de la capitalisation boursiè re totale. Nous xxv classons par B/P au lieu du B/M à la fin de chaque décembre de l'année t-1 en trois groupes: Bas, Moyen et Haut cela dé pend des points de rupture des 30e et 70e percentiles de A-share. Enfin, l'intersection de ces six groupes fait les six portefeuilles, qui restent les mê mes de juillet de l'anné e t à juin de l'année t+1, et les portefeuilles sont ré formé s en juillet de l'année t+1. (5)

Similairement, la construction de portefeuilles sur la rentabilité opé rationnelle (OP) et l'investissement (Inv) est similaire en celle des portefeuilles sur le ratio B/P. À la fin de chaque mois de juin, les entreprises sont trié es en trois portefeuilles OP basé sur des points ruptures des 30e et 70e percentiles de l'OP, et les trois portefeuilles d'investissement sont formé s à l'aide de points rupture: les 30e et 70e percentiles d'Inv. Ensuite, les facteurs RMW et CMA sont les suivants:

11 RMW ( Petit Robuste+Grand Robuste) ( Petit Faible+Grand Faible ) 22  (6) 1 CMA ( Petit Conservatif+Grand Conservatif) 2 1 ( Petit Agressif+Grand Agressif ) 2   (7)
Ré sumé de la thè se en franç ais xxvi Nous construisons trois sé ries de portefeuilles: six portefeuilles Taille-B/P pondé ré es en valeurs, six portefeuilles Taille-OP pondé ré es en valeurs et six portefeuilles Taille-Inv pondé ré es en valeurs, en tant que variables dé pendantes pour effectuer les ré gressions.

Ré sultats et conclusions

Le Modè le FF3F peut expliquer la majorité des variations chronologiques des rentabilité s des actions, compte tenu des caracté ristiques spé cials du marché boursier chinois. Au cours des pé riodes de juillet 2004 à mai 2015, il existe une prime de taille positif dans la rentabilité d'actions sur le marché boursier chinois A-share, toutefois, nous constatons le manque de prime de valeur. Le bê ta du marché est capable d'expliquer la variation transversale des rentabilité s moyens pour les 25 portefeuilles pondé ré s en valeur (avec des t-statistiques SH ajusté s né gatifs).

Pour tous les trois sé ries de portefeuilles que nous avons construits dans la recherche du Modè le FF5F, il existe un effet de taille; tandis qu'il existe un effet de valeur dans les portefeuilles Taille-B/P, l'effet de rentabilité dans les portefeuilles Taille-OP et l'effet d'investissement dans les portefeuilles Taille-Inv. Les coefficients sur RMW ne sont significatives que dans la serie des portefeuilles qui formé s à partir de taille et OP. En ce qui concerne le facteur CMA, les coefficients significatives sont concentré es dans les groupes OP ou Inv extrê mes, tels que le groupe OP faible, le groupe OP robuste, les groupes Inv agressifs et conservatif. Cependant, pour les portefeuilles Taille-B/P, les coefficients significatifs de CMA sont relativement dispersifs.

Nous comparons la performance entre le Modè le FF3F et le Modè le FF5F au cours de la pé riode de recherche, si le Modè le FF5F fonctionne mieux que le Modè le FF3F sur le marché boursier chinois A-share n'est pas trè s clair. Le pouvoir explicatif du Modè le FF5F est diffé rent parmi les sé ries de portefeuilles diffé rents. Par rapport au Modè le FF3F, la pré sence de facteurs de rentabilité et d'investissement ne capturer pas plus de variations des rendabilité s des actions espé ré s que le modè le à trois facteurs, à l'exception des six portefeuilles pondé ré es en valeurs qui formé s à partir de la taille et de la rentabilité opé rationnelle, bien que l'amé lioration soit limité e.

Nous comparons é galement performances des Modè les FF entre le marché boursier chinois et le marché boursier amé ricain. Les ré sultats ré vè lent que le Modè le FF3F et le Modè le FF5F expliquent la variation de sé ries chronologiques des rendabilité s meilleure sur le marché boursier amé ricain par rapport au marché boursier chinois. En ce qui concerne les deux facteurs supplé mentaires, le facteur de rentabilité RMW et le facteur d'investissement CMA, sont capables de capturer partiellement les variations de sé ries chronologiques des Ré sumé de la thè se en franç ais xxvii rendabilité s des trois sé ries portefeuilles sur le marché boursier amé ricain, alors que sur le marché boursier chinois, le facteur de rentabilité semble ê tre un facteur explicatif seulement pour les six portefeuilles Taille-OP.

Chapitre 2 Fama-French Facteurs et Innovations des Variables d'é tat sur le Marché Boursier Chinois Objectif

Le Modè le FF3F a ré alisé un é norme succè s empirique depuis son apparition, donc il est considé ré comme l'un des modè les les plus controversé s d'é valuation actif. Cependant, les facteurs sont construits empiriquement .donc ils manquent de fondements thé oriques. En particulier, leurs liens é conomiques avec le risque systé matique ne sont pas clairs. Par consé quent, la performance impressionnante du Modè le FF3F a suscité des recherches nombreuses qui tentent de fournir une interpré tation é conomique claire des facteurs HML et SMB.

Les liens é conomiques sous-jacents des facteurs FF sont plutôt controversé s. Parmi des nombreuses des explications concurrentes pour le succè s du Modè le FF3F, suivant que [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], dans ce chapitre, nous concentrons sur celui basé sur des opportunité s des investissements qui variant dans le temps et dans le contexte d'Intertemporal Capital Asset Pricing Model (ICAPM ci-aprè s) de Merton (1973a).

Dans ce chapitre, nous examinons si les innovations des quatre variables d'é tat, rendement du dividende agré gé e, taux de T-bonds en un mois, l'é cart de terme et l'é cart de dé faut, sont capables de capturer les rentabilité s excé dentaires des actions dans les sé ries chronologiques et sé ries transversales. Nous examinons é galement si FF Facteurs SMB et HML sont les proxys pour les innovations de variables d'é tat sé lectionné es, qui dé crivent les opportunité s d'investissement futures sur le marché boursier chinois A-share.

Ré sumé de la thè se en franç ais xxviii

Donné es et mé thodologie

Le mê me sé rier des variables d'é tat que [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] est choisi en plus des facteurs FF dans notre test empirique: rendement de dividende agré gé e (DIV), l'é cart de terme (TERM), l'écart de défaut (DEF) et taux de T-bonds en un mois (RF), qui sont parmi les variables é conomiques qui sont utilisé es les plus communes dans les litté ratures. La pé riode de recherche est de dé cembre 2006 à mai 2015 (102 mois).

Selon ICAPM, seul le composant inattendu de la variable d'é tat devrait commander une prime de risque. Le composant inattendu est normalement appelé innovations. Au lieu d'utiliser directement les variables d'é tat pour l'implémentation empirique de l'ICAPM, [START_REF] Campbell | Understanding Risk and Return[END_REF] suggè re d'utiliser des innovations dans telles variables d'é tat pour pré voir les changements dans le sé rier des opportunité s d'investissement futures. Pour dé river les termes de l'innovation, nous appliquons la mé thode vecteur autoré gressif (VAR).

                         (8)
Où 'A' est une matrice 7 × 7, et représente un vecteur d'innovations de 7 × 1 pour chaque é lé ment. Il y a six innovations correspondant au rendement du dividende, au taux de Tbonds en un mois, à l'écart de terme (TERM), à l'écart de défaut, au SMB et au HML, qui sont extraits de et designé s IDIV, IRF, ITERM, IDEF, ISMB et IHML.

Les innovations peuvent ê tre exprimé es dans le cadre de l'ICAPM:

    k K k i ,t f ,t i ,t i ,m M ,t f ,t t i ,t i, 1 R R R R e             (9)
où, k t  est l'innovation de l'é tat variable k au temps t.

Ensuite, les innovations des variables d'é tat sont sé paré ment orthogonalisé es au facteur du marché . Pré cisé ment, l'innovation de la rentabilité excé dentaire du marché reste inchangé e, l'innovation du rendement de dividende IDIV est orthogonalisé à la rentabilité excé dentaire du marché . De mê me, IRF est orthogonalisé e au facteur du marché . Les autres innovations des variables d'é tat ITERM, IDEF, ISMB et IHML sont traité es par la mê me maniè re.

xxix Puis l'approche à deux étapes de Fama-MacBeth est implé menté e pour effectuer les ré gressions pour cinq modè les comparatifs, et la correction de Shanken est é galement effectué e pour ajuster le problè me EIV dans les ré gressions transversales.

Cinq modè les comparatifs

Modè le 1

i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,ISMB i ,IHML i ,t R R ( R R ) IDIV ITERM IDEF IRF ISMB IHML e                    (10) Modè le 2 i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,SMB i ,HML i ,t R R ( R R ) IDIV ITERM IDEF IRF SMB HML e                    (11) Modè le 3 i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t R R ( R R ) IDIV ITERM IDEF IRF e               (12)
Modè le 4 [START_REF] Ohlson | Financial ratios and the probabilistic prediction of bankruptcy[END_REF]. Les modè les qui utilisent l'information du marché pour estimer le risque de dé tresse sont les modè les basé s sur le marché , repré senté s par le modè le de 'option-pricing' de [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF]

       i ,t f i i ,m M ,t f i ,ISMB i ,IHML i ,t R R ( R R ) ISMB IHML e     (
           (15)
et le modè le de de 'option-pricing' de [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF] (modè le basé sur le marché ) [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] soulignent que leur probabilité dé faut (DP) estimé e en utilisant du modè le de Merton n'est pas le DP ré el, au lieu de cela, le DP calculé basé sur la distribution empirique du modè le KMV de Moody est le DP actuel. Ainsi, ils appellent leur mesure de DP comme l'indicateur de probabilité par dé faut (DLI).

2 A,t A t t A V 1 ln T X2 DP=N T                  (16) Vassalou et
Afin d'é tudier si les trois facteurs FF sont des proxys pour le risque de dé tresse, un modè le augmenté à quatre facteurs, qui comprend le facteur de marché (bê ta du marché ), le facteur Ré sumé de la thè se en franç ais xxxii de taille (SMB), le facteur de valeur (HML) et le facteur de risque de dé tresse (DRF), est examiné :

         i ,t f i i M ,t f i i i i ,t R R a b ( R R ) s SMB h HML d DRF (17)
Si toutes les informations dans SMB et HML sont lié es au risque de dé tresse financiè re, il est probable de trouver que SMB et HML perdent toute leur capacité à expliquer les rentabilité s des é quité s. en pré sence de DRF.

Donné es et mé thodologie

Introduction Background

The factor models have been the dominant models in the asset pricing field for decades since the come up of Capital Asset Pricing Model (CAPM) of [START_REF] Sharpe | Capital asset prices: A theory of market equilibrium under conditions of risk[END_REF], [START_REF] Lintner | The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[END_REF] and [START_REF] Black | Capital market equilibrium with restricted borrowing[END_REF], a model which was aimed to estimate required return on assets under the main assumptions of Markowitz's portfolio theory. Even before the introduction of the popular CAPM, [START_REF] Markowitz | The book-to-market and size effects in a general asset pricing model: Evidence from seven national markets[END_REF] proposed the use of a single-factor model to explain security returns. Sometimes referred to as index models, factor models often rely on the use of factor analysis to identify factors that influence asset returns.

The original CAPM can be regarded as the single-index factor model and has advantages of being easy to implement and interpret; however, it is criticized by many analysts for its assumptions and lack of explanatory power of stock market anomalies. Countless researchers have devoted themselves to develop a model that overcome the defects of CAPM, and the opponents of CAPM who see its lack of explanatory power, claim that there must be other factor(s) apart from excess market returns that derive the asset return. The asset pricing models that have more than one factor are called multifactor models.

Multifactor models can be divided into three types -fundamental, macroeconomic and statistical factor models. [START_REF] Connor | The Three Types of Factor Models: A Comparison of Their Explanatory Power[END_REF] gives a comprehensive overview of these three types of factor models: Fundamental factor models use the returns to portfolios associated with observed security attributes such as dividend yield, the book-to-market ratio, and industry identifiers; macroeconomic factor models use observable economic time series, such as inflation and interest rates, as measures of the pervasive shocks to security returns; statistical factor models derive their pervasive factors from factor analysis of the panel data set of security returns. The fundamental and macroeconomic factor models are models with known factors, while the statistical factor cannot directly observable or easily interpreted in contrast to known factors, they are also called latent factors. Latent factors are estimated by applying a statistical methodology known as factor analysis and the model generated is referred to as a factor model by statisticians, which is beyond the scope of this study.

The known factors normally used are observable economic, company and industry attributes and market data as "descriptors" (e.g. GDP growth, interest rate, price/earnings ratios, book-to-price ratios, estimated earnings growth, trading activity, and the business cycle). However, the descriptors are not factors, instead, they are the candidates for risk factors and are selected in terms of their ability to explain historical stock returns. The descriptors selected are then used to construct risk factors (economic or political factors or industry factors or country factors) and referred to as risk indices. The most popular factors today-Value, Growth, Size, Momentum-have been studied for decades as part of the academic asset pricing literature and the practitioner risk factor modeling research.

The underlying premise of these multifactor models is that certain common factors may be identified which capture the types of risk that are rewarded over investment horizons.

Factor models are widely used by investors to link the risk exposures of the assets to a set of factors. In most of these models, the market index developed in the context of the CAPM is one of the factors, representing "market risk."

One of the fundamental multifactor models is the Arbitrage Pricing Theory (APT) introduced by [START_REF] Ross | The arbitrage theory of capital asset pricing[END_REF]. In this theory, most of the assumptions underlying the CAPM are relaxed. APT assumes that there are n factors that cause asset returns to systematically deviate from their expected values, however, the theory does not specify how large the number n is, nor does it identify what the factors are.

Another epoch-making paper was published by Fama and French (FF) in 1993, they deduce a three-factor model which includes a factor related to firm size (SMB) and a factor related to firm's book-to-market equity ratio (HML) in addition to market beta of CAPM, that is the well-known Fama-French Three-Factor Model (FF3F Model) 1 . They provide strong empirical evidence that the three-factor model captures most variation of cross-sectional excess stock returns in U.S. stock market. And the new factors have been demonstrated to add significantly to the prior understanding of returns based on the standard CAPM.

Furthermore, the open source on the website of Kenneth R. French also facilitates following researchers. It is also worth noting that the FF model is one of the key reasons for Professor Fama being awarded the 2013 Nobel Prize in Economics. Since the came up of FF3F Model, an enormous amount of work has been implemented based on FF3F Model, such as focusing on finding new factors or examining how FF3F Model is doing on different stock markets all around the world. Nowadays, more researchers turn to seeking the economic underpinning behind the factors or the applications in practice.

Why the heat of factor models continues for decades and no any trace of decrease until now? There is a reason, the factor models, especially CAPM and FF3F Model, do not only occupy a pivotal place in the development of the asset pricing theory, but also make great contributes to market practice and investment analysis. The factor models are implemented such as to select securities, construct a portfolio and control risk, quantify the risk exposure of a portfolio relative to a benchmark index, measure performance, and in portfolio manager evaluation.

Motivation

The factor models, are mentioned in a host of academic papers, and are widely used by portfolio managers, institutional investors, financial managers, and individual investors to predict asset returns; especially the original CAPM and FF3F Model which have each been recognized by the Nobel Committee, are among the most implemented factor models in the practice. For instance, a portfolio manager evaluates the impact of a series of broad factors on the performances of various securities; in this sense, a reliable factor model provides a valuable tool to assist portfolio managers with the identification of pervasive factors that affect large members of securities. Researchers use multifactor models to back-test and fine-tune strategies, and traders use these models to control investment risk over short horizons, etc.

The use of the factor models as a basis for research has become standard in the finance literature. Evidence of the fact that the FF factors are widely used can be found in the leading journals in the field, The Journal of Finance and Journal of Financial Economics. Both of these leading journals are ranked as A-star journals (the highest possible rating). They are commonly ranked as being in the top two or three finance journals worldwide.

Most recently, Fama and French (2015a) propose a five-factor model aims at capturing the size, value, profitability, and investment patterns in average excess stock returns on U.S. stock market in the Journal of Financial Economics; and provide the international test of the five-factor model [START_REF] Fama | International tests of a five-factor asset pricing model[END_REF].

Furthermore, more empirical or practical evidence that factor models are widely used can be found in The Journal of Portfolio Management (JPM), which is one of the journals that offers cutting-edge research on asset allocation, performance measurement, market trends, risk management, portfolio optimization, and so on. Articles issued by JPM are not only from most renowned researchers but also from the renowned practitioners. Particularly, JPM issued a special issue of 2017 to celebrate its 40 years, which contains the most recent researches related to risk factors or factor models. Three articles [START_REF] Bass | Total Portfolio Factor, Not Just Asset, Allocation[END_REF], [START_REF] Cocoma | Facts about Factors[END_REF][START_REF] Bender | Quality Assurance: Demystifying the Quality Factor in Equities and Bonds[END_REF][START_REF] Bender | Quality Assurance: Demystifying the Quality Factor in Equities and Bonds[END_REF]) take the subject of factor-based portfolio allocation; four articles are on the basis of factor-based investing. Another two articles tend to the methodologies in studies of construction factor portfolios: Amenc et al.

(2017) provide two methods of building multifactor portfolios, while [START_REF] Liu | Pure Quintile Portfolios[END_REF] proposes a pure quintile portfolio with new factor construction framework.

We list below several applications of factor models in practice:

-

Portfolio management

The power of a multifactor model is that given the risk factors and the risk factor sensitivities, a portfolio's risk exposure profile can be quantified and controlled. A portfolio manager can also analyze their current risk and understand the size and location of their bets. On the other hand, factor models can be used to decompose portfolio risk according to common factor exposure and to evaluate how much of a portfolio's return was attributable to each common factor exposure. Consider a portfolio with more than 100 assets, instead of estimating the variance-covariance matrix of its assets, it only necessary to estimate the portfolio's factor exposures and the variance-covariance matrix of the factors, a computationally much easier task. Using a multifactor risk model and an optimization model, a portfolio that has the minimum active risk relative to its benchmark for a given number of assets held can be constructed. Similarly, a portfolio manager can construct a portfolio that tilts towards a specified factor, and has no material active exposure to any other factor. Furthermore, multifactor risk models allow a manager and a client to assess the potential performance of a portfolio or trading strategy relative to a benchmark. In sum, multifactor models can be used to analyze portfolio risk, construct portfolios that optimally trade off risk with expected returns, and analyze skill and value added associated with past returns. Consequently, the factor models offer a useful extension of the CAPM and the APT because they advance our understanding of how key factors influence portfolio risk and return.

-

Required return estimation and equity valuation

The factor models are used largely to estimate the required return on equity, given the relevant risk. That is, the model has the purpose of estimating normal risk-adjusted returns.

Estimating normal risk-adjusted returns are also required for a number of purposes including setting regulated returns and for the purposes of determining whether a portfolio or trading strategy shows out-performance on a risk-adjusted basis. The use of the factor models, especially FF3F Model, as a basis for estimating required returns has become standard in the finance literature. For example, the issues of February 2014 and December 2013 of the Journal of Finance feature five articles that use the FF factors for the purposes of estimating required returns. The volume (2014) of the Journal of Financial Economics features four articles that use the FF factors for the purposes of estimating required returns. Indeed, the use of the Fama-French factors, for the purpose of estimating the required return on equity, is so widespread in the academic literature, its use as a measure of normal returns has become a matter of course.

If investors expect a return of a particular stock higher than required return, then the stock is undervalued; in contrast, if expected return is less than required rate of return, then the stock is overvalued. The required rate of return is a component in many of the metrics and calculations used in corporate finance and equity valuation.

The main goal of equity valuation is to estimate its inherent value. For investors, they are concerned with the value of their investment, they all want to make sure that the product they buy or sell is worth the value (price) they pay or receive. Inherent value is the "true" or "real" value of an asset that is obtained and supported by rational, hypothetical, unbiased mathematical models that consider all relevant factors that drive the value of an asset. However, the inherent value is unobservable, so the best we can do is to estimate it using asset pricing models. Such, the factor models are one category of the models that are supposed to estimate the inherent value of common equities2 . Inherent value can differ from market value, in which case stock becomes overvalued or undervalued depending on whether the inherent value is lower or higher than market value.

Equity valuation is a central part in many activities such as stock selection, stock analysis, inferring market expectations, evaluation of corporate events (mergers and acquisitions, divestitures, spin-offs), and private business valuation. Equity portfolio managers do equity valuation of companies they consider including in a portfolio. Active managers, in particular, do valuation because their primary goal is to identify mispriced (undervalued or overvalued) securities. Investment banks who play an intermediary role in corporate events, for example in mergers and acquisitions, also carry out the valuation of the target company.

A stock analyst evaluates the stocks she follows to give recommendations (buy, hold, sell). Analysts or researchers also frequently use valuation models to extract (infer) market expectations. For example, an analyst may input the current market prices and interest rates, dividends, and other factors, into an equity valuation model in order to find what growth rate the market implies.

-

Corporate finance practice and the cost of equity estimation

The cost of capital is the required return necessary to make a capital budgeting project and includes the cost of debt and the cost of equity. The factor models are generally used to measure the cost of equity (COE). COE is the return that stockholders require for their investment in a company. A firm's COE represents the compensation that the market demands in exchange for owning the asset and bearing the risk of ownership. Common shareholders expect to obtain a certain return on their equity investment in a company, the equity holders' required rate of return is a cost from the company's perspective. The cost of equity is basically what it costs the company to maintain a share price that is theoretically satisfactory to investors. On this basis, the most commonly accepted method for calculating the cost of equity comes from CAPM and FF3F Model.

If you ask participants involved in capital allocation decisions at large corporations "What model do you use to estimate the cost of equity capital?" the most common answer is the CAPM. However, when you evaluate the responses in detail you observe a large proportion of respondents make adjustments to the CAPM estimate of the cost of equity capital to account for other risk factors. What is proposed in the use of the FF model is an objective measurement of risk that is consistent with the empirical evidence on stock returns. 3In 1999, a survey was conducted amongst 392 representatives of large corporations in the U.S. [START_REF] Graham | The theory and practice of corporate finance: Evidence from the field[END_REF]. In 2002, the same set of questions was posed to 313 representatives of large corporations in the U.K., the Netherlands, Germany, and France [START_REF] Brounen | Corporate finance in Europe: confronting theory with practice[END_REF]. In response to the question, "How do you determine your firm's cost of equity capital?" the percentage of respondents who said they always or almost always used the CAPM ranged from 34% to 73% across the five countries. However, this is not the only evaluation technique used in estimating the cost of equity. Another alternative answer was "using the CAPM but including some extra risk factors." The proportion of respondents who stated that they always or almost always incorporated extra risk factors into the CAPM ranged from 15% to 34%, with an aggregate percentage of 28%. As SFG report states that if corporate finance practice is used to determine how regulation should evolve, the benchmark would be to use the factor models (the CAPM with additional risk factors).

-

Factor-based investment

Factor investing has become a widely discussed part of today's investment canon. Investment researchers use multifactor risk models to run controlled back tests of future investment strategies. For this, their needs are similar to those of portfolio managers. They need to implement strategies optimally on historical data and understand the subsequent performance of those strategies. Researchers can use back tests to enhance their strategies. They can also use performance analysis and portfolio risk characterization to improve their understanding of the bets they are testing. The evidence that factor-based investment is in vogue nowadays can also be found in the latest special issue (2017) of Journal of Portfolio Management, two articles [START_REF] Dimson | Factor-Based Investing: The Long-Term Evidence[END_REF] and [START_REF] Kim | Robust Factor-Based Investing[END_REF]) focus on factor-based investing and two articles [START_REF] Podkaminer | Smart Beta is the Gateway Drug to Risk Factor Investing[END_REF], [START_REF] Alford | Implementing a Smart Beta Index: The Implications of a Dual Performance Objective and Limited Liquidity[END_REF]) about smart beta which is a currently popular factor-based investment strategy. For example, MSCI has created a family of factor indexes (smart beta indexes) that provide access to six solidly grounded factors-value, low size, low volatility, high yield, quality, and momentum.

Of course, those mentioned above are not all the applications of factor models in practice.

Other examples like pension plan sponsors can use multifactor risk models to coordinate their multiple managers. Portfolio risk characterization allows them to understand any gaps or overlaps among their managers or in their asset allocation mixes. Plan sponsors also use performance analysis to assess their managers' value added and to check on their managers' styles.

The extensive research and widely practical use of factor models are two of the motivations for this dissertation, another one is the Chinese stock market. Significant economic growth in China over the past few decades has been universally acknowledged, China now has the second-largest economy in the world, and is the biggest developing country. The Chinese stock market, established in 1990, is one representative of the emerging markets with relative short history. Its development along with its immaturity has attracted considerable attention from researchers, and also has brought into question of whether the asset pricing models such as FF model are also applicable to its domestic markets.

Therefore, both the popular of factor models and the attractive emerging stock market prompt the original intention in the study of factor models (risk factors) on Chinese stock market. One may say that this again another study of factor models on the basis of FF3F

Model, but what we want to emphasize is that FF3F Model has become the cornerstone of factor studies, the research on factor models have been a hot research topic for decades, and it will continue to be a key topic of asset pricing field in the future.

Objective and Structure of Dissertation

The work presented in this dissertation contains three chapters, mainly explore the risk factors on Chinese stock market on the basis of FF3F Model, and the studies of each chapter are closely linked while relatively independent as well. The success of FF3F Model on U.S. stock market impels the studies of the applicability in other developed or emerging markets all around the world. China has attracted more and more researchers' attention, the applicability of FF3F Model on Chinese stock market has also been a hot topic for years. This dissertation begins with re-testing the FF3F Model using data of Chinese A-share (CNAS) stock market in order to answer the question that whether FF3F Model is applicable on CNAS stock market, and the following work is then unfolded on the basis of FF3F Model.

Chapter 1 re-investigates the FF3F Model and explore the latest FF5F Model on CNAS stock market, aims to examine the applicability of both models in China. Furthermore, we compare the regression results of both models to test whether FF5F performs better than FF3F Model in capturing the variation of average stock returns as they are proved so in U.S. market. It is worth noting that we take into account several special features of Chinese stock market that are non-negligible in order to benefit a more reliable research results.

To implement the investigation, we construct all five factorsexcess market return, size factor SMB, value factor HML, profitability factor RMW and investment factor CMA using data of CNAS stock market, [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] two-stage approach is applied for the time-series regression (TSR) and cross-sectional regression (CSR). Since the Fama-MacBeth (FM hereafter) two-stage approach caused the classical errors-in-variables problem, the correction procedure proposed by [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] is applied.

Though the great achievement of FF factor models, it is also one of the most controversial asset pricing model, mainly for its purely empirical-based considerations and lack of theoretical underpinnings. The success of FF3F Model on CNAS stock market stimulates the chasing down for economic foundation of FF factors, especially the SMB factor. In chapter 2, we proceed with the research in line with one of the dominant explanations, which is based on time-varying investment opportunities in the context of ICAPM. We examine whether FF factors proxy for the innovations of selected state variables that describe the future investment opportunities on CNAS stock market, and we choose four economic variables in accordance with [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF]: aggregate dividend yield, onemonth T-bill rate, term spread and default spread, which in order to model two aspects of investment opportunity setthe yield curve and the conditional distribution of asset returns.

To extract the innovation terms, the vector auto-regression (VAR) process has been utilized; and as [START_REF] Campbell | Understanding Risk and Return[END_REF] emphasizes that "it is hard to interpret estimation results for a VAR factor model unless the factors are orthogonalized and scaled in some way", we orthogonalize innovations of state variables to the excess market return, which is the first element of the vector in VAR process. The [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] two-stage approach is then implemented for both TSR and CSR for the research.

In chapter 3, we choose distress risk factor as the augmented factor of the original FF3F Model among plenty risk factors that have been discovered. Since firm's distress risk is an important indicator of a firm's performance and is also one of the most concerned characteristics by investors and firms. What's more, the financial distress risk has been proved closely related to stock returns and the viewpoint of value effect is regarded as the distress risk effect are proposed by time-series literature.

The main objective is to test whether distress risk factor FF factors are proxies for distress risk on CNAS stock market during the period July 2005 to May 2015, if not, whether augmented four-factor model better explains expected average stock returns than FF3F Model. Especially, we apply both accounting-based (Ohlson's O-score) and market-based (Vassalou and Xing's DLI) models to measure the financial distress in order to identify whether different methods of predicting distress risk matter to the empirical results. In addition, the relationship between stock returns and distress risk, and whether the size and value effects are related to distress risk have also been examined on CNAS stock market.

Contributions and Discussion

Though it seems that we are one of the countless studies of testing FF3F Model on Chinese stock market initially in Chapter 1, actually we consider several special features of Chinese stock market and examine not only the time-series but also cross-section validation of FF3F Model. Furthermore, we examine the performance of the latest FF5F Model using data of CNAS stock market, while the comparisons between the performance of both models on CNAS stock market, and the performance of same models between Chinese and U.S. stock market are also implemented.

Despite the extensive evidence that confirm the capability of FF factors in capturing variations of expected average stock returns on Chinese stock market, however, to the best of our knowledge, few studies have authentically focused on the economic underpinning behind FF factors in China. We are the advance ones who explore one of the most popular explanations which is based on time-varying investment opportunities in the context of ICAPM, examine whether FF factors proxy for innovations of selected economic variables on Chinese stock market.

Moreover, developing an early warning system for prediction of firms' financial distress has been a hot topic over the years in China; the research on Chinese market are mainly focused on testing the predictive accuracy of commonly used models in estimating distress risk and measuring default risk of Chinese companies without studying the relationship between default risk and stock returns. We are also the rare ones who propose a mimicking distress factor and investigate the distress risk factor in the frame of FF3F Model.

Overall, our research has new implications in practice (such as for the factor-based investment and assessing the performance of portfolios) on Chinese stock market. The Chinese stock market developed along with extraordinary economic growth and overall institutional reforms so that it might be much different from the mature stock markets such as U.S. stock market. Therefore, for further research, it might be more appropriate to construct risk factors that feature Chinese own characteristics and introduce which to the factor model, thus help researchers to understand the real economic meaning of FF factors on Chinese stock market. 1.1 Reviews of the main asset pricing theories and models

The evolution of the asset pricing models

The history of the theory of the financial asset pricing can be traced back to Bernoulli's famous St Petersburg paper of 1738, since then, researchers have been focusing on this subject for centuries. In the early life of financial fields, describing the market environment and valuing individual securities are the emphasis, which are transformed with the appearance of [START_REF] Markowitz | Portfolio selection[END_REF] paper on portfolio selection. After the birth of Portfolio Selection theory, the discussions of pricing on the financial asset can also be divided into two different periods. Before the 1980s, researchers mainly focus on pure theory, applying Markowitz's optimal selection theory into their research. But after the 80s, as [START_REF] Sharpe | Capital asset prices: A theory of market equilibrium under conditions of risk[END_REF], [START_REF] Lintner | The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[END_REF] and [START_REF] Black | Capital market equilibrium with restricted borrowing[END_REF]'s CAPM becoming a research paradigm, the focal point has transferred to two directions: extending the original CAPM and the empirical research of the model.

The initial extension involved extending the single-period model into a multi-period framework, which turns out to be one of the major developments of modern finance. Merton (1973a) proposes an Intertemporal CAPM (ICAPM) and shows that the classical CAPM would not in general hold in continuous time periods. [START_REF] Breeden | An intertemporal asset pricing model with stochastic consumption and investment opportunities[END_REF]'s Consumption CAPM (CCAPM) links the consumption and stock returns and the model relies on the aggregate consumption in order to understand and predict future asset prices instead of the market portfolio's return in the traditional CAPM.

Meanwhile, [START_REF] Jensen | The capital asset pricing model: Some empirical tests[END_REF] performed the first strict tests of the original CAPM by constructing ''two-pass'' methodology. While the researchers were trying by all means to test the CAPM, [START_REF] Roll | A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory[END_REF] shows that the CAPM never could be tested unless the market portfolio were known with certainty. Even many researchers have tried to tackle the Roll's critique, unfortunately, it turns out that CAPM seems not to hold and there are amounts of evidence that other risk factors also affect the stock returns. The factors will be listed in section 1.2 below.

Around the same time [START_REF] Ross | The arbitrage theory of capital asset pricing[END_REF] develops the Arbitrage Pricing Theory (APT) as an alternative model that could potentially cover the CAPM's short falls, while still retaining the underlying message of the latter. The APT starts by assuming that there are n factors that cause asset returns to systematically deviate from their expected values, however, the theory does not specify how large the number n is, nor does it identify the factors. Empirically, the APT has been investigated by using either factor analytic methods [START_REF] Roll | An empirical investigation of the arbitrage pricing theory[END_REF], to estimate multiple measures of systematic risk, or pre-specified macroeconomic factory [START_REF] Chen | Economic forces and the stock market[END_REF], in which the studies look at pricing relative to a

1.1 Reviews of the main asset pricing theories and models 13 set of observable macroeconomic variables, or factors, selected primarily based on economic intuition.

Reviews of Fama-French Three-Factor Model

The facts that there are other risk factors can also explain the variation of stock returns have been verified by a huge number of research. The factors which are already been verified include the earnings/price ratio [START_REF] Basu | Investment performance of common stocks in relation to their priceearnings ratios: A test of the efficient market hypothesis[END_REF], company size [START_REF] Banz | The relationship between return and market value of common stocks[END_REF], book-to-market equity [START_REF] Fama | The cross-section of expected stock returns[END_REF]) and a variety of other systematic influences on asset price [START_REF] Dimson | A brief history of market efficiency[END_REF]. An asset pricing model who can better explain the risk and the stock returns is demanded in the financial market and many researchers are devoted to do this work. Among which, [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] [hereafter FF] deduce a three-factor model as an alternative way to predict the stock returns or an extension of the original CAPM, and their model not only reveals the primary factors that drive stock return but also provides a strategy for using those factors in the portfolio for a potentially higher expected long-term return, which makes it an extraordinary model and also represent another important progress in the history of asset pricing development.

In fact, [START_REF] Fama | The cross-section of expected stock returns[END_REF] studied the joint roles of market beta, size, leverage, Earnings/Price (E/P) ratio and book-to-market equity (B/M) ratio in the cross-section of average stock returns for NYSE, Amex and NASDAQ stocks over the period . In that study, the authors find that beta has almost no explanatory power. On the other hand, when used alone, size, E/P, leverage and B/M ratio have significant explanatory power in explaining the cross-section of average returns. When used jointly, however, size and B/M equity ratio are significant and they seem to absorb the effects of leverage and E/P in explaining the cross-section average stock returns. [START_REF] Fama | The cross-section of expected stock returns[END_REF] therefore argued that if stocks are priced rationally, risks must be multidimensional. [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF]'s analysis was extended to both stocks and bonds. Monthly returns on stocks and bonds were regressed on five factors: returns on a market portfolio, a portfolio for size and a portfolio for the book-to-market equity effect, a term premium and a default premium. For stocks, the first three factors were found to be significant and for bonds, the last two factors. As a result, [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] construct a three-factor asset pricing model for stocks that includes the conventional market beta and two additional risk factors related to size and book to market equity. They find that this expanded model captures much of the cross section of average returns amongst US stocks.

Compared to the original CAPM, FF3F Model shows that the expected return on a portfolio in excess of the risk-free rate is explained by the sensitivity of its return to three factors: first, the excess return of the market portfolio; second, the difference between the returns of the small size portfolio and those of the big size portfolio (SMB) and third, the difference between the returns of the high book-to-market portfolio and those of the low book-tomarket portfolio (HML). The model is as followed:

i ,t f i i M ,t f i i i ,t R R a b ( R R ) s SMB h HML e        (1.1)
Where:

i ,t
R is the value-weighted return on portfolio i in period t; f R is the risk-free rate;

M ,t f RR 
is the difference between the return of market portfolio (market beta) and the return of risk-free rate; SMB is the size factor (small minus big) and HML is the value factor (high minus low); i b is the coefficient for the excess return of the market portfolio; i s is the coefficient for the excess return of portfolios with small equity class over portfolios of big equity class; i h is the coefficient loading for the excess average returns of portfolios with high book-to- market equity class over those with low book-to-market equity class; i ,t e is the error term for portfolio i at time t.

Reviews of Fama-French Five-Factor Model

Motivated by the valuation theory and recent empirical findings on the strong profitability and investment effects in asset returns4 . Fama and French (2015a) propose a five-factor model contains the market factor and factors related to size, book-to-market equity ratio, profitability and investment, which performs better than the three-factor model of [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF]:

i ,t f i i M ,t f i i i i i ,t R R a b ( R R ) s SMB h HML r RMW c CMA e          (1.2)
From equation (1.2), it is obvious that the five-factor model has two more factors than the three-factor model, RMW and CMA. RMW is the factor related to firm's profitability which is the difference between the returns on portfolios of robust (high) profitability and weak (low) profitability firms. CMA is the one related to investment, which is the difference between the returns of conservative (low) investment portfolios and aggressive (high) investment portfolios.

In this paper, Fama and French suggest that the theoretical starting point is the "Dividend Discount Model":

tt 1 m E( d ) / ( 1 r )       (1.3)
where t m is the share price at time t, t E( d )  is the expected dividend per share for the period t , and r is (approximately) the long-term average expected stock return or, more precisely, the internal rate of return on expected dividends. This model states that the value of a stock today will be the sum of the discounted present value of all its future dividends.

With a little bit manipulation, the dividend per share t d  is the difference between t Y  , the equity earnings for period t+τ, and

t t t 1 dB B B   



, which is the change in book equity.

Then the dividend discount model (equation (1.3)) becomes:

t t t 1 M E( Y dB ) / ( 1 r )          (1.4)
Divided by book equity at time t gives,

tt t1 tt E(Y dB ) / ( 1 r ) M BB         (1.5)
Equation (1.5) implies three statements about expected stock returns.

-Firstly, fix everything except the expected stock return r and the current value of the stock t M , a lower market value t M , or equivalent to a higher B/M ratio implies a higher expected stock return.

-Next, fix everything except the expected earnings t Y  and expected stock returns r , more profitable companies which with higher expected earnings have higher expected returns.

-Finally, controlling for the expected growth t dB  (investment) and expected stock returns while fixing other elements, firms with higher expected growth in book equity implies a lower expected return.

The dividend discount model and its transformation indicate the relationship between the variables and average asset returns. FF point out that the nature of equation (1.3) and equation (1.5) is the reason why they choose profitability and investment factors to augment the model.

The construction of profitability factor and investment factor and the portfolios are demonstrated in the following section.

Retrospective of empirical work of Fama-French factor models

Overviews of the data and methodologies of FF factor models

Construction of Fama-French three factors and portfolios

To do the regressions, Fama and French use stocks in the intersection of American stock markets , NYSE, AMEX, and NASD to construct the portfolios on size and B/M ratio, among which, financial firms and firms with negative B/M equities are eliminated from the sample. To obtain the size and value portfolios, they use a firm's market capitalization at June of year t to measure its size and at the end of December of year t-1 to compute book-to-market equity ratio. So in June of each year t, the stocks are sorted into two size groups: small firms (S) and big firms (B), according to their market value. They also break stocks into three B/M equity groups at each December of year t-1: low B/M equity ratio (L), medium B/M equity ratio (M) and high B/M equity ratio (H) firms, according to the breakpoint 30% and 70% of values of B/M equity for all the stocks. After these steps, they have two size groups and three B/M equity groups at each year t. The intersections of these groups are constructed into six portfolios: small low (SL), small medium (SM), small high (SH), big low (BL), big medium (BM), and big high (BH) portfolios. For instance, The SL portfolio contains stocks in the small size (S) group which meanwhile have low B/M equity ratio (L); the BH portfolio contains stocks in the big size (B) group that also in the high B/M equity group (H). The value-weighted monthly returns are calculated from July of year t to June of year t+1, during which the portfolios remain the same, and the portfolios are reconstructed in July of year t+1 (B/M ratio should exist at December of year t-1).

Finally, the Fama-French three factors obtain as follows. The market factor is the excess market return which is computed as the difference between the value-weighted returns of all A-shares and the risk-free rate. The SMB factor is then the difference between the simple average of the monthly returns of the three small-size portfolios (SL, SM, and SH) and the simple average of monthly returns of the three big-size portfolios (BL, BM, and BH). Similarly, HML is equal to the simple average monthly return of the two portfolios with high book-to-market equity (SH and BH) minus which of the two portfolios with low book-to-market equity (SL and BL).

1 SMB ( Small Low+Small Medium+Small High) 3 1 ( Big Low+Big Medium+Big High ) 3   (1.6) 11 HML ( Small High+Big High ) ( Small Low+Big Low ) 22 
(1.7)

Construction of profitability factor and investment factor

Similar to FF three factors that are constructed using the 6 value-weighted portfolios formed on size and book-to-market equity. The Fama-French 5 factors (2x3) are constructed using the 6 value-weight portfolios formed on size and book-to-market (Size-B/M portfolios), the 6 value-weight portfolios formed on size and operating profitability (Size-OP portfolios), and the 6 value-weight portfolios formed on size and investment (Size-Inv portfolios). The Size-OP portfolios and Size-Inv portfolios are formed in the same way as the Size-B/M portfolios, except the second sort variable is operating profitability or investment.

The operating profitability (OP) for June of year t is calculated as annual revenues minus cost of goods sold, interest expense, and selling, general, and administrative expenses divided by book equity for the last fiscal year end in t-1. The Investment portfolios are formed on the change in total assets from the fiscal year ending in year t-2 to the fiscal year ending in t-1, divided by t-2 total assets at the end of each June using NYSE breakpoints.

To be more clear: The size breakpoint for year t is the median NYSE market equity at the end of June of year t. The construction of portfolios on OP and investment are similar with that of portfolios on book-to-market equity. At the end of each June, the firms are sorted into three OP portfolios based on the breakpoints of the 30th and 70th NYSE percentiles, and the three investment portfolios are formed in the same way using NYSE breakpoints-30th and 70th NYSE percentiles.

Then at the end of each June, the intersections of two portfolios formed on size -small (S) and big (B), and three portfolios formed on profitabilityweak profitability (W), neutral profitability (N) and robust profitability (R) are constructed into six "Size-OP" portfolios: SW, SN, SR, BW, BN and BR5 . Similarly, the "Size-Inv" portfolios, which are also constructed at the end of each June, are the intersections of two portfolios formed on size and three portfolios formed on investment-conservative investment (C), neutral investment (N) and aggressive investment (A). Thus, the six Size-Inv portfolios are constructed: SC, SN, SA, BC, BN, and BA6 .

In Fama-French five-factor (FF5F) Model, the market factor and value factor remain the same as in the three-factor model, while the size factor SMB need to be reconstructed with profitability and investment factors, which is the average return on the nine small stock portfolios minus the average return on the nine big stock portfolios.



(1.14) [START_REF] Fama | The cross-section of expected stock returns[END_REF] show that two easily measured variables, size and book-to-market equity, seem to capture the cross-section of average stock returns. Then the article of FF (1993) extends the FF's (1992) study by using a time-series regression (TSR) approach, and the analysis was extended to both stocks and bonds markets. Monthly returns on stocks and bonds were regressed on five factors: returns on a market portfolio, a portfolio for size and a portfolio for the book-to-market equity effect, a term premium and a default premium. For stocks, the first three factors were found to be significant. As a result, FF (1993) construct a three-factor asset pricing model for stocks that composed by the conventional market beta and two additional risk factors related to size and book to market equity. They find that this model captures much of the cross section of average returns of U.S. stock markets.

1 CMA ( Small Conservative+Big Conservative) 2 1 ( Small Aggressive+Big Aggressive ) 2   (1.15)

Reviews of the empirical tests for Fama-French Three-Factor Model

Empirical results of FF on some developed countries' stock markets

In addition, they also find that the slopes on SMB for stocks are related to size, in every B/M ratio quintile of stocks, the slopes on SMB decrease significantly from smaller-size quintiles to bigger-size quintiles. Similarly, the slopes on HML are related to B/M ratio, in each size quintile, slopes of HML increase from the lower B/M quintile to the higher B/M quintile. Researchers have suggested the following possible explanations for the size effect. Small firms' stocks are more illiquid and trading in them attract greater transaction costs; there is also less information available about small firms and therefore the cost of monitoring a portfolio of small stocks will generally be greater than that of a portfolio of large firms, and also given that small shares trade less frequently, their beta estimates might be less reliable. However, all these remain hypothetical explanations for the size effect, as there is no rigorous theory explaining convincingly why the size effect should be present. The B/M ratio effect shows that average returns are greater the higher the book-to-market value ratio and vice versa. It is also referred to as the value premium. The high book value firms are underpriced by the market and are therefore good buy and hold targets, as their price will rise later. This anomaly undermines the semi-strong form efficiency of the market. These two variables explain average return differences across portfolios that cannot be accounted for by beta. [START_REF] Fama | Size and book-to-market factors in earnings and returns[END_REF] analyze the characteristics of firms with high B/M ratio and those with low B/M ratio. They find that firms with high B/M ratio tend to be persistently distressed and those with low B/M ratio are associated with sustained profitability. They conclude that the returns to holders of high B/M ratio stocks are therefore a compensation for holding less profitable and riskier stocks. They show that book-to-market equity and slopes on HML in the three-factor model proxy for relative distress. Weak firms with persistently low earnings tend to have high B/M ratio and positive slopes on HML; strong firms with high earnings have low B/M ratio and negative slopes on HML.

Similarly, [START_REF] Chan | Structural and return characteristics of small and large firms[END_REF] posit that small and large firms have different risk and return characteristics. Small firms on the New York Stock Exchange are firms that have not been doing well, are less efficiently managed and are highly levered. As a result, small firms tend to be riskier than large firms and that risk is not captured by the market index. After introducing multiple risk exposures to the market index; a leverage index and a 1.2 Retrospective of empirical work of Fama-French factor models 21 dividend-decrease index to mimic the marginal firms, the size effect loses its explanatory power. Risk exposures to these indices are as powerful as size in explaining average returns of size-ranked portfolios.

However, Kothari et al. (1995a) and MacKinlay (1995a) argue that a substantial part of the premium is due to survivor bias and data snooping. The data source for book equity contains a disproportionate number of high B/M firms that survive distress, so the average return for high B/M equity firms is overstated. The data snooping hypothesis posits that researcher's fixation to search for variables that are related to average return, will find variables, but only in the sample used to identify them. But a number of papers have weakened and even dismissed the survivorship-bias and the data snooping hypothesis. For instance, Lakonishok et al. (1994a) find a strong positive relation between average returns and B/M ratio for the largest 20 percent of NYSE-Amex stocks, where survivor bias is not an issue. Similarly, FF (1993) find that the relation between B/M ratio and the average return is strong for value-weight portfolios. As value-weight portfolios give most weight to larger stocks, any survivor bias in these portfolios is trivial. There are also are many studies using different sample periods on US data and samples in different countries confirming the existence of the size and book-to-market equity effects. FF (1998) provide additional valuable out-of-sample evidence. They tested the FF three-factor model in thirteen different markets over the period 1975 to 1995. They find that 12 of the 13 markets record a premium of at least 7.68 percent per annum to value stocks (high B/M ratio). Seven markets show statistically significant B/M betas. Maroney and Protopapadakis (2002) test the FF three-factor model on seven stock markets of Australia, Canada, Germany, France, Japan, the UK and the US. The size effect and the value premium survive for all the countries examined. They conclude that the size and B/M effects are international in character. Using a Stochastic Discount Factor (SDF) model, and a variety of macroeconomic and financial variables, do not diminish the explanatory power of B/M ratio and market value. Their evidence suggests that the B/M and size effects are not artifacts of the inadequacies of the augmented CAPM as an asset-pricing model or of omitting macroeconomic and financial variables. The positive relation of returns with B/M and their negative relation with market value remain strong under a general SDF model. [START_REF] Faff | An examination of the Fama and French three-factor model using commercially available factors[END_REF] uses Australian data over the period 1991 to 1999 to examine the power of the FF3F Model. He finds strong support for the FF3F Model, but a significant negative rather than the expected positive, premium, to small size stocks. [START_REF] Faff | An examination of the Fama and French three-factor model using commercially available factors[END_REF] concludes that his results appear to be consistent with other recent evidence of a reversal of the size effect. [START_REF] Gaunt | Size and book to market effects and the Fama French three factor asset pricing model: evidence from the Australian stockmarket[END_REF] studies the FF3F Modl in the Australian setting and provides further out of sample (non-US) tests of the model. The study covers the period 1991 to 2000 of firms listed on the Australian Stock Exchange. He finds that beta risk tends to be greater for smaller companies and those with lower BM ratios. Contrary to FF, the betas are on average significantly less than one. There is also evidence of the value effect increasing monotonically from the lowest to the highest book-to-market equity portfolios. There is a monotonic increase of loadings on the SMB factor as well when moving from the largest to the smallest portfolios. They find large and positive intercepts for the small portfolios. The explained variation as measured by the adjusted 𝑅 2 is also much higher compared to the CAPM. The author concludes that the three-factor model provides a better explanation of observed Australian stock returns than the CAPM.

Numerous studies examined various global markets following research of FF. Studies on the UK market by [START_REF] Chan | An Empirical Re-Examination of the Cross-Section of Expected Returns: UK Evidence[END_REF] fail to find a significant beta-return relationship. Subsequent studies by [START_REF] Hung | CAPM, Higher Co-moment and Factor Models of UK Stock Returns[END_REF] and [START_REF] Morelli | Beta, size, book-to-market equity and returns: A study based on UK data[END_REF], again examining the UK market all provide further evidence against an unconditional relationship between beta and returns. [START_REF] Morelli | Beta, size, book-to-market equity and returns: A study based on UK data[END_REF] find a significant relationship between beta and returns in the presence of size and book-to-market equity, but the author documents that size is not a significant risk variable, whereas B/M ratio is a significant determinant of security return on UK market. Studies of other European markets including, [START_REF] Lilti | Beta, size and returns: a study on the French Stock Exchange[END_REF] in the French market, [START_REF] Isakov | Is beta still alive? Conclusive evidence from the Swiss stock market[END_REF] in the Swiss market, and [START_REF] Elsas | Beta and returns revisited: evidence from the German stock market[END_REF] in the German market, all find beta to be a significant risk measurement

Summary of empirical results in emerging Asian markets

Most Asian stock markets are emerging market which draws researchers' attentions, and it's interesting and meaningful to study the FF3F Model which is well performed in U.S. on the emerging Asian markets. Researches are done which concerning Fama-French factors and stock market anomalies on the emerging stock market in Asia: such as India, Thailand, Indonesia, Malaysia, Singapore, Korea, Vietnam and Hong Kong.

Early in 1995, [START_REF] Claessens | Return behavior in emerging stock markets[END_REF] study the cross-section of stock returns from twenty emerging markets, among which, several Asian markets (Indonesia, Korea, Malaysia, Philippines, Thailand) are included. They find that besides market risk, firm size, E/P ratio and turn over factors are significant in explaining a cross-section of stock returns. Among those Asian countries, the market beta has no explanatory power on most of the stock markets, only India, Malaysia and Thailand stock market have size effect. [START_REF] Chui | Book-to-market, firm size, and the turn-of-the-year effect: Evidence from Pacific-Basin emerging markets[END_REF] conduct empirical tests on the robustness of the multifactor model in the Asian region. They examine the relationship between expected stock returns and market beta, size and B/M equity in five Asian emerging stock markets: Hong Kong, Korea, Malaysia, Taiwan, and Thailand. Their results suggest a weak relationship between average stock returns and the market beta for all five markets. But the book-to-market equity can explain the cross-sectional variation of expected returns in Hong Kong, Korea, and Malaysia, while the size effect is significant in all five markets except Taiwan. [START_REF] Drew | Beta, Firm Size, Book-to-Market Equity and Stock Returns[END_REF] compares the explanatory power of FF3F Model in Hong Kong, Korea, Malaysia and Philippines, and the author documents that size and value effects exist for all four markets but the multifactor model of FF provides a parsimonious description of the cross-section of returns for these Asian markets over the 1990s. Furthermore, [START_REF] Shum | Common risk factors in returns in Asian emerging stock markets[END_REF] apply FF3F Model on three Asian emerging markets: HK, Singapore and Taiwan over the period July 1986 to December 1998, and they conclude that the model largely explains the variations in average returns when using the contemporaneous market factor, but the impact of size effect and value effect is very limited and insignificant in most cases. [START_REF] Sehgal | Tests of equity market anomalies for select emerging markets[END_REF] test the equity market anomalies for six emerging market including China, India, Indonesia, South Korea and South Africa. They find that there is size effect in India and both size and value effect in South Korea. [START_REF] Connor | Tests of the Fama and French model in India[END_REF] find a pervasive influence of FF3F model on random stock returns in India from 1989 to 1998, however, the market factor alone cannot explain the cross-sectional stock returns. [START_REF] Sehgal | Robustness of fama-french three factor model: further evidence for indian stock market[END_REF] re-examine the robustness of CAPM and FF3F model using data from 1996 to 2010, and results turn out that FF3F model does a better job in explaining the returns on most portfolios constructed based on firm size and B/M equity ratio. Ranjan [START_REF] Ranjan Dash | Conditional multifactor asset pricing model and market anomalies[END_REF] propose a multifactor model which include liquidity, market leverage, and momentum along with size and value factors to investigate the firm-specific anomaly effect and to identify market anomalies that account for the cross-sectional regularity in the Indian stock market. Though the anomaly effect is weak, their five-factor model is able to capture the B/M equity, liquidity, and medium-term momentum effect, and size, market leverage, and short-run momentum effect are found to be persistent in the Indian stock market. Based on the data of period Jun 2001to Jun 2006, Jun 2004to Jun 2009, Oct 1998to Sep 2013, Jan1997 to Jun 2012and Jan 1997to Aug 2014, separately, Bahl (2006), [START_REF] Taneja | Revisiting fama french three-factor model in indian stock market[END_REF], [START_REF] Das | Empirical evidence of conditional asset pricing in the Indian stock market[END_REF], [START_REF] Balakrishnan | Multifactor explanations of CAPM anomalies: An evidence for Indian stock market[END_REF] and [START_REF] Balakrishnan | Size, Value, and Momentum Effects in Stock Returns: Evidence from India[END_REF]'s research continues to prove the existent of the size and value effect in the Indian stock market.

In other Asian emerging markets, [START_REF] Ferdian | Firm Size, Book to Market Equity, and Security Returns: Evidence from the Indonesian Shariah Stocks[END_REF] find that market beta alone is not sufficient to describe the variation in average equity returns, but there exist size and value premium for Indonesian Shariah Stocks over the period September 2007 to September 2009. However, [START_REF] Sudiyatno | STUDY OF THREE FACTORS MODEL FAMA AND FRENCH IN INDONESIA STOCK EXCHANGE[END_REF] find no prove of size and value effects but a significant positive relationship between the risk premium and stock returns over the period 2007 to 2009 in Indonesia stock exchange. [START_REF] Amanda | Empirical Test of Fama French Three Factor Model and Illiquidity Premium in Indonesia[END_REF] explore FF3F Model along with liquidity in Indonesia from 2003 to 2013, and they conclude that there are market risk premium, size premium, value premium and liquidity risk premium which can explain the excess return in Indonesia. [START_REF] Lau | Stock returns and beta, firms size, E/P, CF/P, book-to-market, and sales growth: evidence from Singapore and Malaysia[END_REF] examine the relationship between stock returns and beta, size, the earnings-to-price ratio, the cash flow-to-price ratio, the book-to-market equity ratio, and sales growth. And they proved the existence of anomalies in Singapore and Malaysia for the period June 1988 to December 1996. [START_REF] Drew | A closer look at the size and value premium in emerging markets: Evidence from the Kuala Lumpur Stock Exchange[END_REF] present evidence of the size and value premium for the case of the Malaysia. They report that the factors identified by FF explain the variation in stock returns in Malaysia and are not sample specific. The analysis was restricted to firms with available returns data from December 1992 to December 1999. Their findings clearly document evidence of a size and B/M equity effect that small and high B/M equity stocks generate higher returns than big and low B/M stocks in Malaysia. The results also show that the explanatory power of the variables is powerful throughout the sample period and not solely in January. [START_REF] Lam | The relationship between size, book-to-market equity ratio, earningsprice ratio, and return for the Hong Kong stock market[END_REF] investigates the relation between stock returns and size, leverage, B/M ratio, and earnings-price (E/P) ratio in Hong Kong stock market using FF approach. And he proves that market beta is unable to explain the average monthly returns on stocks listed in Hong Kong Stock Exchange over the period July 1984 to June 1997. But size, book-tomarket equity, and E/P ratio seem able to capture the cross-sectional variation in average monthly returns over the period. Other two variables book and market leverages, are also able to capture the cross-sectional variation in average monthly returns. But their effects seem to be dominated by size, book-to-market equity, and E/P ratio, and considered to be redundant in explaining average returns when size, book-to-market equity, and E/P ratios are also considered. [START_REF] Ho | On the conditional pricing effects of beta, size, and book-to-market equity in the Hong Kong market[END_REF] examine whether market beta, size and B/M ratio are priced under different market conditions on Hong Kong stock market, such as the up or down market. It is found that, for the whole market, size and B/M ratio were priced but not market beta. However, separate the whole market into up and down markets, there exists a significant systematic relation between market beta and stock returns. But size effect is insignificant in up markets, and B/M effect is negligible in down markets Moreover, [START_REF] Homsud | A study of Fama and French three factors model and capital asset pricing model in the Stock exchange of Thailand[END_REF] prove the efficiency of FF3F model in The Stock Exchange of Thailand over the period July 2002 to May 2007 and they conclude that FF3F model can explain risk in stock returns better than the traditional CAPM. [START_REF] Phong | Applying Fama and French Three Factors Model and Capital Asset Pricing Model in the Stock Exchange of Vietnam[END_REF] assess the application of FF3F Model in Vietnam's stock market from Jan 2007 to Dec 2011, and the results show that FF3F Model explaining average stock returns superior to CAPM.

In general, there are pervasive size and value effects while the market beta seems not able to explain cross-sectional stock returns on most Asian emerging markets. Thus, the FF3F 1.2 Retrospective of empirical work of Fama-French factor models 25 Model performs better than CAPM in explaining the anomalies of stock returns, especially size and value anomalies according to the researches mentioned above.

Empirical tests in Chinese stock market

As the biggest emerging market in Asian, Chinese stock market has attracted considerable attention, the cross-sectional relationship between firm-specific characteristics, such as firm size and B/M equity, and stock returns is also an intriguing issue for researchers. Previous studies identify several important factors in explaining stock returns in various stock markets around the world. There is limited literature that investigate the CNAS market in this respect until recent years (after 2010) and more researchers consider the special features of Chinese stock market, which we will precise in next section. This part will review the studies that apply the FF3F Model to Chinese mainland stock market returns. [START_REF] Drew | Firm size, book-to-market equity and security returns: Evidence from the Shanghai Stock Exchange[END_REF] use data of Shanghai Stock Exchange for the period 1993 to 2000, and test the multifactor approach to asset pricing in China considering the non-tradable and tradable market value. Their analysis suggest that market beta alone is not sufficient to explain the variation in the average stock returns, and small and growth firms generate superior returns than big and value firms, but value effect is not as pervasive as was found for the US portfolios and other international markets. In addition, the authors also conclude that there is no proof of seasonal effects, such as the January and/or Chinese New Year effect, which can determine the size and value effects. However, they only run the onestage time series regressions using mimic portfolios based on size and book-to-market equity, no cross-sectional pricing analysis was conducted. [START_REF] Wang | What Determines Chinese Stock Returns?[END_REF] investigate FF3F Model on CNAS stock market including both the Shanghai and Shenzhen A-share stock markets for the sample period July 1996 to June 2002. Firm size is proved to explain the cross-sectional differences in average stock returns, but contrary to the findings on U.S. market, their results showed the B/M ratio had no effect on the Chinese stock markets.

Both [START_REF] Eun | Asset pricing in China's domestic stock markets: Is there a logic?[END_REF] and [START_REF] Wang | The cross section of expected stock returns in the Chinese A-share market[END_REF] explore the cross-sectional relationship of average stock returns and several Chinese firms-specific characteristics in the CNAS stock market and both find that market beta lacks the explanatory power even when the beta effect is examined respectively. [START_REF] Wang | The cross section of expected stock returns in the Chinese A-share market[END_REF] propose that the absence of a market beta effect may be attributed to some specific market characteristics in the A-share market, such as government intervention, irrational behavior of individual investors, and the prohibition of short sales (reference to [START_REF] Kang | Contrarian and momentum strategies in the China stock market: 1993-2000[END_REF], [START_REF] Hu | The evolution of China stock market and its institutions[END_REF] and [START_REF] Wang | Relative strength strategies in China's stock market: 1994-2000[END_REF]). However, their results suggest the existence of value effects in addition to size effect over their research periods, which is contrary to the findings of [START_REF] Wang | What Determines Chinese Stock Returns?[END_REF]. [START_REF] Rutledge | Is there a size effect in the pricing of stocks in the chinese stock markets?: The case of bull versus bear markets[END_REF] investigate whether there is a size effect in case of bull and bear markets in Chinse stock market over a six-year period from 1998 to 2003. And they find small firms have significantly greater positive excess returns than large firms during the bull market, however, small firms have significantly greater negative returns (using total market value), or no significant difference in returns (using float market value) during the bear market period. [START_REF] Wong | The cross-section of stock returns on the Shanghai Stock Exchange[END_REF] and [START_REF] Morelli | Security returns, beta, size, and book-to-market equity: evidence from the Shanghai A-share market[END_REF] both focus on the A-share stock market of Shanghai Stock Exchange in China. The former explores the cross-sectional stock return behavior and estimate the beta, size and value effects over the period 1993 to 2002, results show that smaller firms and value stocks perform better. Systematic risk is negatively significant in down markets. The latter explores the cross-sectional relationship between security returns and beta, size and book-to-market equity, and there is no proof of an unconditional relationship between market beta and returns. However, a conditional relationship is found when the data is split into up and down markets, the relationship holds even in the presence of size and book-to-market equity. Both size and book-to-market equity are found to display both an unconditional and conditional relationship with stock returns.

Researches are applied on Chinese stock market during recent years, especially after 2010. Xuanjuan Chen et al. ( 2010) take 18 firm-specific variables which are demonstrated to predict cross-sectional stock returns in U.S and examine their relationship with stock returns in Chinese stock market over the period 1995 to 2007. But only five variables are able to predict stock returns (B/M equity, assets growth, and illiquidity, etc.), and not as in U.S. market, in multivariate regression tests few variables succeed in multivariate regression tests.

Contradict with most of the existing literature that there exist size and value effect across the returns of Chinese stock market7 , [START_REF] Wu | The value and size effect-are there firm-specific-risks in China's domestic stock markets?[END_REF] apply FF3F model on CNAS markets: Shanghai Stock Exchange (SSE) and Shenzhen Stock Exchange (SZSE), separately, June 1992 to April 2009 for SSE and February 1996 to April 2009 for SZSE. The results of CSRs suggest that market beta has no explanatory power when examined alone or with other factors, and there is evidence of value effect on SSE but no size effect was found. Finally, the author has the conclusion that the model works better in SSE than in SZSE. Contradictorily, [START_REF] Chen | Fama-French in China: Size and Value Factors in Chinese Stock Returns[END_REF] find a strong size effect but no value effect cross returns based on the data period July 1997 to December 2013 in Chinese stock market, the results, which is consistent with [START_REF] Wang | What Determines Chinese Stock Returns?[END_REF].

It is noteworthy that more and more researchers take the special features of Chinese stock market into consideration. For instance, [START_REF] Chen | Cross-Sectional Variations and Three Factors Asset Pricing Model: Empirical Evidences from China A Share Market[END_REF] 8 examines the performance of the Fama-French three-factor model for CNASs. The author sorts stocks by their tradable shares' market value into three size groups using breakpoints at the 30% and 70% percentiles. The portfolio returns are value-weighted by the tradable shares' market value. [START_REF] Mao | Long-run Return Performance Following Listed Rights Issue: Based on the Improved Three-factor Model[END_REF] 9 apply the FF3F Model to study the long-run return performance after Chinese listed firms completed rights offering. To construct the three factors, they also sort stocks into two size groups by their tradable shares' market value. [START_REF] Liao | Fama-French Three Factors Model and the Effect of the Split-share Structure Reform[END_REF] 10 use FF3F Model to examine stock price reaction to Chinese listed firms' completion of the split-share structure reform that was initiated in April 2005. To construct the size factor, they separate small and large stocks by the median of their tradable shares' market value, which is defined as the number of tradable shares at the beginning of each year multiplied by share price. To construct the value factor, they use the net assets per share divided by share price as the B/M ratio because of the market segmentation in China. The portfolio returns are value-weighted by the tradable shares' market value, which implicitly assumes that the portfolios include only tradable shares. In order to examine the explanatory power of the FF3F Model on Chinese bond returns, [START_REF] Liu | Application of Fama-French multi-factor model in China's bond market during recent financial crisis[END_REF] 11 sort stocks by their price-to-book ratio into three groups, and the portfolio returns are value-weighted by the total market value; to construct the size factor, they sort stocks by their total market value into two groups. The results show that two factors, SMB and HML, do not contribute significantly to explaining Chinese bond returns. [START_REF] Zhang | The fama-french three factors in the Chinese stock market[END_REF] provide an empirical evidence of to what extent the three factors explain the variation in Chinese stock returns and identify some pitfalls that arise in the application of the three-factor model to Chinese stock returns. They summarize three special features of Chinese stock market that potentially affect the three factors considerably which also have the influence to the explanatory power of FF three-factor model. In addition to the tradable and non-tradable shares and market segmentation in Chinese stock market, they also take into account that whether Small Medium Enterprise 8 Chen, Zhanhui. ( 2004), 'Cross-sectional Variations and Three Factors Asset Pricing Model: Empirical Evidence from China A-Share Market', Chinese Journal of Management Science 6: 13-18 (in Chinese). 9 Mao, X-Y., Chen, M-G. and Yang, Y-H. ( 2008 Board (SME) and the Growth Enterprise Board (GEB) listed firms should be excluded in determining the breakpoints for the size factor. They experiment with different ways of constructing the three factors in order to evaluate the effect of these special features in China, the results turn out to be that the formation of the three factors can have a big impact in empirical studies applying the FF3F Model to Chinese stock market. Overall, FF3F Model can explain more than 93% of the variation in the portfolio returns on CNASs for the period of 1996 to 2013, and it does not affect the explanatory power of FF3F model whether or not the SME and GEB stocks are included to determine the portfolio breakpoints. The explanatory power of the three-factor model is higher when the market portfolio includes only tradable shares than when the market portfolio includes both nontradable and tradable shares, and when the book-to-price ratio (B/P) are used instead of the book-to-market ratio.

Though there is less research in Chinese stock market comparing to U.S. and other developed stock markets, there is time-series literature provide evidence that size or value (or both) effect(s) on Chinese stock market but the market beta seems not have explanatory power in explaining the cross-sectional stock returns in China. What's more, considering the special features of Chinese stock market seems to be the right direction to apply the FF3F Model to Chinese stock market as the literature documented, since the explanatory power of FF3F Model has clearly improved.

Profitability and investment factors and Fama-French Five-Factor Model

Cooper and Maio (2016) state that "The investment anomaly can be broadly classified as a pattern in which stocks of firms that invest more exhibit lower average returns than the stocks of firms that invest less", and "the investment anomaly can be broadly classified as a pattern in which stocks of firms that invest more exhibit lower average returns than the stocks of firms that invest less". [START_REF] Sloan | Do stock prices fully reflect information in accruals and cash flows about future earnings?[END_REF] is the first who document that accruals are negatively related to future profitability and that higher accruals predict lower stock returns. Following, an extensive literature initiated by [START_REF] Sloan | Do stock prices fully reflect information in accruals and cash flows about future earnings?[END_REF], such as [START_REF] Chan | Earnings Quality and Stock Returns[END_REF] also indicate that accruals are reliably and negatively related to future stock returns (See also [START_REF] Xie | The mispricing of abnormal accruals[END_REF], [START_REF] Richardson | Accrual reliability, earnings persistence and stock prices[END_REF], and [START_REF] Richardson | The implications of accounting distortions and growth for accruals and profitability[END_REF]). [START_REF] Novy-Marx | The other side of value: The gross profitability premium[END_REF] uncovers a positive relationship between profitable firms and expected returns that profitable firms earn significantly higher average returns than unprofitable firms. Haugen and Baker (1996b) and [START_REF] Cohen | Who underreacts to cash-flow news? Evidence from trading between individuals and institutions[END_REF] find that controlling for B/M, average returns are positively related to profitability. [START_REF] Fairfield | Accrued earnings and growth: Implications for future profitability and market mispricing[END_REF] find that the well-documented accrual anomaly extends to growth in long-term 1.2 Retrospective of empirical work of Fama-French factor models 29 net operating assets, thus the accrual anomaly documented in [START_REF] Sloan | Do stock prices fully reflect information in accruals and cash flows about future earnings?[END_REF] is a subset of a larger anomaly with respect to a general market mispricing of growth in net operating assets.

Working within the confines of a valuation equation, [START_REF] Abarbanell | Abnormal returns to a fundamental analysis strategy[END_REF], [START_REF] Frankel | Accounting valuation, market expectation, and crosssectional stock returns[END_REF], [START_REF] Dechow | The relation between analysts' forecasts of long-term earnings growth and stock price performance following equity offerings[END_REF], combine analyst' forecasts of earnings with assumptions about future investment to estimate expected stock returns. General results indicate that higher expected net cash flows (expected profitability minus expected investment) relative to current market value forecast higher stock returns. [START_REF] Titman | Capital investments and stock returns[END_REF] show that firms which increase capital investment tend to have future negative risk-adjusted returns; and a similar conclusion of a negative relation between average returns and investment is obtained by [START_REF] Richardson | External financing and future stock returns[END_REF]. Both [START_REF] Anderson | Empirical evidence on capital investment, growth options, and security returns[END_REF] and [START_REF] Cooper | Asset growth and the cross-section of stock returns[END_REF] find that firm-level investment growth is a robustly significant predictor of the cross-section stock returns, furthermore, the former propose that the investment anomaly appears to contain information similar to that of the B/M ratio. [START_REF] Fama | Dissecting anomalies[END_REF] investigate the anomalies which including the asset growth and profitability, and they provide evidence that higher profitability tends to be associated with abnormally high returns among profitable firms.

By applying a standard q-theory, Xing (2008a) constructs an investment growth factor, defined as the difference in returns between low-investment stocks and high-investment stocks. The author finds that the investment factor contains information similar to the FF (1993) value factor HML, and can explain the value effect about as well as HML. Similarly, [START_REF] Lyandres | The new issues puzzle: Testing the investment-based explanation[END_REF] construct the same investment factor as [START_REF] Xing | Interpreting the Value Effect Through the Q-Theory: An Empirical Investigation[END_REF] and their results indicate that the investment factor earns a significantly positive average return.

In the paper of [START_REF] Fama | Profitability, investment and average returns[END_REF], they have already studied for the three variables, B/M ratio, profitability, and investment effects, which are related to expected stock returns according to dividend discount model and the valuation equation. And they confirm the implies of valuation theory that high rates of investment are related to low expected returns when controlling B/M ratio and profitability, while controlling two other variables, high profitable stocks have higher expected stock returns. Supporting FF valuation perception, [START_REF] Aharoni | Stock returns and the Miller Modigliani valuation formula: Revisiting the Fama French analysis[END_REF] find a positive relation between expected profitability and returns, and crucially a negative relation between expected investment and returns. They emphasize that "measuring investment at the firm level rather than per share level is the key to empirically understanding the simultaneous relation between expected returns, B/M, expected profitability, and expected investment".

Especially, [START_REF] Hou | Digesting anomalies: An investment approach[END_REF] examine nearly 80 anomalies in the literature from January 1972 to December 2012 on U.S. market based on q-theory, but about one-half of the anomalies seems exaggerated their explaining power for average stock returns. They come to a conclusion that a four-factor model which includes the market factor, size factor, profitability factor and investment factor explains the cross-sectional average stock returns to a large extent, and outperforms the FF3F model and [START_REF] Carhart | On Persistence in Mutual Fund Performance[END_REF] four-factor models.

Inspired by recently research that give evidence to the remarkable existence of profitability and investment effects, based on the dividend discount model (equation (1.3)), Fama and French (2015a) propose a five-factor model contains the market factor and factors related to size, book-to-market equity ratio, profitability and investment and test the performance of the five-factor model for the U.S. market using the data from July 1963 to December 2013. (Data period July 1963-December 2013). They use three sets of factors 12 in order to examine whether the specifics of factor construction do have an important impact on the results of the test of asset pricing models. Furthermore, they show GRS statistic of [START_REF] Gibbons | A test of the efficiency of a given portfolio[END_REF] to test whether the intercepts are indistinguishable from zero in the regressions of the portfolios' excess returns on the models' factor returns so that to distinguish whether a model can completely capture expected returns.

The results show that the factors from the 2x3, 2x2 and 2x2x2x2 sorts obtain much the same results in testing of a given model, and although the GRS tests 13 indicate that all the models are incomplete descriptions of expected average returns, the FF5F model outperforms FF3F model by adding profitability and investment factors. As FF themselves say, "Despite rejection on the GRS test, the five-factor model performs well: unexplained average returns for individual portfolios are almost all close to zero".

Meanwhile, FF find that when the profitability and investment factors are added into FF3F model, the value factor HML seems to become redundant in explaining average expected returns. Thus, they draw a conclusion that the value factor HML is a redundant factor for 12 The three sets of factors are: 2x3 sorts on Size and B/M, or Size and OP, or Size and Inv; 2x2 sorts on Size and B/M, or Size and OP, or Size and Inv; and 2x2x2x2 sorts on Size, B/M, OP and Inv (see details in Fama and French, 2014). 2x3 sorts on Size and B/M is that the size and value factors are independently sort stocks into two size groups and three B/M groups, and construct the size factor SMB and value factor HML as of FF3F model; the 2x3 sorts on Size and OP or Size and Inv are the same as Size and B/M except the sort for B/M groups are replaced by operating profitability or investment. 2x2 sorts method is similar as 2x3 sorts except that the stocks are all independently sorted into two groups. In 2x2x2x2 sorts is that the size factor SMB equal weights high and low B/M, robust and weak OP, and conservative and aggressive Inv portfolio returns. 13 The GRS test examine whether an asset pricing model completely captures expected returns. If the five-factor model can explain all cross-sectional variation in expected stock returns, then the intercept will be indistinguishable from zero in a regression of an asset's excess returns on the model's factor returns.

describing average returns in FF5F model, which is consistent with the previous findings of [START_REF] Anderson | Empirical evidence on capital investment, growth options, and security returns[END_REF] and Xing (2008a). They explain this outcome is because "the average HML return is captured by the exposures of HML to other factors (market factor, SMB, HML and especially RMW and CMA)".

FF's (2015a) results suggest that a five-factor model performs better than their FF3F Model. But the five-factor model fails to capture low average returns on small stocks with high investment and low profitability. They also show that the model's performance is not affected by the way the factors are calculated. With two additional factors, their results also suggest that the value factor (HML) becomes redundant.

There is not much research on FF Five-Factor model out of America. FF (2015b) proceed the international tests of FF5F model in North America, Europe, Japan, and Asia-Pacific. Expected stock returns increase with the B/M ratio and profitability and decrease with investment for North America, Europe, and Asia Pacific, however, the average stock returns show little relation to profitability or investment factors. On Brazilian market, [START_REF] Martinsa | Pricing Assets with Fama and French 5-Factor Model: a Brazilian market novelty[END_REF] test the performance of FF5F model during the period January 2002-December 2012 and find that FF5F Model performs better than their previous work in the three-factor model. The market factor, SMB, and HML capture most of the variation in average returns in the TSR, however, the two new factors RMW and CMA have shown less explanatory power. [START_REF] Chiah | A better model? An empirical investigation of the Fama-French five-factor model in Australia[END_REF] investigate the FF5F Model on Australia market, and they find that the profitability and investment factors have significantly positive premium. FF5F Model is proved to be able to explain average stock returns better than FF3F Model in Australia, in contrary to FF (2015a) results, the value factor (HML) remains its explanatory power in the presence of the investment and profitability factors.

To the best of our knowledge, there is no such a work on Chinese stock market so far. In next section, we will present the empirical results that we apply FF5F Model on CNAS stock market.

Introduction of Chinese stock market

Background of Chinese stock market

In the past 30 years, China experienced extraordinary economic growth and has become an increasingly important member of the global economy. One of the critical economic reforms was the introduction and the development of the stock markets. Still young and immature, the Chinese stock markets have grown rapidly and now become the second largest in terms of market capitalization.

On Chinese stock market, there are three kinds of stocks: A-share stocks, B-share 'stocks, and H-share stocks. The 'A-shares' do not refer to the 'class' of common or preferred stocks as usual, it refers to shares that are purchased and traded on the SSE and SZSE, which are two membership institutions governed directly by the China Securities Regulatory Commission (CSRC). These companies are incorporated in mainland China and their shares are denominated in the local currency Chinese yuan, or RenMinBi (RMB). For individual investors, these stocks of the A-share market are strictly off limits to non-Chinese investors. Meanwhile, some Chinese companies are listed in Shanghai and Shenzhen, but their shares trade in U.S. dollars. These stocks, known as 'B-Share', were designed to give Chinese companies a way to raise capital from overseas. 'B-Shares' also allow foreign (non-Chinese) investors to invest in this market without the restrictions associated with 'A-shares'. 'H-shares' are also Chinese companies, but these securities are traded on the Hong Kong Stock Exchange rather than on the mainland, and they are priced in Hong Kong dollars.

The Chinese stock market is a young market with relative short history, and it has grown and expanded rapidly since the establishment of Shanghai stock exchange (SSE) on November 26th, 1990 -in operation on December 19th of the same year and the other stock exchange-Shenzhen stock exchange(SZSE) on December 1st, 19901st, (opened on July 3rd, 1991)). The total listed firms on A-share stock market increase rapidly from 14 of the year 1991 to more than 1000 of the year 2001, and more than 2500 until now (in SSE and in SZSE). This rapid growth has attracted considerable academic interests; many studies have examined the ability of FF3F model to predict the stock price movements of Chinese stock. This figure shows the performance of both Shanghai Stock Exchange A-Share (SHASHR) Index and Shenzhen Stock Exchange A-Share (SZASHR) Index from 1992 to 2015. The upper part is the index point, white for SHASHR Index and green for SZASHR Index; the nether part is the volume, grey for SHASHR Index and rose red for SZASHR Index. This figure shows the performance of both SHASHR Index and NYSE Composite (NYA) Index from 1992 to 2015. The upper part is the index point, white for SHASHR Index and green for NYA Index; the nether part is the volume, grey for SHASHR Index and red for NYA Index.

while the green one is NYA Index. Thought the index price of NYA Index is much higher than that of SHASHR Index, the trends of both indexes are much similar.

Table 1.1 shows the summary of Chinese stock market, the annual total listed firms on the whole stock market and listed firms respectively on SSE and SZSE from 1990-2014, listed stocks of A-share stock market, total market capitalization (whole stock market, A-share The first column is the year from 1990 to 2014, and total listed firms, listed firms on SSE (denoted as SSE) and SZSE (denoted as SZSE), listed stocks of A-share (Stocks of A), and total market capitalization (Total market cap) of whole Chinese stock market, A-share market (A) and B-share market (B) are represented in the following columns. The last column is the percentage of B-share value in total market capitalization (B value in total). The unit of total market capitalization is 100 million yuan. 1.3 shows the total listed firms and that of SSE and SZSE from 1990 to 2014, listed stocks of A-share stock market are also presented. Figure 1.4 represents the total market capitalization of the whole stock market and also respectively of A-share stock market and B-share stock market from 1992 to 2014.

From Table 1.1 andthe figures 1.3 and1 than 1% from 2007 (2.93% of year 2001, 0.46% of year 2014). Our research will focus only on CNAS stock market.

Special features of Chinese stock market

The emerging empirical literature suggests that Chinese market has some special features, and it is inevitable to consider those special features if researchers want to have more accurate results in China. Chen ( 2004), [START_REF] Mao | Long-run Return Performance Following Listed Rights Issue: Based on the Improved Three-factor Model[END_REF], [START_REF] Zhang | The fama-french three factors in the Chinese stock market[END_REF], [START_REF] Liu | Application of Fama-French multi-factor model in China's bond market during recent financial crisis[END_REF] and [START_REF] Hung | Non-Tradable Share Reform, Liquidity, and Stock Returns in China[END_REF] all do their research considering one or several special features on Chinese stock market. We summarize three primary features which are also most frequently employed by literature.

-Firstly, it is well known that China, like many markets in the Asian region, has substantial holdings of non-traded shares which mean that these shares are not effectively valued. Before April 2005, listed companies had two kinds of shares outstanding which are tradable shares and non-tradable shares. Non-tradable shares were held by government agencies or government-related enterprises and were nontradable in the public market.

37

-Another important special feature is the segmentation of Chinese stock market, more than 170 Chinese listed firms have issued multiple class shares which have the same cash flow and voting rights but are traded in different markets. Some of them have A-shares and B-shares, some have A-shares and H-shares and others have the A-shares and shares in other foreign markets. Since these shares share the same cash flow and voting rights, they usually have the same claim on the firm's book value of equity. Our research focus only the CNAS stock market, in order to obtain the book-to-market equity ratio per A-share of a company with multiple class shares, it is incorrect to divide the firm's total book value equity from its balance sheet by the total market value. Instead, the correct way is to calculate the book value of equity per share divided by the A-share price.

-Thirdly, China has two main boards for the firms to go public, the SSE and the SZSE. In addition, the SME and the GEB were set up in May 2004 and October 2009, respectively, and both are hosted by the Shenzhen Stock Exchange. Fama and French use NYSE-listed firms to determine the breakpoints between small and big firms in order to avoid the overwhelming influence of the large number of small NASDAQ firms. Therefore, whether SME and GEB listed firms should be excluded in determining the breakpoints for the size factor in China need to be examined. [START_REF] Zhang | The fama-french three factors in the Chinese stock market[END_REF] conclude in their paper that the SME and GEB stocks are included or excluded from the sample to divide firms into size groups do not have a distinct difference.

Based on these special features of Chinese stock market, [START_REF] Zhang | The fama-french three factors in the Chinese stock market[END_REF] construct FF three factors and process the regressions separately with and without these special features. They come to the conclusions that the performance of FF3F Model is better when the nontradable shares are excluded from the sample and when the book-to-price ratio (B/P) are used instead of the B/M ratio.

On account of the special features of Chinese stock market study in literature, we construct value-weighted stocks by their tradable shares, use B/P ratio instead of B/M ratio, and construct of size factor by the total market capitalization including SME and GEB in our following research.

Empirical Analysis and Results of FF3F Model

Data and methodology

Data

All the firms on CNAS stock market, excluding financial firms18 and firms with negative market-to-book values, are collected from Shanghai A-Share Index and Shenzhen A-Share Index. In addition, a firm is eliminated if the relevant information is missing in a particular month or period, and the obvious errors are corrected manually.

For the period of July 2004 to May 2015 (131 months), monthly index prices and stock prices are obtained from Bloomberg, so as to their market capitalization, book value per share, total shares outstanding and listed shares outstanding. Furthermore, risk-free rate (RF rate) is a typically proxy for the return on a one-month Treasury bill. But in China, the onemonth Treasury bill has never been issued until February 2007. To keep it consistent with our sample period, we replace it with 'Three-Month Treasury Bill Rate (3M T-Bill Rate)' and the one-month risk-free rate is then equal to the 3M T-Bill Rate divided by three.

Considering the special features of Chinese stock market, and as already demonstrated in the section 1.3.2 that the best performance of three-factor model is achieved when the three factors are constructed by using the market portfolio that includes only tradable shares; using the total market value to determine size breakpoints; and when the B/P ratio is used instead of the B/M equity ratio.

For each stock:

-The stock return is defined as the logarithm of the difference of monthly price.

-The firm's size is defined as the natural logarithm of the market capitalization in local currency Chinese 'yuan' (RMB). -Instead of B/M equity ratio, B/P ratio is calculated as a firm's book value per share divided by its price. -To calculate the value-weighted returns, the tradable market value of equity instead of the total market value of equity is used, the tradable market value of equity equals to the stock price of each month times the number of tradable shares (Listed shares outstanding).

Construction of Fama-French portfolios on Chinese market

We follow FF method as demonstrated in section 1.2.1 and construct the 6 Size-B/P portfolios on Chinese stock market, SL, SM, SH, BL, BM, and BH, to form the size factor SMB, at the end of June of each year t, all the stocks are sorted into two size groups, Small and Big, the breakpoint is the median total market capitalization including SME and GEB listed firms. For the value factor HML, we sort by the B/P ratio instead of B/M ratio at the end of each December of year t-1 into three groups: Low, Medium and High. The breakpoints are the 30th and 70th A-shares percentiles. Finally, the intersection of these six groups makes the six portfolios, which remain the same from July of year t to June of year t+1, and the portfolios are reformed in July of year t+1.

The "market" portfolio return series, which covers both the Shanghai and Shenzhen exchanges, is not readily available. We first compute the monthly returns of Shanghai and Shenzhen composite A-share indexes separately, then compute the value-weighted average of the returns using the relative (aggregate) market values of the two exchanges observed at the end of each month as weights. The weighted average market returns thus obtained are used as our proxy for market returns.

Then the market factor is the excess market return which is computed as the difference between the value-weighted returns of all A-shares and the RF rate. The SMB factor is then the difference between the simple average of the monthly returns of the three small-size portfolios (SL, SM, and SH) and the simple average of monthly returns of the three big-size portfolios (BL, BM, and BH). Similarly, HML is equal to the simple average monthly return of the two portfolios with high book-to-market equity (SH and BH) minus which of the two portfolios with low book-to-market equity (SL and BL)

Most literature including FF themselves construct 25 portfolios which are the intersection of five portfolios formed on size (Small, 2, 3, 4, and Big) and five portfolios formed on B/M ratio (Low,2,3,4,and High). The 25 Size-B/P portfolios are formed much like the six Size-B/P portfolios discussed above, we firstly sort firms into five size groups at the end of June of year t, the breakpoints are all the A-share market equity quintiles. Then independently, we sort firms into five B/P ratio groups at the end of year t-1, for which the breakpoints are all A-shares quintile. Similarly, the portfolios remain unchanged from July of year t to June of year t+1, and the portfolios are reconstructed at June of year t+1.

Thus, to be included in our data set, a stock must have market equity data for December of t-1 and June of t, and (positive) price data for t-1, in addition, firms must have monthly returns for at least 24 out of 131 months between July 2004 to May 2014. Ultimately, the total number of stocks which meet our selecting criteria on A-share market is 2267. Besides, the number of firms which have the available tradable market value is less than 400 before 2004. To reduce the bias of the regression results, we choose the time interval July 2004 to May 2015 and construct three factors during 131 months.

Empirical results on

To construct the three factors, the monthly price of the market portfolios (SSE A-Share Index and SZSE A-Share Index) and the eligible stocks, total market capitalization, tradable market value, and book value per share of CNAS market are obtained from Bloomberg. The 3-month Treasury Bond Trading Rate, which downloaded from Bloomberg as well, and the monthly risk-free rate is the 3M T-Bill Rate divided by three.

Table 1.3 reports the statistic description of FF six Size-B/P ratio portfolios. The five parts: annual average of firm size, annual average of B/P ratio, average of annual percent of market value in portfolio, average of annual number of firms in portfolios and average excess returns are represented in Panel A, B, C, D and E respectively. Firstly, across the two size groups, high B/P ratio portfolios have relatively bigger size, and then across the three B/P ratio groups, big size portfolios have relatively higher B/P ratio than small size portfolios. In Panel C, the big size portfolios contribute about 86.30% in total with the nearly number of firms as the small size portfolios (733 firms for small size portfolios and 732 firms for big size portfolios). The average excess returns in Panel E are consistent with FF, in which big size portfolios tend to have lower excess returns than small size portfolios. However, the average excess returns across the B/P ratio seem not to have a clear tendency, only in the big size groups, the excess returns decrease with B/P ratio, which is opposite to U.S. stock market.

In Table 1.4, Panel A displays the summary statistics of FF three factors (excess market return, SMB and HML) on CNAS stock market. Panel B and Panel C shows the correlation coefficients among dependent variables (FF three factors) and correlation coefficients between independent variables (excess returns of six Size-B/P portfolios) and dependent variables. Panel B indicates that the correlation coefficients between market beta and size factor SMB is 0.0014, and between the market factor and value factor HML is 0.1857, which are both low. The correlation coefficients between SMB and HML (-0.3224) indicates that size factor and value factor are negatively correlated. In Panel C, all the six portfolios and market factor are positively highly correlated. Small size portfolios are all Evidence from Panel A is consistent with both FF findings and Table 1.3, across each B/P quintile, the average excess returns decrease with the size of portfolio increases. Still, there seems no regular variation across each size quintile. However, it is not so clear as six Size-B/P portfolios that higher B/ P ratio portfolios have relatively bigger size, and big size portfolios have relatively higher B/P ratio than small size portfolios. In Panel B, we cannot tell the difference except the biggest size quintile, in which the size of portfolios increases with B/P ratio. There is no obvious size difference across the B/P quintiles as showed in Panel C. Firm number of portfolios are relatively even, the portfolio of the biggest size and lowest B/P ratio has the most number of firms (78).

Time-series regressions

Table 1.6 shows the regression results obtained from the TSR of excess returns of six value-weighted Size-B/P portfolios on FF three factors, excess market returns, SMB and HML using a firm's tradable market value as a portfolio weight in computation of valueweighted returns and using all the market value to determine the breakpoints of size and B/P ratio groups. In Table 1.6, The left part of the table is the coefficients obtained from the regressions, a is the intercept, b , s and h are the regression coefficients s of FF three factors separately, and adjusted R-square. Correspondingly, the right part of the table is tstatistics and the standard error of estimation. Numbers in bold are the t-statistics which are significant at 5% confidence level. Coefficients of the market factor and SMB are all significant at the 5% confidential level, both are highly and positively related to stock returns, and three out of six coefficients are significant at the 5% level for HML factor. The adjusted R-squares are around 0.9 with averaged value 0.9081. The standard errors of estimation are relatively low and close to zero, which also means the satisfactory results. Overall, the regression results demonstrate that the FF3F explains most time-series variations of average excess stock returns on CNAS stock market during the research period.

According to the regression results, no one can ignore the significant role of the market factor in explaining Chinese stock returns. FF find that size and B/M equity are related to average expected portfolio returns (size is negatively related to averages expected returns and B/M ratio is positively related to expected returns), similarly on CNAS stock market (Table 1.6), small firms have persistently higher returns (with regression coefficients of 1.2461, 1.1939 and 1.2133 for three small size portfolios) than big size firms (with regression coefficients 0.1669, 0.2867 and 0.1997). And across the size groups, firms with higher B/P ratio have higher returns and lower B/P ratio firms have relatively poor even negative returns. Besides, all the intercepts of six portfolios are not indistinguishable from zero, that is to say, FF three factors cannot completely capture the variation of excess returns. Regression: Similar as the TSR on FF six Size-B/P portfolios, the market factor still plays an important role in explaining the portfolio excess returns, as shown in each portfolio, all the coefficients of the market factor are dramatically significant. Regarding the size factor SMB and value factor HML, in accordance with [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] findings, that the average excess returns decrease as the firm size increase, the t-statistics (t-stats hereafter) of regression coefficients for the size factor are all significant at 5% confidence level. The excess returns have a positive relationship with firms' B/P ratio, firms with higher B/P ratio tend to have higher excess returns. The top 20% B/P ratio group has the most numbers of significant coefficients with t-stats 2.7737, 3.8859, 4.0028, 4.6418 and 6.6817 respectively, while the medium 20% group has none of the coefficients significant; and the bigger size portfolios seem to have more significant regression coefficients on HML. The adjusted Rsquares are around 0.9 with averaged value 0.8995, the intercepts are all indistinguishable from zero except the portfolio in the third size quintile and the lowest B/P quintile in this regression, which means FF3F model captures the time-series variations of excess returns well on CNAS stock market.

f i i M ,t f i i i ,t R R a b ( R R ) s SMB h HML e        Book-to-Price (B/P) ratio L M H L M H a t (
i ,t f i i M ,t f i i i ,t R R a b ( R R ) s SMB h HML e   
The size and value effects on CNAS stock market are clearly shown in Figure 1.5. Figure 1.5 reports the TSR loadings on FF three factors (b, s, h) of the 25 Size-B/P portfolios (loadings are also reported in Table 1.7), separately. On the x-axis are the 25 portfolios from S1H1

f i i M ,t f i i i ,t R R a b ( R R ) s SMB h HML e       
1.4 Empirical Analysis and Results of FF3F Model 49

.2.3 Cross-sectional results on Chinese stock market

The main contribution of FF3F Model is its success in explaining the cross-section stock returns in U.S market and many other stock markets in the world. We also examine whether FF3F Model can explain the cross-section variations of stock returns on CNAS stock market, both in the frame of 6 Size-B/P portfolios and 25 Size-B/P portfolios. FF apply [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] two-stage approach to perform the regressions, the first stage is the time-series which already demonstrated in previous research. The second stage is the cross-section regressions as shown in equation (1.16), where they use the estimated betas (in this research b , ŝ and ĥ ) which are obtained from the first stage of TSR, as the independent variables in the CSRs. And regress the same portfolios' returns as in the first stage on these estimated betas for a fixed time period to determine the risk premium for each factor.

i ,t f i M i SMB i HML i i ,t ˆR R b s h            (1.16)
Where:

i ,t f RR 
is the excess returns of same portfolios as in the time-series (value-weighted FF six or 25 Size-B/P portfolios); i b , i ŝ and i ĥ are the estimated coefficients from TSRs for the market factor, size factor SMB and value factor HML, separately; M  , SMB  and HML  are the coefficients of CSRs.

Furthermore, it is important to recognize the classical Errors-in-variables (EIV) problem before we perform the CSRs, which occurs from the nature of [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] two-stage approach. When we applying standard OLS formulas to the second step of CSRs, the independent variables  s are assumed to be given; however,  s are estimated from the first step of TSRs, which are not fixed. Though Fama-Macbeth (FM) reduce the measurement error by running CSRs for portfolios instead of individual stocks, [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] argues that the sampling errors for  s associated with the estimated betas still cannot be ignored. Shanken proposes that FM approach for computing standard errors keeps overstated the precision of the gamma estimates. Following [START_REF] Shanken | On the estimation of beta-pricing models[END_REF], we apply a correction procedure to solve the EIV problem. It assumes that the error terms from the TSRs are independently and identically distributed over time and independent of the factors. (Details of Shanken correction is presented in Appendix A)

According to our database, the cross-section regressions are performed at each month (131 months, from July 2004 to May 2015), for both FF six value-weighted Size-B/P portfolios and 25 value-weighted SBP portfolios, then the simple average of constants and coefficients, which are obtained from the 131 times CSRs on estimated betas ( b , s and h ) are calculated. This table presents the results of cross-section regressions on FF3F Model of FF six value-weighted Size-B/P portfolios (Panel A) and 25 value-weighted Size-B/P portfolios (Panel B). In each panel, the first row is the cross-sectional regressions' coefficients (coef.); the second row is the corresponding Fama-MacBeth t-statistics (FM t-stats) at 5% confidence level and the third row is the Shanken corrected t-statistics (SH t-stats), which are in the parentheses. The numbers in bold are the t-stats which are significant at 5% level. The adjusted R-squares are percentage values. Regression: Consistent with most of previous studies, such as [START_REF] Wang | What Determines Chinese Stock Returns?[END_REF], [START_REF] Eun | Asset pricing in China's domestic stock markets: Is there a logic?[END_REF], [START_REF] Wang | The cross section of expected stock returns in the Chinese A-share market[END_REF] and Chen et al. (2015 working paper), the results of crosssection regressions in Table1.8 continue to prove that there is significant positive size premium across the stock returns on CNAS stock market during the periods July 2004 to May 2015. However, contrary to some researches, such as [START_REF] Wong | The cross-section of stock returns on the Shanghai Stock Exchange[END_REF], [START_REF] Eun | Asset pricing in China's domestic stock markets: Is there a logic?[END_REF], [START_REF] Wang | The cross section of expected stock returns in the Chinese A-share market[END_REF], [START_REF] Wu | The value and size effect-are there firm-specific-risks in China's domestic stock markets?[END_REF] and [START_REF] Gan | An empirical cross-section analysis of stock returns on the Chinese A-share stock market[END_REF], we find the lack of value premium on CNAS stock market during our research period. Market beta is able to explain the cross-sectional variation in the average stock returns for the 25 value-weighted SBP portfolios with negative SH adjusted t-stats.

i ,t f i M i SMB i HML i i ,t ˆR R b s h             M  SMB  HML  Adj. 2 R (%)

Comparing with U.S. market (FF3F Model)

Since the Chinese stock market has several special features that we take into account in our empirical research, it is important and interesting to compare the empirical results of Chinese stock market with those of U.S. market. We perform the same regressions with the same time interval from July 2004 to May 2015 using U.S. data. The FF three factors and the FF six (and 25) value-weighted Size-B/M portfolios are downloaded directly from the website of Kenneth R. French. All the empirical results of U.S. stock market are presented in Appendix B. The annual available number of firms that has available OP and Inv are visually displayed in Figure 1.6, the blue bar is operation profitability and the red bar is investment opportunity, the x-axis indicates the year and the y-axis indicates the firm numbers. It is obvious that the number of firms that has OP are much less than that has Inv until the year 2014. And there are few available data of OP before 2010. To be more accurate and reduce the bias generated because of the very few firm numbers (when we sort firms into portfolios, there may be no firms in portfolios with firm numbers less than 30 in a year), we exclude the data before 2010. As shown in Table 1.12, Panel A is the summary statistics of FF five factors on Chinese stock market, the mean, standard deviation, standard error, sample variance and so on. Panel B is the correlation coefficients among the FF five factors, the profitability and investment factors are both positively related to market factor with low correlation coefficients (0.0418 and 0.1190) and negative related to size factor (-0.2227 and -0.2199).

1.5 Construction of profitability and investment factors and empirical results of FF5F Model 57 RMW is negatively related to value factor HML (-0.0217), while CMA is positively and relative highly related to HML with correlation coefficients of 0.4621. And the correlation coefficients between RMW and CMA is -0.3121. 1.13 presents the average excess return of six Size-B/P portfolios (Panel A), Size-OP portfolios (Panel B) and Size-Inv portfolios (Panel C). Across the columns are the two size groups and across the rows are the three B/M groups, three OP groups, and three Inv groups, respectively. It is apparent that there is the size effect, the big size portfolios always have the lower returns than the small size portfolios in each panel. Across the OP groups in Panel B, it is strange that the robust portfolios have lower returns than weak portfolios, perhaps the lack of data for OP causes the bias. Across the Inv groups in Panel C, it seems the neutral investment portfolios have the highest excess returns (0.0158 for small size and neutral investment portfolio, 0.0050 for big size and neutral investment portfolio) than the conservative and aggressive investment portfolios.

Time-series regressions of FF5F model on Chinese A-share stock market

To understand how FF five factors explain the excess return of these portfolios, the TSRs are performed on six Size-B/P portfolios, Size-OP portfolios and Size-Inv portfolios on FF five factors for the period of July 2010 to May 2015 (59 months). The results are demonstrated in Table 1.14, Panel A, Panel B and Panel C are the TSRs results for the value-weighted six Size-B/P portfolios, six Size-OP portfolios and six Size-Inv portfolios, separately. The loadings on market beta (b) are similar for the three sets of portfolios, they are all highly significant at 5% confident level.

We next look at each panel, in Panel A, five out of six (except the portfolio of big size and high B/P ratio) loadings on size factor SMB are significant at 5% confidence level, and the signs of slopes indicate that portfolios of small size have returns that are positively related to SMB, while returns of big size portfolios are negatively related to SMB. All the loadings on HML are highly significant, there exists consistently size and value effect in the regressions of six value-weighted Size-B/P portfolios on FF5F Model. However, none of the loadings on This table presents the time-series regressions results of FF5F model. In each panel, the regression intercept a , the regression coefficients b , s , h , r and c of market factor, size factor, value factor, profitability factor and investment factor, adjusted R square are respectively presented in the left part of the table, the corresponding t-statistics corrected for heteroscedasticity and autocorrelation using the Newey-West estimator and residual standard error are presented in the right part. Panel A is the regressions on six Size-B/P portfolios, across the columns are the two size groups (Small and Big) and across the rows are the three B/P groups (Low, Medium and High). Panel B is the regression results of six Size-OP portfolios, same as Panel A, across the columns are the two size groups and across the rows are the three OP groups (Weak, Neutral and Robust). Panel C is the regression results of six Size-Inv portfolios, across the columns are the two size groups and across the rows are the three Investment groups (Conservative, Neutral and Aggressive). Numbers in bold are the t-stats which are significant at 5% confidence level.

Regression: the profitability factor RMW is significant, while three out of six loadings on the investment factor CMA are significant at 5% confidence level.

i ,t f i i M ,t f i i i i i ,t R R a b ( R R ) s SMB h HML r RMW c CMA e          Panel A
Comparing the TSRs in Panel A with those (Appendix C, Panel A of Table C.1) of the six value-weighted SBP portfolios on FF3F model over the same time interval (July 2010 to May 2015), the results are quite similar for FF three factor (market beta, SMB, and HML).

The adjusted R-squares are much close between both regressions on FF3F Model and FF5F Model, it is suggested that FF profitability and investment factors seem not add explanatory power in capturing time-series variation of excess stock returns on CNAS stock market during the sample period.

In Panel B, the regression results for market beta, SMB, and HML are fairly close to those of Panel A, the big difference is in profitability factor RMW, all loadings on RMW except the portfolio BN are significant; and in each size group, portfolios with robust profitability tend to have higher excess returns than portfolios with weak profitability. Three out of six coefficients of investment factor CMA are significant, two are the portfolios with weak profitability (0.2644 for portfolio SW with t-stats 2.4244 and 0.4613 for portfolio BW with t-stats 5.8956) and one is the portfolio SR (coefficients 0.5398 with t-stats 4.2483).

Comparing to the regressions of the same six value-weighted Size-OP portfolios on the original FF3F Model on Chinese stock market (Appendix C, Panel B of Table C.1), in the presence of RMW and CMA, FF original three factors do not lose their explanatory power.

Chapter1 Fama-French Five-Factor Model vs. Fama-French Three-Factor Model in China 62

Comparing the adjusted R-square of both regressions, FF5F Model explains slightly more variations of time-series average returns (with averaged adjusted R-square 0.9574) than FF3F Model (with averaged adjusted R-square 0.9256) of the six value-weighted Size-OP portfolios.

In Panel C, the regression results of the market factor, SMB, and HML are all satisfactory significant. The loadings on RMW are similar to Panel A, none of which is significant at 5% confidence level. As for the CMA factor, three out of six loadings are significant, furthermore, the three significant loadings are of the portfolios with conservative and aggressive investment. And the investment effect is close to the results of 25 Size-Inv portfolios of Fama and French (2015a), the aggressive investment portfolios tend to have smaller even negative regression loadings, while the conservative investment portfolios have relatively bigger regression loadings. In other words, there exist investment effect and the firm's investment is negatively related to average excess stock returns. Comparing to the regression results of the same portfolios but on FF3F Model (Appendix C, Panel C of Table C.1), it is suggested that RMW and CMA factors seem not add explanatory power in capturing time-series variation of the six value-weighted Size-Inv portfolios' returns (the averaged adjusted R-square are 0.9658 for FF3F Model and 0.9676 for FF5F Model), neither.

To summarize, market beta always plays an important role in explaining time-series variation of excess portfolio returns. For all the three sets of portfolios, there exists size effect that the excess returns are negatively related to firm size. While there exists value effect in SBP portfolios, profitability effect in Size-OP portfolios and investment effect in Size-Inv portfolios. The loadings on RMW are only significant in the set of portfolios sorted by size and OP, but not in two other sets of portfolios. As to the CMA factor, the significant loadings are concentrated in the extreme OP or Inv groups (such as the weak OP group, robust OP group, the aggressive and conservative Inv groups). However, for the Size-B/P portfolios, the CMA significant coefficients are relatively dispersive. In short, whether FF5F Model performs better than FF3F Model on CNAS stock market over the sample period is not quite clear. The explanatory power of FF5F Model seems differs among different sets of portfolios. In comparison with FF3F Model, the presence of profitability and investment factors seem not capture more variations of expected stock returns than the three-factor model except for the six value-weighted portfolios formed on size and OP, though the improvement is limited. Similarly, we compare the performance of FF5F Model on both CNAS stock market and on U.S. stock market. We implement the same regressions in the previous section as reported in Table 1.14 but using data of U.S. market. The six value-weighted Size-B/M portfolios, six Size-OP portfolios, and six Size-Inv portfolios are downloaded directly from Kenneth R. French's website, the TSR results of the three sets of portfolios are presented in Appendix B (Table B.4). The loadings on the excess market return are always strongly positive for all three sets of portfolios of both countries. The loadings on SMB are strongly positive for small stocks and slightly positive or negative for big stocks, there exists size effect on both stock markets.

We next compare between each panel of Table 1.14 (Chinese market) and Table B.4 (U.S. market). Comparing 'Panel A' of both tables, there exists value effect on both stock markets. As to the profitability factor RMW, four out of six loadings on RMW are statistically significant and especially all three loadings on small portfolios are negative significant in U.S.; while none of the loadings on RMW is significant at 5% confidence level in China.

Comparing Panel B of both tables, the regression results of six Size-OP portfolios are approximately close. All the loadings on profitability factor RMW are strongly significant, among which the loadings are strongly negative for the weak OP portfolios (low profitability) and strongly positive for the robust OP portfolios (high profitability) on U.S. stock market; while five out of six loadings on RMW are significant on CNAS stock market with the same pattern as U.S. market. It is noticed that the loadings on CMA factor are significant only for the three big size portfolios in U.S. We find no apparent value effect when regressing the six Size-OP portfolios on FF5F Model on both stock markets.

The regression results for the six Size-Inv portfolios are quite different comparing Panel C of both markets. First, most loadings on HML lose their significance (only one out of six is significant) in U.S.; while all the portfolios have strong negative exposure to HML on Chinese stock market but no value effect. Then the small size portfolios always have significant exposure to RMW in U.S.; while none of the loadings on RMW is significant on CNAS stock market for the Size-Inv portfolios. Last, CMA factor seems explains more time-series variation of excess stock returns in U.S. than in China, since all the loadings on CMA are significant while only four out of six loadings are significant on Chinese stock market. The slopes of conservative (low investment) portfolios are positive and the slopes of aggressive (high investment) portfolios are negative on both markets, which is consistent with FF's expected pattern.

Furthermore, the adjusted R-squares of six Size-OP portfolios (with averaged adjusted Rsquares 0.9545 on Chinese market, and 0.9861 on U.S. market) and six Size-Inv portfolios (with averaged adjusted R-squares 0.9676 on Chinese market, and 0.9855 on U.S. market) are slightly bigger in U.S than that in China, which indicates that FF5F Model explains the two sets of portfolios slightly better on U.S. stock market than on CNAS stock market. In addition, the profitability factor and investment factor are able to capture partially timeseries variation of all three sets of portfolios' returns on U.S. stock market, while on Chinese stock market, the profitability factor seems to be an explanatory factor only for the six value-weighted Size-OP portfolios.

Conclusions

Fama and French draw a conclusion that risk (market beta) was not able to identify all the stock return variations during 1963-1990 on US stock market, two other factors, size and book-to-market equity, combined to capture the cross-sectional variation in average stock returns unite with market β. To investigate whether size and value factors also explain excess returns on Chinese stock market, this chapter first performs the empirical tests of FF3F Model on CNAS stock market.

As the results shown in the empirical tests on CNAS stock market (July 2004-May 2015), FF3F model can explain a majority of time-series variation of the stock returns, when using tradable market value to weight the portfolios, total market capitalization to decide the size breakpoint and book-to-price ratio instead of B/M equity ratio. We conduct the CSRs and the results are consistent with most of the previous studies on Chinese stock market, there exists positive size premium across the stock returns on CNAS stock market, however, we find no value premium during the periods July 2004 to May 2015. While after adjusted by Shanken correction, the market beta is also a determinant factor in explaining the crosssectional excess stock returns (25 value-weighted Size-B/P portfolios).

Despite the quite significant results of regressions on CNAS stock market, FF three factors (size factor and book-to-market equity combined with the market factor) still cannot explain all the variation of stock returns.

According to Fama and French, firm size and B/M equity ratio are related to the systematic pattern of profitability and growth. They are potentially major sources of risk in return. These two mentioned variables were known in most studies as two specific market indicators that raise questions about the model. These findings diminished the credence of Based on the valuation theory and recent empirical findings on the strong profitability and investment effects in asset returns, FF (2015a) propose a five-factor model contains the market factor and factors related to size, book-to-market equity ratio, profitability and investment. We apply FF5F Model on CNAS stock market during the period July 2010 to May 2015 and construct three sets of portfolios similarly as FF, six value-weighted Size-B/P portfolios, six value-weighted Size-OP portfolios and six value-weighted Size-Inv portfolios. For all the three sets of portfolios, market factor, size factor and value factor have strong explanatory power for the expected excess returns in the presence of profitability and investment factors. There always exists size effect that the excess returns are negatively related to firm size, while there exists value effect in Size-B/P portfolios, profitability effect in Size-OP portfolios and investment effect in Size-Inv portfolios. The CMA factor do have explanatory power for certain portfolios in all three sets of portfolios. However, the RMW factor only has explanatory power in six Size-OP portfolios.

In comparison with FF3F Model, profitability and Investment factors seem not having much additional explanatory power except for the six value-weighted portfolios formed on size and OP. The explanatory power of FF5F Model seems differs among different sets of portfolios comparing with the original three-factor model on CNAS stock market during the research period July 2010 to May 2015. Since the research period is relatively short in this study, we suggest to apply the examination with a longer time interval for the FF5F Model on Chinese stock market in the future.

We also implement the regressions that performed on CNAS stock market over the same period using U.S. data. The empirical results reveal that both FF3F Model and FF5F Model explain slightly better time-series variation of average excess stock returns on U.S. stock market than on CNAS stock market. As for the two additional factors, profitability factor and investment factor are able to capture partially time-series variation of all three sets of portfolios' returns on U.S. stock market, while on Chinese stock market, the profitability factor seems to be an explanatory factor only for the six Size-OP portfolios. Surprisingly, we find that FF3F Model do not have cross-sectional explanatory power on U.S stock market from July 2004 to May 2015.

Write between Chapter 1 and Chapter 2

Empirical research into the CAPM first documented that market risk was a factor that did not perform well in explaining cross-sectional stock returns, then documented that other factors -size factor SMB and value factor HML -did perform well in explaining stock returns. Researchers had already observed that small stocks earned higher returns than large stocks, and high book-to-market stocks earned higher returns than low book-to-market stocks. [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] constructed factors on the basis of this observation, and propose the FF3F Model. They demonstrated that the size and value factors did, indeed, perform quite well in explaining cross-sectional stock returns. It is no exaggeration to say that since the publication by [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF], the FF3F Model has been accepted as the most widely used expected returns model amongst researchers, and has become the cornerstone of factor studies.

However, as is well-known that FF factors are based on purely empirical work, and there is no clear theoretical foundation to identify the risk factors, which makes it one of the most controversial asset pricing model. The huge success of FF3F Model lead to the question that whether there is a body of theory to support the use of the particular factors that Fama and French have identified. For next two decades a substantial body of literature devoted to theoretical explanations for the explanatory power of SMB and HML.

There is debate amongst researchers who have attempted to explain why it is the two FF factors explain stock returns and what risks are reflected in the size and book-to-market factors. One dominant theoretical explanation is based upon the asset pricing theory already established well before the empirical papers by FFthe Intertemporal CAPM (ICAPM) of [START_REF] Merton | An intertemporal capital asset pricing model[END_REF].

In the one-period CAPM, investors do not need to consider what happens outside of their investment horizon. This is the basis for the intertemporal term in the model. While the ICAPM assumes that investors trade continuously and maximize their expected utility of lifetime consumption; investors care about what happens after the initial investment ends, so will care about risks associated with future developments in the economy. So assets will be priced, in a multi-factor model, according to investor expectations about future states of the economy. For instance, investors might be concerned about future investment opportunities. Over longer time periods, investment opportunities might shift as expectations of risk change, resulting in situations in which investors may wish to hedge. In other words, investors will seek to hedge against not only shocks to wealth as in the traditional CAPM, but also against shocks to future investment opportunities.

The main difference between ICAPM and traditional CAPM is the additional state variables such as economic variables that acknowledge the fact that investors hedge against changes in the future investment opportunity set. The ICAMP is a linear factor model with wealth and state variables that forecast changes in the distribution of future returns or income.

Our empirical results of chapter 1 demonstrate the applicability of FF3F Model on CNAS stock market during July 2004 to May 2015; specifically, the size factor SMB explains the cross-sectional variation of average excess stock returns well during the sample period. Such results give rise to the questions: what are the economic explanation of FF factors on Chinese stock market? Could they be explained in the context of ICAPM which has been proved to be so by such as [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] in the U.S stock market?

In order to answer the questions, we implement in the following chapter the theoretical explanation based on time-varying investment opportunities in the frame of ICAPM using data of CNAS stock market. Following [START_REF] Campbell | Understanding Risk and Return[END_REF] who suggest using innovations in state variables to forecast the changes in the future investment opportunity set, instead of using the state variables directly for the empirical implementation of the ICAPM, we consider the innovations of state variables that capture uncertainty about future investment opportunities in our research; and examine whether FF factors proxy for innovations of selected state variables on CNAS stock market. FF3F Model has achieved huge empirical success since it came up, which makes it a popular as well as one of the most controversial asset pricing models. However, these factors are based on purely empirical considerations, lack theoretical underpinnings, and are built in a rather arbitrary manner. In particular, their economic links to systematic risk are not clear. Therefore, the impressive performance of FF3F Model has aroused numerous researches that trying to providing a clear economic interpretation of the factors HML and SMB.

Some researchers attribute the success of FF factors to the survivor bias (Kothari et al., 1995b), and data snooping (MacKinlay, 1995b). Lakonishok et al. (1994b) argue that the B/M effect reflect investors' incorrect inference of firms' past earnings growth, suggesting that investors undervalue firms with poor past performances while they overvalue firms that have performed well in the past. [START_REF] Daniel | Evidence on the characteristics of cross sectional variation in stock returns[END_REF], however, suggest that it is the characteristics of stocks rather than the covariance structure of returns that appear to explain the cross-sectional variation in stock returns. While more researchers focus on the alternative factors (such as macroeconomic variables) that are able to capture the variation of equity returns in addition to the market return and have economic significance 19 .

The underlying economic links of FF factors are rather controversial, among plenty competing explanations for the success of FF3F Model, following [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], in this chapter we focus on the one based on time-varying investment opportunities which is in the context of Merton (1973a)'s Intertemporal Capital Asset Pricing Model (ICAPM hereafter).

ICAPM framework

Intertemporal Capital Asset Pricing Model (ICAMP) is put forward by Merton (1973a), which as an improvement or extension of CAMP of [START_REF] Sharpe | Capital asset prices: A theory of market equilibrium under conditions of risk[END_REF] and [START_REF] Lintner | The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[END_REF]. It is well documented in the literature that the CAPM is a static model which assumes betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. However, the single-period nature of CAPM has been criticized, since most investors do not participate in financial markets for one year, but instead for multiple years. Over longer time periods, investment opportunities might shift as expectations of risk change, resulting in situations in which investors may wish to hedge. For example, an increase in expected future returns will have a positive effect on current consumption through decreased savings, in addition, an increase in the expected volatility of returns will have a negative effect on current consumption through an increase in precautionary savings [START_REF] Khan | Are accruals mispriced? Evidence from tests of an Intertemporal Capital Asset Pricing Model[END_REF].

The ICAPM assumes that investors trade continuously and maximize their expected utility of lifetime consumption. It states that besides the market risk, the risk of unfavorable shifts in the investment opportunity set, as approximated by the changes of the state variables, will induce additional risk premiums and should be compensated20 . In other words, investors will seek to hedge against not only shocks to wealth as in the traditional CAPM, but also against shocks to future investment opportunities. As specified by [START_REF] Dotsis | The Market Price of Risk of the Variance Term Structure[END_REF], investors will bid up the prices of assets that do well when future investment opportunities are expected to deteriorate, and consequently lower their expected returns. These assets command a smaller risk premium because they increase the investor's ability to hedge against unfavorable changes in investment opportunities. On the other hand, investors will require a higher premium for holding assets that do badly when future investment opportunities worsen.

The main difference between ICAPM and traditional CAPM is the additional state variables that acknowledge the fact that investors hedge against changes in the future investment opportunity set. The ICAMP is a linear factor model with wealth and state variables that forecast changes in the distribution of future returns or income [START_REF] Cochrane | Asset Pricing[END_REF].

In this study, the discrete-time version of the ICAPM is assumed to account for the crosssectional asset returns. Following [START_REF] Campbell | Understanding Risk and Return[END_REF] who suggest using innovations in state variables to forecast the changes in the future investment opportunity set, instead of using the state variables directly for the empirical implementation of the ICAPM, we consider the innovations of state variables that capture uncertainty about future investment opportunities in this research. According to ICAPM, both the excess market return and innovations in state variables that forecast changes in the future investment opportunity set should show up as pricing factors in the cross-section of asset returns.

We assume the unconditional expected returns can be expressed in the frame of ICAPM as follows:

      kk K i ,t f ,t i ,m m ,t i , ,t k1 E R R , i            (2.1) where   i ,t f ,t E R R 
is the excess return of asset i,

f ,t R is the risk-free rate of return, m ,t
 is the market risk premium, k ,t   is the risk price for innovations of state variable k. The  s are the coefficients that can be estimated through following TSR:

    k K k i ,t f ,t i ,t i ,m M ,t f ,t t i ,t i, 1 R R R R e             (2.2) where i ,t f ,t RR  is the excess return of asset i at time t, M ,t f ,t
RR  is the excess return of the market portfolio at t, and k t  is the innovation of state variable k at time t.

The beta terms in equation (2.1) measure how much risk should be priced while the gamma terms measure the price of risk, with the excess market return and innovations of state variables as risk factors.

What are the proper candidates for the state variables?

The ICAPM suggests that we should use variables that forecast stock market returns as proxies for investment opportunities, however, it provides little guidance for identifying them. Thus what are the proper candidates for the state variables has raised many discussions. Theoretically, state variables should be factors that have predicting power of the future investment opportunity set. Empirically, numerous researchers have explored various candidates that for the most part, are macroeconomic variables that related to business cycle fluctuations. [START_REF] Fama | Stock returns, real activity, inflation, and money[END_REF], [START_REF] Fama | Stock returns, expected returns, and real activity[END_REF], [START_REF] Geske | The fiscal and monetary linkage between stock returns and inflation[END_REF], and [START_REF] Schwert | Stock returns and real activity: A century of evidence[END_REF] document that U.S. stock returns are positively related to the future growth rate in the gross national product (GNP) 21 . [START_REF] Stock | New indexes of coincident and leading economic indicators[END_REF] find interest rates are particular useful predictors of future economic activity. Later, [START_REF] Brennan | Estimation and test of a simple model of intertemporal capital asset pricing[END_REF] develop and test a model assumes that the investment opportunity set is completely described by real interest rate and the maximum Sharpe ratio. The estimated real interest rate and Sharpe ratio both show strong business cycle-related variation and both state variables have significant risk premium in the cross-sectional asset test. [START_REF] Liew | Can book-to-market, size and momentum be risk factors that predict economic growth?[END_REF] suggest to use the return on a market portfolio, dividend yield, short-term interest rates, term spreads, growth in the Gross Domestic Product (GDP) and the industrial production as indicators for the business cycle.

Other studies that identify significant predictors of the equity risk premium include: Lintner (1975), the interest rate; Campbell and Shiller (1988) and [START_REF] Fama | Dividend yields and expected stock returns[END_REF], the market dividend yield; [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], the term spread and the junk bond yield spread; [START_REF] Kothari | Book-to-market, dividend yield, and expected market returns: A time-series analysis[END_REF], the book-to-market ratio; Dumas and Solnik (1995) exchange risk.

Among the attempts to find the economic variables that are able to help explain expected asset returns, [START_REF] Fama | Asset returns and inflation[END_REF] prove that common stock returns associated with expected and unexpected components of the inflation rate22 ; Jagannathan and [START_REF] Jagannathan | The conditional CAPM and the cross-section of expected returns[END_REF] include the return on human capital (using labor income growth as a proxy) as a new factor in addition to market beta; [START_REF] Campbell | Understanding Risk and Return[END_REF] also find the future labor income growth a significant priced factors in determining excess stock returns; while [START_REF] Parker | Consumption risk and the cross section of expected returns[END_REF] and [START_REF] Hansen | Consumption strikes back?: Measuring longrun risk[END_REF] examine the relationship between expected asset returns and the future consumption. [START_REF] Chen | Economic forces and the stock market[END_REF] explore series of economic state variables related to industrial production, inflation (change of Consumer Price Index), risk premium (the spread between high-and low-grade bonds), term structure (the spread between long and short interest rate), consumption, etc., and examine whether innovations in those macroeconomic variables help explain the cross-section of average returns on NYSE stocks. They find several of these economic variables were found to be significant in explaining expected stock returns, variables related to industrial production, risk premium, term structure, and, somewhat more weakly, variable related to inflation.

Similarly, [START_REF] Keim | Predicting returns in the stock and bond markets[END_REF] show that default spread and term spread forecast stock and bond returns. Moreover, Chen (1991) also confirm that the default spread, the term spread, the one-month T-bill rate, the lagged industrial production growth rate, and the dividend-price ratio are important determinants of future stock market returns. However, [START_REF] Li | Intertemporal Asset Pricing Without Consumption Data: Empirical Tests[END_REF] implement tests of ICAPM using forecasting variables (a yield spread measuring term premium, a yield spread for default risk, the dividend yield, one-month T-bill rate and the lagged market return) as risk factors; the evidence rejects the hypothesis that the forecasting variables are the risk factors that explain the time-series and cross-sectional variation in expected stock returns. [START_REF] Ferson | The variation of economic risk premiums[END_REF] strengthen the evidence that the predicted variation of asset returns is related to their sensitivity to the economic variables through the analysis of a group of six economic variables. Results turn out that the premiums associated with interest rate, term structure shifts, and default spreads are the important variables for capturing the predictable variation of asset returns in addition to the market risk premium.

Furthermore, [START_REF] Campbell | Stock returns and the term structure[END_REF], [START_REF] Campbell | A Variance Decomposition for Stock Returns[END_REF], Campbell and Shiller (1988a), [START_REF] Fama | Dividend yields and expected stock returns[END_REF], [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], [START_REF] Harvey | Time-varying conditional covariances in tests of asset pricing models[END_REF] and [START_REF] Kothari | Book-to-market, dividend yield, and expected market returns: A time-series analysis[END_REF], have proposed various candidates related to the yield curve shape and aggregate dividends.

For instance, [START_REF] Campbell | Stock returns and the term structure[END_REF] document that the term structure of interest rates predicts excess stock returns in U.S.; [START_REF] Campbell | A Variance Decomposition for Stock Returns[END_REF] shows that the unexpected stock returns are related to changes in expected future dividends or expected future returns. [START_REF] Kothari | Book-to-market, dividend yield, and expected market returns: A time-series analysis[END_REF] provide evidence that B/M ratio and dividend yield are related to timeseries variation in expected stock returns during the period 1926 to 1991. 23 [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF] use three variables to forecast returns, which are dividend yield on the valueweighted NYSE portfolio, the default spread defined as the difference between yield on a portfolio of 100 corporate bonds and yield on a portfolio of bonds with Moody's Aaa ratings, and the term spread between the yield on the Aaa corporate bond portfolio and the one-month T-bill rate.

Inspiring by those findings and as [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF], 1995, 1996) had themselves suggested that their SMB and HML factors could be interpreted as proxies for state variables which describe time variation in the future investment opportunity set in the context of Merton's ICAPM. 24 Furthermore, one of the macroeconomic explanations behind the success of FF3F Model is based on the time-varying investment opportunities, FF two factors SMB and HML are proxy for state variables. Many types of research are proceeded by relating the FF factors to macroeconomic variables that are closely related to business cycle fluctuations. Numerous empirical evidence in the literature suggests that the size factor SMB and value factor HML indeed carry information about future investment opportunities.

For choosing variables that have forecasting power for future investment opportunities, [START_REF] Fama | Efficient capital markets: II[END_REF], [START_REF] Campbell | Understanding Risk and Return[END_REF] have pointed out that ICAPM should not be used as only 23 Many studies have found dividend yield to have predictive power in both cross-section Litzenberger and Ramaswamy (1979) and time series Rozeff (1984), [START_REF] Fama | Dividend yields and expected stock returns[END_REF], [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], and Campbell and Shiller (1988b). 24 Simpson and Ramchander (2008) provide evidence that the FF3 model outperforms the standard CAPM in its ability to capture surprises related to various macroeconomic indicators.

2.1 Economic explanation of Fama-French factors in the context of ICAPM 75 criteria for selecting factors. Only factors that forecast future investment opportunities should be included in the model.

Both [START_REF] Liew | Can book-to-market, size and momentum be risk factors that predict economic growth?[END_REF] and [START_REF] Vassalou | News related to future GDP growth as a risk factor in equity returns[END_REF] report that FF factors SMB and HML convey significant information about future GDP growth not present in the market portfolio.

Especially, [START_REF] Liew | Can book-to-market, size and momentum be risk factors that predict economic growth?[END_REF] provide evidence by using data from ten developed countries. [START_REF] Vassalou | News related to future GDP growth as a risk factor in equity returns[END_REF] find that when news related to future GDP growth presented in the asset pricing model, SMB and HML lose much of their explanatory power in the crosssectional variation of average asset returns. [START_REF] Hanhardt | Do the Fama and French Factors Proxy for State Variables that Predict Macroeconomic Growth in the Eurozone?[END_REF] found that this result extends to twelve countries of the Eurozone.

Prior study of [START_REF] Chan | An exploratory investigation of the firm size effect[END_REF] explore multifactor pricing equation that consists of five economic variables to explain the firm size effect. The five variables are (1) the change in the state of the economy measured by the growth rate of industrial production;

(2) the change in expected inflation;

(3) the difference between the realized inflation rate; (4) the change in the long term rate measured by the difference between the return of a portfolio of long-term government bonds and the T-bill rate; (5) the changing risk premium measured by the behavior of bonds of different perceived riskiness. Among those economic variables, a measure of the changing risk premium and a measure of the changing state of the economy explained a large portion of the size effect. [START_REF] Xing | Interpreting the value effect through the Q-theory: An empirical investigation[END_REF] claims that FF value factor HML may approximate by an investment growth factor defined as the difference in returns between low-investment stocks and highinvestment stocks. [START_REF] Campbell | Bad beta, good beta[END_REF], [START_REF] Brennan | Estimation and test of a simple model of intertemporal capital asset pricing[END_REF] and [START_REF] Petkova | Is value riskier than growth?[END_REF] all show that the value premium is correlated with innovations in their measures of investment opportunities. [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] examine two bond-market factors TERM (the difference between the long-term government bond return and one-month T-bill rate) and DEF (the difference between the return on a market portfolio of long-term corporate bonds and the long-term government bond return) as measures of unexpected changes in interest rates and the likelihood of default separately. They confirm that the tracks of both factors show up clearly in the time-series variation of stock returns. They also find both factors capture common variation in stock and bond returns when they are examined alone in the bond market or the stock market.

Both term spread and default spread are well known to forecast aggregate stock market returns [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] and [START_REF] Keim | Predicting returns in the stock and bond markets[END_REF]). Term spreads and default spreads have been shown to have time series predictive ability to forecast stock market returns [START_REF] Fama | Dividend yields and expected stock returns[END_REF]

76

(1989)), so they are also widely used as potential conditioning variables in cross-sectional tests. Hahn andLee (2001, 2006) emphasize in their articles that since term spread and default spread are two of the most widely used proxies for future interest rates and time-varying risk premium separately, they are likely to capture well the hedging concerns to investors associated with variations in interest rates and risk premium. The authors choose both term spread and default spread as proxies for SMB and HML and specify a three-factor model in which the factors are the excess market return, changes in the default spread (def) and changes in the term spread (term). They conclude that def and term capture most of the systematic risks proxied by the FF factors SMB and HML in both time-series and crosssectional dimensions (def is proxy for size factor while term proxy for B/M factor), and in the presence of def and term, FF factors are superfluous in explaining the size and B/M effects.

Following [START_REF] Campbell | Understanding Risk and Return[END_REF] argument that instead of relying on choosing important macroeconomic variables as empirical implementations of ICAPM, the factors that are related to innovations in state variables which forecast future investment opportunities should be considered in the model. Researchers like [START_REF] Campbell | Bad beta, good beta[END_REF], [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], [START_REF] In | A note on the relationship between Fama-French risk factors and innovations of ICAPM state variables[END_REF] and [START_REF] Aretz | Macroeconomic risks and characteristicbased factor models[END_REF] implement their research with innovations of state variables rather the economic variables themselves. [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] chooses a set of four innovations of state variables, including the short-term T-bill rate, term spread, aggregate dividend yield and default spread instead of some important macroeconomic variables. And she comes to a conclusion that FF factors SMB and HML are significantly correlated with innovations in state variables that describe investment opportunities and a model which uses innovations in SMB and HML and in the predictive variables explains the cross-sectional average returns better than the FF3F model. As a result, the author concludes that Fama-French factors proxy for innovations in predictive variables. More specifically, she denotes that HML proxies for a term spread surprise factor in returns, while SMB proxies for a default spread surprise factor.

Using the same set of four state variables as [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], [START_REF] In | A note on the relationship between Fama-French risk factors and innovations of ICAPM state variables[END_REF] adopt a new approach of wavelet analysis and examine to what extent FF factors SMB and HML share information with the innovations of state variables that describe investment opportunities. It is found that SMB and HML seem to play only a limited role in capturing alternative investment opportunities in the short run, but they share much information with alternative investment opportunities in the long run.

More recently, [START_REF] Aretz | Macroeconomic risks and characteristicbased factor models[END_REF] consider a series of innovations of state variables that include innovations in economic growth expectations, inflation, the aggregate survival probability, the term structure of interest rates, and the exchange rate. They prove that most of the macroeconomic factors considered are priced, and B/M ratio, size and momentum capture cross-sectional variation in exposures to those macroeconomic factors. Specifically, the authors show B/M conveys useful information about term structure risk and economic growth, and size conveys information about default risk and term structure risk.

However, there are researchers deduce different conclusions, the ability of macroeconomic state variables to predict portfolio excess returns and the significance of factor loadings in TSRs are not encouraging. For instance, [START_REF] Campbell | Understanding Risk and Return[END_REF] own results are mixed. In his paper, he argued that CAPM ignores time variation in expected stock returns and the fact that human capital is also an important component of wealth, but still a good approximate model of stock and bond pricing in some limited senses.

Chen (2002) develop a model with time-varying expected market returns and time-varying market volatilities to reflect the changes in the investment opportunity set. The author examines the size effect, value effect and momentum effect but neither the value effect nor the momentum effect can be explained using changes in the investment opportunity set.

Thus the author concludes that accounting for the changes in the investment opportunity set does little in explaining the cross-section of stock returns. [START_REF] Shanken | Economic forces and the stock market revisited[END_REF] and [START_REF] Lewellen | A skeptical appraisal of asset pricing tests[END_REF] express rather pessimistic views.

The former re-examine the five macroeconomic factors studied by [START_REF] Chen | Economic forces and the stock market[END_REF] and [START_REF] Chan | An exploratory investigation of the firm size effect[END_REF]. Contrary to the previous literature, the authors show that only the industrial production factor is significantly priced in the overall period 1958 to 1983; the bond return premium, a highly significant factor in the earlier studies, is insignificantly negative for the whole period. The five factors only account for about 25% or 30% of the time-series variation in 20 size portfolio returns and the authors fail to find the evidence of factor pricing over the sub-period 1968 to 1977. In the latter article, the authors review the models suggest new risk factors to help explain expected returns (growth in macroeconomic output and investment and innovations in state variables included), which seem to do a good job explaining the size and B/M effects. They critique the empirical methods used in the literature and offer improving empirical tests and find that several models do not work as well as originally advertised.

Especially, on the contrary to [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], [START_REF] Lioui | Misunderstanding risk and return?[END_REF] find that the method that used to make innovations in predictive variables is rather arbitrary, and loadings on innovations of state variables are rarely significant when tested on the 25-portfolios sorted by size and B/M equity. These innovations of state variables have extremely limited explanatory power in both time-series and cross-section regressions when extending the portfolio universe to include 30 industry portfolios. They also concluded that there is no proof that the FF factors proxy for time-varying investment opportunities, and the explanatory power of innovations on SMB and HML is almost inexistent in time-series and marginal in cross-sections, while SMB and HML themselves remain as significant as in the FF3F Model.

More recently, [START_REF] Boons | State variables, macroeconomic activity, and the cross section of individual stocks[END_REF] find that a series state variables such as the default spread, the term spread, the short-term T-bill rate, robustly forecast macroeconomic activity. However, they find that FF factors SMB and HML are unable to drive out the risk premiums of those state variables and their underlying characteristics are able to do so only partially.

Evidence from outside of the U.S. market

Though the conflict point of views on whether macroeconomic variables are able to explain expected stock returns, the evidence that stock prices tend to fluctuate with economic news is supported by numerous empirical literatures. For instance, the early studies of [START_REF] Fama | Stock returns, real activity, inflation, and money[END_REF], [START_REF] Fama | Stock returns, expected returns, and real activity[END_REF], [START_REF] Chen | Economic forces and the stock market[END_REF], [START_REF] Schwert | Stock returns and real activity: A century of evidence[END_REF], and [START_REF] Ferson | The variation of economic risk premiums[END_REF] have found that macroeconomic variables have explanatory power for U.S. stock returns. While this observation is not found only in U.S., such as [START_REF] Asprem | Stock prices, asset portfolios and macroeconomic variables in ten European countries[END_REF], [START_REF] Beckers | The relative importance of common factors across the European equity markets[END_REF], [START_REF] Ferson | The risk and predictability of international equity returns[END_REF] and [START_REF] Cheung | What are the global sources of rational variation in international equity returns?[END_REF]. have reached a similar conclusions using data of other international market out of U.S. [START_REF] Asprem | Stock prices, asset portfolios and macroeconomic variables in ten European countries[END_REF] investigates the relations between stock indices, asset portfolios and macroeconomic variables in ten European countries. The results show that changes in stock prices are correlated to some measures of real economic activity, in particular positive related to future industrial production, exports, the yield curve in the U.S.; and negatively related to employment, the exchange rate, imports, inflation and interest rates. The author suggests these economic variables may be representatives of state variables in the ICAPM.

Hanhardt and Ansotegui Olcoz (2008) discuss the economic rationale of FF factors SMB and HML in Eurozone market in the context of [START_REF] Merton | An intertemporal capital asset pricing model[END_REF] ICAPM. The authors also extend their research by including a momentum factor of Carhart (1997) WML, and they test to what extent the profitability of the factors can be related to future economic growth measured by growth in the gross domestic product (GDP) in the Eurozone. Their results document that only the size factor SMB seems to contain strong and robust information with respect to future growth in GDP, while they fail to find the same significance for HML and WML (there appears to be a positive but not significant relationship between HML and GDP growth,). Thus they conclude that at least SMB, and to some extent HML, may serve 2.1 Economic explanation of Fama-French factors in the context of ICAPM 79 as state variable that predict future changes in the investment opportunity set in the context of ICAPM. [START_REF] Docherty | Can we treat empirical regularities as state variables in the ICAPM? Evidence from Australia[END_REF] provide an empirical analysis of whether empirical regularities (they denote the size, value and momentum premium as empirical regularities) previously identified in the Australian market are related to macroeconomic risk factors such that they may be considered as the state variables of [START_REF] Merton | An intertemporal capital asset pricing model[END_REF] ICAPM. The authors examine two groups of macroeconomic fundamentals in their paper. The first group are the state variables employed by [START_REF] Chen | Economic forces and the stock market[END_REF] 25 , and the second group are a series of macroeconomic forecast variables shown in the prior literature to predict equity returns.

They report that all three empirical regularities examined change with the business cycle (HML is negatively related to the business cycle while SMB and momentum factor has the positive direction). Their results support the contention that the empirical regularities may be explained as macroeconomic risk factors in the Australian stock market. The authors suggest that the three anomalies are correlated with innovations of those macroeconomic variables that describe future investment opportunity set. [START_REF] Cheung | What are the global sources of rational variation in international equity returns?[END_REF] examine two potential sources of international real return variation: changes in expected future cash flows and changes in discount rates in 18 national stock markets, and the authors give evidence that the global economic variables that proxy for the two sources of return variation significantly capture large fraction of total variation of the international stock market returns.

Cheung and Ng (1998) investigate the relationship between stock market indexes and measures of aggregate economic variables (the real oil price, real output, real money supply, and real consumption) on five countries stock market (Canada, Germany, Italy, Japan, and the U.S.) by adopting the cointegration approach. The authors find evidence of long-run comovements between the returns on national stock indexes and measures of the countryspecific aggregate economic real variables. They further explore an error correction model which provides incremental information about the variation of stock returns that not found in other measures of return variation such as dividend yields, default and term spreads, and future GNP growth rates. 25 The authors examine all the state variables documented by [START_REF] Chen | Economic forces and the stock market[END_REF] except the default spread: unexpected inflation, changes in expected inflation, industrial production growth and the term spread. As the authors claim that the default risk spread is not included in their forecast model due to the illiquidity of Australian bond markets.

Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market 80 [START_REF] Charles | International stock return predictability: Evidence from new statistical tests[END_REF] investigate the relationship between stock returns and a range of economic fundamentals including short-term interest rates, several financial ratios (dividend-price ratio, dividend yield, E/P ratio, dividend-payout ratio) and technical indicators (price pressure, change in volume) on international markets (16 Asia-Pacific and 21 European stock markets). They show that the financial ratios have the weak predictive ability for stock returns while the price pressure and the short-term interest rate appear to have strong predictive power for stock return.

In emerging market, [START_REF] Hosseini | The role of macroeconomic variables on stock market index in China and India[END_REF] examine the relationship between stock market indices and four macroeconomic variables (crude oil price, money supply, industrial production and inflation rate) in China and India. Their results indicate that there exists the link between four macroeconomic variables and stock market index in both long and short run in both countries.

Pramod [START_REF] Kumar | The impact of macroeconomic fundamentals on stock prices revisited: An evidence from Indian data[END_REF], [START_REF] Tripathi | Stock market performance and macroeconomic factors: The study of Indian equity market[END_REF] and [START_REF] Gaur | Macroeconomic Factors and Performance of Indian Stock Market[END_REF] investigate the impact of selected macroeconomic variables on the performance of Indian stock market, all of them find significant relationship between stock price and the selected macroeconomic factors (such as industrial production, inflation, short-term interest rate, exchange rate). On Malaysia stock market, Siti Noorahayusolah (2011) find a series of macroeconomic factors (inflation, interest rates, money supply, and exchange rates) has a significant impact on stock market returns. [START_REF] Liang | Decoupled or Not? What Drives Chinese Stock Markets: Domestic or Global Factors?[END_REF] and [START_REF] Liang | Chinese stocks during 2000-2013: Bubbles and busts or fundamentals?[END_REF] provide evidence that the performance of Chinese stock market is related to both its domestic economic fundamentals, the policydriven factors such as exchange rate and bank deposits and bank loans have strong impacts on stock performance. However, the real economic factors such as industrial production seem not as significant as the policy-driven factors in explaining Chinese stock returns.

The latest empirical study of [START_REF] Mu | A Study on Dynamic Relationship between Macroeconomic Variables and Stock Markets in the United States, Germany, and Hong Kong[END_REF] investigates the relationship between seven selected macroeconomic variables (interest rate, inflation, oil price, unemployment rate, industrial production index, money supply, and exchange rate) and the stock markets in the US, Germany, and Hong Kong. Both short-term and long-term relationships between macroeconomic variables and the stock markets are shown in all the three countries.

Plenty researchers confirm the ability of FF factors (at least the size factor SMB) in explaining average excess stock returns on Chinese stock market. We consider several special features of Chinese stock market, and examine FF3F Model using data on CNAS stock market. We provide evidence that FF3F Model explains time-series variation of average excess stock returns well, and there always exists size premium. Though there are researchers who find the relevance between the performance of Chinese stock market and the domestic economic variables, rare have examined whether the economic underpinning of FF factors are related to the economic fundamentals of Chinese stock market, which is what we are going to investigate in this study.

Following the framework of [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], we choose the same set of four variables in this study  including aggregate dividend yield, short-term T-bill rate, term spread and default spread. Our choice is also consistent with the standpoint of [START_REF] Campbell | Understanding Risk and Return[END_REF] that instead of choosing those important macroeconomic variables, variables which have forecasting power for future investment opportunities should be considered in the model. The four variables are choosen to relate two aspects of investment opportunities, the yield curve and the conditional distribution of asset returns, and all these variables have been frequently used among literature.

We apply the vector autoregressive (VAR) approach of [START_REF] Campbell | Understanding Risk and Return[END_REF] in this study to obtain the innovation terms of selected state variables and examine the performance of innovations of predictive variables on CNAS Stock Market during December 2006 to May 2015. In addition, we also investigate whether innovations of selected variables have the proxy ability of FF factors in China.

This chapter proceeds as follows: Section 2 presents our data and the VAR process to extract innovations of state variables; the TSR results of the five comparing models are demonstrated in section 3; section 4 test the cross-sectional validation of the five models; finally, the conclusions and discussions are in the last section.

Innovations in predictive variables and Vector Autoregressive approach

State variables

We choose the same set of state variables as [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] in addition to the FF factors in our empirical test: dividend yield (DIV), term spread (TERM), default spread (DEF) and one-month T-bill rate (RF), which are among the most common used economic variables in the literatures as illustrated previously. The four predictive variables are chosen to model two important aspects of the investment opportunity set, the yield curve and the conditional distribution of asset returns. "The ICAPM dictates that the yield curve is an important part of investment opportunity set" [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], [START_REF] Litterman | Common factors affecting bond returns[END_REF] indicate that the two most important factors driving the term structure of interest rates are its level and its slope. One-month T-bill rate and the term spread are to capture variations in the level and slope of the yield curve. [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] points out that the conditional distribution of asset returns is also a crucial aspect of investment opportunity set in the context of ICAPM. And growing literature indicates that the conditional distribution of asset returns which are characterized by its mean and variance, varies over time. The aggregate dividend yield, the default spread, and interest rates are among the most generally identified variables by numerous literature. Table 2.1 lists a partial of papers that document the relationship between the performance of equity market and the four state variables that we are going to apply in the following research. [START_REF] Fama | Dividend yields and expected stock returns[END_REF], [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], [START_REF] Kothari | Book-to-market, dividend yield, and expected market returns: A time-series analysis[END_REF], [START_REF] Chen | Financial Investment Opportunities and the Macroeconomy[END_REF] Term spread [START_REF] Campbell | Stock returns and the term structure[END_REF], [START_REF] Keim | Predicting returns in the stock and bond markets[END_REF], [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], [START_REF] Chen | Economic forces and the stock market[END_REF], [START_REF] Chan | An exploratory investigation of the firm size effect[END_REF], [START_REF] Chen | Financial Investment Opportunities and the Macroeconomy[END_REF] Default spread [START_REF] Fama | Business conditions and expected returns on stocks and bonds[END_REF], [START_REF] Chen | Economic forces and the stock market[END_REF], [START_REF] Chan | An exploratory investigation of the firm size effect[END_REF], [START_REF] Chen | Financial Investment Opportunities and the Macroeconomy[END_REF] Short-term T-bill rate [START_REF] Brennan | Estimation and test of a simple model of intertemporal capital asset pricing[END_REF], [START_REF] Fama | Asset returns and inflation[END_REF], [START_REF] Stock | New indexes of coincident and leading economic indicators[END_REF], [START_REF] Chen | Financial Investment Opportunities and the Macroeconomy[END_REF] In addition to FF factors SMB and HML, the four other state variables we selected on Chinese market are:

Aggregate Dividend yield (DIV) is the sum of dividends over the last 12 months, divided by the actual value of the market index. Our study focuses on CNAS Stock Market, so we take all the CNAS stocks (both Shanghai A-share Stock Market Index and Shenzhen Ashare Stock Market Index) present value as the actual value of the market index.

Term spread (TERM) is the difference between the yields of a 10-year government bond and a 1-year government bond. We download Generic China 10Y Government Bond and Generic China 1Y Government Bond which fit the definition.

Default spread (DEF) is the difference between the yields of a long-term corporate Baarated bond and a long-term government bond. Mention that the Baa-rated bond is rated by Moody's rating system, which is not available in Chinese bond market through Bloomberg. Thus we compute the default spread as the difference between the yields of a long-term corporate bond index (China 10Y Corporate Bond) and a long-term government bond index (China 10Y Government Bond).

Short-term

Vector Autoregressive method

According to ICAPM, only the unexpected component of the state variable should command a risk premium. The unexpected component is normally we called innovations (or unexpected shocks to state variables). Instead of using the state variables themselves directly for the empirical implementation of the ICAPM, [START_REF] Campbell | Understanding Risk and Return[END_REF] suggests using innovations in such state variables to forecast the changes in the future investment opportunity set.

To derive the innovations of state variables26 , in the article of [START_REF] Chen | Economic forces and the stock market[END_REF], the author proposes using a vector autoregressive model to derive the residuals of the state variables as the unanticipated innovations in the economic factors. [START_REF] Campbell | A Variance Decomposition for Stock Returns[END_REF] also state that "The resulting vector autoregressive (VAR) system can be used to calculate the impact that an innovation in the expected return will have on the stock price, holding expected future dividends constant" Following [START_REF] Campbell | Understanding Risk and Return[END_REF], [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] also adopts the first-order vector auto-regression model to derive the innovations of the state variables in her model. All the studies observed significant risk premiums induced by innovations in the state variables.

The Vector Autoregressive (VAR) Model generalizes the univariate autoregressive model (AR model) by allowing for more than one evolving variable. What is more, the VAR model is one of the most successful, and easy to use models for the analysis of multivariate time series. As [START_REF] Zivot | Modeling financial time series with S-Plus®[END_REF] say that "the VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting".

Following [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], we adopt the VAR approach proposed by [START_REF] Chen | Economic forces and the stock market[END_REF][START_REF] Campbell | A Variance Decomposition for Stock Returns[END_REF] in this study. All variables in a VAR enter the model in the same way: each variable has an equation explaining its innovation based on its own lags and the lags of the other model variables. We write the excess market return as the first element of the vector t z , the other elements are the state variables which proxy for changes in the investment opportunity set. The assumption is that the vector 𝑧 𝑡 follows a first-order VAR:

  t t 1 t z Az u (2.3)
where, t z is a k ×1 vector which has k time-series variables, and t1 z  is called the 1-lag of t z , which has the one-period back observation of the variables in t z . A is a k × k matrix which is known as the companion matrix of the VAR. The error term t u is also a k ×1

vector, and the residuals in t u are the innovation terms that are regarded as the risk factors.

Petkova (2006) underlines that "these innovations are risk factors since they represent the surprise components of the state variables that proxy for changes in the investment opportunity set".

The assumption that the VAR is first-order is not restrictive since a higher-order VAR can always be stacked into first-order (companion) form in the manner discussed by Campbell and Shiller (1988a).

Innovations in state variables

In

                                         (2.4)
Where A is a 7×7 matrix, and t u represents a 7×1 vector of innovations for each element in the state vector t z . From t u we extract six innovation series corresponding to the dividend yield, one-month T-bill rate, term spread, default spread, SMB and HML, which are denoted as IDIV, IRF, ITERM, IDEF, ISMB and IHML. [START_REF] Campbell | Understanding Risk and Return[END_REF] emphasizes that it is hard to interpret estimation results for a VAR factor model unless the factors are orthogonalized and scaled in some way. In his research, he orthogonal the innovations of the state variables to both excess market return and labor income. [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] article, the author implements the similar way as Campbell: the residuals t u are orthogonalized from the market return m ,t R , and scaled to have the same variance as the market return. [START_REF] Aretz | Macroeconomic risks and characteristicbased factor models[END_REF] orthogonalize the market return with respect to their other macroeconomic fundamentals in order to isolate the variation in market returns not attributable to the macroeconomic fundamentals.

Following Petkova, in this study, the innovations of state variables are orthogonalized to the market factor separately. Precisely, the innovation of excess market return remains unchanged, innovation of dividend yield IDIV is orthogonalized to the excess market return; similarly, then innovation of the one-month T-bill rate IRF is orthogonalized to market factor. We do in this way to the other innovations of state variables ITERM, IDEF, ISMB and IHML. The innovations of the state variables are not orthogonalized from each other because this could add noise through the arbitrary ordering of the variables Boons (2016).

Time-series evidence on Chinese A-share stock market

This section is to examine the performance of the innovations of state variables which proxy for the future investment opportunities on CNAS stock market, and whether FF factors are proxies for innovations of these predictive variables. And we make comparisons Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market 86 among models that contain different factors, involving TSRs on excess market return, innovations of four state variables and innovations of FF factors (Model 1); regressions on excess market return, innovations of four state variables and original FF factors (Model 2); regressions on excess market return and innovations of the four state variables (Model 3); regressions only on excess market return and innovations of FF factors IHML and ISMB (Model 4); and time-times regressions on the original FF3F Model (Model 5).

Fama-French factors and innovations of state variables

Statistics description

Table 2.2 represents the summary statistics of the original FF three factors, the four state variables, and their innovations during the period December 2006 to May 2015 (102 months) in China. The mean of innovations of state variables (IDIV, ITERM, IDEF, and IRF) and innovations of FF factors (ISMB and IHML) are all close to zero. Not surprising that the t-statistic of SMB is significant at 5% confidence level, however, neither the Primarily, we perform regressions with the single innovation in addition to excess market return (the results are presented in Appendix D), in order to have the first glance of whether such small values of innovations related to the average excess stock returns. It is shown that among the four innovations of state variables, 23 out of 25 loadings on IDIV is significant at 5% confidence level and negatively related to stock returns; while none of the loadings on ITERM and none of the loadings on IDEF is significant or exhibit any significant systematic patterns related to size or B/P ratio. There are 11 out of 25 loadings on IRF that are significant, and it seems that the loadings are not related to size or B/P neither. It is probably that IDIV and IRF are able to capture variation in average excess stock returns, while the ITERM and IDEF probably not. Whether innovations are related to size or B/P ratio is not clear.

Table 2.3 shows the correlation matrix for all the risk factors which are demeaned FF three factors ( m ,t R , SMB and HML), the innovations of state variables (IDIV, ITERM, IDEF, and IRF) and the innovations of SMB and HML (ISMB and IHML). Notably, SMB and HML are very highly correlated with their innovations with correlation coefficients 0.9943 between SMB and ISMB, 0.9720 between HML and IHML. Similarly, [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] find the returns on FF factors are also very highly correlated with their respective innovations (the correlation Considering the absolute value, the correlation among other risk factors are relatively weak, still there are factors share common information to some extent, such as SMB and HML (-0.3495), SMB and IDIV (-0.2593), SMB and IRF (-0.2288), HML and ITERM (-0.3077), HML and IRF (0.2380). The correlation coefficients are almost close to zero between the excess market return m ,t R and the innovations, from which we can infer that the innovations have no correlation to the market factor.

Relation between FF factors and innovations of state variables

To test whether Fama-French factors are proxies for innovations of state variables on CNAS stock market. First of all, we perform two types of TSRs: (1) regressions of SMB and HML respectively on market factor and innovations of state variables, (2) regressions of each innovation of the state variables on FF three factors. Results of the two types of TSRs are presented separately in Table 2.4 and Table 2.5, showing intuitively the relation among those risk factors.

We first examine the relationship between two FF factors (SMB and HML) and four innovations of state variables estimated from a VAR process, controlling for the market factor, using the following two regression equations:

i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t SMB a ( R R ) IDIV ITERM IDEF IRF             (2.5) i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t HML a ( R R ) IDIV ITERM IDEF IRF             (2.6)
Table 2.4 reports the regression coefficients and corresponding t-stats of equation (2.5) and (2.6). Corresponding t-stats are in the parentheses below the regression coefficients, corrected for heteroscedasticity and autocorrelation using the Newey-West estimator with five lags.

Table 2.4 Estimated coefficients of SMB and HML from risk factor regressions

This table presents the regression results of two FF factors, SMB and HML, on the other risk factors (market factor and innovations of state variables). The adjusted R-square is represented in the last column. Three FF factors and four state variables are all demeaned, and the t-statistics are corrected for heteroscedasticity and autocorrelation using the Newey-West estimator with five lags. The sample period is from December 2006 to May 2015.

Regressions: Regression results indicate that SMB is related only to the innovations of aggregate dividend yield (IDIV), while HML is related only to the innovation of term spread ITERM. Consistent with [START_REF] Hahn | Yield spreads as alternative risk factors for size and book-tomarket[END_REF] and [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], the authors provide evidence that HML is related to a term spread factor. However, we do not find a relationship between SMB and a default spread factor on CNAS stock market as the authors demonstrated on U.S. stock market. Instead, we find a significant and negative relationship between SMB and IDIV. We suspect that SMB shares information with IDIV, while HML shares information with ITERM. However, the negative relation between HML and ITERM we found is contrary to [START_REF] Hahn | Yield spreads as alternative risk factors for size and book-tomarket[END_REF] and [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF]'s statement that the HML factor is positively related to the innovation of the term spread. The regression results show an insignificant relationship between the two FF factors and innovations of default spread IDEF, means that IDEF has no explanatory power for SMB or HML.

i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t SMB a ( R R ) IDIV ITERM IDEF IRF               i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t HML a ( R R ) IDIV ITERM IDEF IRF               i a i ,m  i ,IDIV  i ,ITERM  i ,IDEF  i ,IRF  2 Adj. R SMB (t-
We next perform the TSRs of contemporaneous innovations of state variables on FF three factors:

t i i M ,t f i i i ,t a b ( R R ) s SMB h HML        (2.7)
where we denote t  as the innovations of the four state variables and the regression results are shown in Our findings of HML and ITERM is consistent with [START_REF] Hahn | Yield spreads as alternative risk factors for size and book-tomarket[END_REF] who provide evidence that HML is related to a TERM factor and [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] who also find that ITERM covaries significantly with HML return. Furthermore, they also provide evidence of a relationship between SMB and DEF factor (or innovations of DEF), which seems not the case in our study. Inconsistent with Petkova, we find both SMB and HML are significantly related to IRF, none of FF factors are significantly related to IDEF.

The results from both types of regression suggest that FF factors might be related to the innovations of state variables, and it is reasonable to examine whether FF factors are proxies of innovations of state variables on CNAS stock market.

Time-series regressions and results

Following the two-step estimation approach developed by [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF]  are the regression coefficients.

         n i ,t f i ,t i ,m M ,t f i , j j ,t i ,t 1 R R R R R e    (

Five comparative models and time-series regressions

The five TSR models are:

Model 1 i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,ISMB i ,IHML i ,t R R ( R R ) IDIV ITERM IDEF IRF ISMB IHML e                    (2.9) Model 2 i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,SMB i ,HML i ,t R R ( R R ) IDIV ITERM IDEF IRF SMB HML e                    (2.10) Model 3 i ,t f i i ,m M ,t f i ,IDIV i ,ITERM i ,IDEF i ,IRF i ,t R R ( R R ) IDIV ITERM IDEF IRF e               (2.11) Model 4        i ,t f i i ,m M ,t f i ,ISMB i ,IHML i ,t R R ( R R ) ISMB IHML e    
(2.12)

Model 5        i ,t f i i ,m M ,t f i ,SMB i ,HML i ,t R R ( R R ) SMB HML e     (2.13)
The dependent variables in the five models are the 25 value-weighted Size-B/P portfolios we constructed in Chapter 1, which remains unchangeable in the regressions. The regression results of Model 1 are shown in Table 2.6, the market factor still has strong explanatory power for the average excess stock returns. Both innovations of SMB (ISMB) and HML (IHML) are important factors in capturing average excess stock returns, all the tstats of loadings on ISMB are statistically significant, and almost half of loadings (10 out of 25) on IHML are significant. Specifically, the highest B/P quintile has the most (all five) significant t-stats, while none of the loadings of the median B/P quintile is significant. The significant t-stats are concentrated on the lower B/P portfolios, the higher B/P portfolios, and bigger size portfolios. What's more, consistent with our previous findings on SMB in Chapter 1, the slopes on ISMB are systematically related to size, within each B/P quintile, the loadings decrease as the size increases. The loadings on IHML are also systematically positively related to B/P ratio, the loadings increase within each size quintile as B/P ratio increases, except the portfolio which has the smallest size and lowest B/P ratio.

As to the four innovations of state variables IDIV, ITERM, IDEF and IRF, only IDIV has several slopes that are significant (4 out of 25), none of other innovations have revealed the relationship with stock returns. Furthermore, none of the loadings on the innovations have shown a relationship with size or B/P ratio according to our results. Though the adjusted Rsquared are relatively high (with averaged adjusted R-square 0.9018), which means that the average excess portfolio returns are well explained by Model 1, the majority of statistically significant of intercepts indicate that the average excess portfolio returns cannot fully explained by Model 1. since SMB and HML are highly correlated to their innovations (refer to Table 2.3).

Table 2.8 displays the TSR results on innovations of four selected state variables in addition to excess market return (Model 3) over our sample period. Without FF factors or their innovations in the presence of regressions, IDIV plays an important role in capturing time-series variation of average excess returns with 23 out of 25 loadings are statistically significant at 5% confidence level (t-stats are corrected for heteroscedasticity and autocorrelation using the Newey-West estimator with five lags). Furthermore, the loadings on IDIV are all negative, within each B/P quintile, most of the loadings increase from smaller size portfolios to bigger size portfolios except the smallest size quintile, and the biggest size portfolios tend to have higher returns.

None of the loadings on ITERM or on IDEF is significant, only one out of 25 loadings on IRF is significant. However, consistent with [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] that the loadings on ITERM are related to B/P ratio, within each size quintile, the higher B/P ratio portfolios tend to have smaller loadings, at least for the three higher B/P portfolios. Both [START_REF] Hahn | Yield spreads as alternative risk factors for size and book-tomarket[END_REF] and [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF] find the innovation of default spread is systematically related to size, though, we find no such a relationship between loadings on IDEF and firm size in this study. IRF seems to fluctuate with size, bigger size portfolios tend to have smaller loadings on IRF within each B/P quintile.

Comparing the adjusted R-squares of Model 1, Model 2 and Model 3, We notice that the adjusted R-square of Model 3 (with averaged adjusted R-square 0.7228) are much lower than those of Model 1 (with averaged adjusted R-square 0.9018) and Model 2 (with averaged adjusted R-square 0.9021), which indicate the lower descriptive power of Model 3, which contains only innovations of four state variables without FF factors (or innovations of FF factors).

Table 2.9 reports the TSR results on excess market return and innovations of SMB and HML (ISMB and IHML). Loadings on ISMB are all statistically significant at 5% confidence level and have an inverse relationship with size across each B/P quintile. Almost half of loadings on IHML (10 out of 25) are significant, and consistent with results of Model 1, the loadings are positively related to B/P ratio apart from the portfolio with the smallest size and lowest B/P ratio. The adjusted R-squares are all around 90% (with averaged adjusted R-square 0.9030).

Chapter The TSR results of Model 5 (the original FF3F Model) in Table 2.10 are extremely like those of Model 4 (Table 2.9), FF3F Model still explains the time-series average excess returns well on CNAS stock market during December 2006 to May 2015. All the t-stats of loadings on excess market return and SMB are highly significant, and 10 out of 25 loadings on HML are significant as well, the adjusted R-squared are all around 90%, similar as those in Table 2.9. However, the majority of significantly intercept continues indicate that the average excess stock returns on CNAS stock market cannot fully capture by FF3F Model.

4: i ,t f i i ,m M ,t f i ,ISMB i ,IHML i ,t R R ( R R ) ISMB IHML e            Size B/

Brief comparison and summary

Comparing Model 1 and Model 2, the difference is that we include innovations of FF factors (ISMB and IHML) or FF factors themselves (SMB and HML) in addition to excess market return and innovations of state variables. The results tell no remarkable differences between the TSRs of the two models. It is revealed that FF factors and their innovations have approximately the same explanatory power for stock returns on CNAS stock market.

Comparing Model 3 with Model 2 (or Model 1), the regression results suggest that the regression model contains only the innovations of state variables without FF factors (or their innovations) as independent variables dramatically reduce the explanatory power of the model. The connections between innovations and size or B/P ratio (IDIV and size, ITERM and B/P ratio, and IRF and size) disappear when the regressions are performed with FF factors (or their innovations). Furthermore, in the presence of FF factors (or their innovations), the innovations of state variables -especially IDIV -seem not able to explain time-series variation of expected stock returns.

Comparing 107 only IDIV has explanatory power for average return; while in the presence of FF factors (or innovations of FF factors), IDIV loses its capability in capturing time-series variation of expected stock returns. FF factors contain the information of innovations of aggregate dividend yield (IDIV) on CNAS stock market over our research period. In the next section, we will perform the CSRs among the comparing five models, and examine whether innovations of state variables have explanatory power in cross-section variation of excess stock returns, furthermore, whether FF factors proxy for the innovations of state variables in the cross-section.

5: i ,t f i i ,m M ,t f i ,SMB i ,HML i ,t R R ( R R ) SMB HML e           

Cross-sectional validation of five comparing models

In this section, following Petkova ( 2006), we examine cross-section validation that FF factors proxy for innovations of state variables on CNAS stock market over our sample period. The objective is to test whether an asset's loadings with respect to these risk factors are important determinants of its average return.

In the second pass of Fama and MacBeth's approach, the CSRs are performed by regressing the portfolios' excess returns on the estimated betas obtained from the first step of Fama-MacBeth's two-stage approach, for a given date.

      n i ,t f 0 m i ,m j i , j i ,t 1 ˆRR      (2.14)
where, the independent variables,  s are the loadings which have been estimated from the TSRs and stand for exposures to the corresponding risk factor.  s are the coefficients of the CSRs and stand for the reward for bearing the risk of that factor ('price of risk' or 'risk premium'). "If loadings with respect to innovations in a state variable are important determinants of average returns, then there should be a significant price of risk associated with that state variable" 27 .

As documented in Chapter 1, the [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] two-stage approach has the classical Errors-in-variables (EIV) problem, thus, we also report [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] CSRs have been performed using OLS regressions, then the regression constants and the coefficients have been averaged over the 102 estimations.

We perform the cross-section regressions of five models corresponding to the five timeseries models we have examined in the previous section: The results show that whether we regress innovations of state variables with SMB and HML (or with ISMB and IHML) does not change the empirical outcomes.

Model 1#           i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF ISMB i ,ISMB IHML i ,IHML i ,t ˆˆˆˆR R ˆ                (2.15) Model 2#           i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF SMB i ,SMB HML i ,HML i ,t ˆˆˆˆR R ˆ                (2.16) Model 3#         i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF i ,t ˆˆˆˆR R            (2.17) Model 4#       i ,t f 0 m i ,m ISMB i ,ISMB IHML i ,IHML i ,t ˆˆR R        (2.18) Model 5#       i ,t f 0 m i ,m SMB i ,SMB HML i ,HML i ,t ˆˆR R        (2.
The very similar results obtained from Model 4# and Model 5# prove again that the FF factors (SMB and HML) and their innovations (ISMB and IHML) make no big difference between the CSR results. The market factor and ISMB are priced in Model 4#, correspondingly, the market factor and SMB are significantly priced in Model 5#. It is noteworthy that Model 5# is exactly the CSR of the original FF3F Model, the market beta is an important determinant in explaining the cross-sectional variation of the excess portfolio returns during the period December 2006 to May 2015, and the estimated coefficient of the loadings on market beta is negative (-0.0334) with FM t-stats -2.1285 and Shanken adjusted t-stats is -3.3191. Consistent with previous findings, size factor SMB is positively significantly priced and value factor HML still remains not significantly priced in the cross section of portfolio returns. This finding indicates that the ability of market factor and SMB in capturing cross-sectional variation of stock returns is robust at least over our research periods28 .

Model 1#: i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF ISMB i ,ISMB IHML i ,IHML i ,t ˆˆˆˆˆˆR R                          Model 2#: i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF SMB i ,SMB HML i ,HML i ,t ˆˆˆˆˆˆR R                          Model 3#: i ,t f 0 m i ,m IDIV i ,IDIV ITERM i ,ITERM IDEF i ,IDEF IRF i ,IRF i ,t ˆˆˆˆR R                    Model 4#: i ,t f 0 m i ,m ISMB i ,ISMB IHML i ,IHML i ,t ˆˆR R              Model 5#: i ,t f 0 m i ,m SMB i ,SMB HML i ,HML i ,t ˆˆR R             

112

-Comparing Model 3# with Model 1# or Model 2# (we take the pair of Model 3# and Model 2# as example since the results of Model 1# and Model 2# are quite similar), when the CSRs are performed on the loadings of market factor and innovations of four state variables (Model 3#) eliminating SMB and HML (or ISMB and IHML), only loadings on excess market return and on IDIV is significantly priced (EIV adjusted). Never IDEF or ITERM or IRF has significant loadings in CSRs regardless of regressing with only innovations of state variables (Model 3#) or with FF factors (Model 2#). Especially, though the loading on IDIV is the only significant determinant of average returns, in the presence of FF factors or their innovations, the significance of loading on IDIV disappears. The information contained in IDIV seems totally captured by the market factor and size factor in explaining the cross-sectional variation of average portfolio returns.

-Comparing Model 4# with Model 1# and Model 5# with Model 2#, the analyze is much similar for both pairs of models, thus we take Model 5# and Model 2# for example. In Model 2#, none of the loadings on IDIV, ITERM, IDEF or IRF is important determinants of average returns; and the presence of innovations of the four state variables do not drive FF factors out.

-Comparing all the five models, inconsistent with [START_REF] Petkova | Do the Fama-French factors proxy for innovations in predictive variables?[END_REF], the loadings on the excess market return are always negatively statistically significant on CNAS stock market, which suggest that there exists robust negative market premium. The exposures to ITERM, IDEF and IRF are not significant variables by all means in cross section (Petkova finds that loading of ITERM is a significant factor in the cross section of 25 portfolios). SMB or ISMB is an important determinant in explaining the variation of cross-sectional stock returns but HML or IHML is not; the existence of size premium and the lack of value premium are robust to the different research periods on CNAS stock market. In terms of the average adjusted R-square of the five models, it is obvious that Model 3# has the lowest one (46.66%). While the other models explain relatively a larger percentage of the cross-sectional variation in average returns of portfolios than Mode 3, in which the independent variables are only market excess return and innovations of state variables.

We summarize the findings of CSR in Table 2.11 and answering the questions proposed at the beginning of this section. The presence of the four innovations of state variables that forecast future investment opportunities does not drive FF factors out. The information contained in the innovation of aggregate dividend yields IDIV seems totally captured by the combination of market beta and SMB (or ISMB). Though the model involves both FF factors and innovations of state variables as risk factors performs slightly better than the original FF3F Model (considering the averaged adjusted R-square terms), FF factors might have played a limited role in capturing alternative investment opportunities proxied by innovations of state variables.

A supplement conclusion of Chapter 1: market beta and SMB are able to explain the crosssectional variation of average stock returns except for the value factor HML over the period December 2006 to May 2015 on CNAS stock market. Furthermore, it seems that there exist robust negative market premium and positive size premium but no value premium on CNAS stock market, which is independent of research periods.

Conclusions

This paper investigates the explanatory ability of the innovations of four macroeconomic variables: aggregate dividend yield, one-month T-bill rate, term spread and default spread on CNAS stock market, using monthly data during the period December 2006 to May 2015 (102 months). To examine whether the innovations of the selected four predictive variables are able in capturing average excess stock returns in both time-series and cross-section, further whether FF factors SMB and HML proxy for the innovations of state variables that describe future investment opportunities on CNAS stock market, the TSRs and CSRs are performed on FF 25 Size-B/P portfolios on five comparing models separately.

Results from the TSR indicate that FF factors don't lose their explanatory power no matter when examined alone or in combination with innovations of state variables on CNAS stock market. When regressed alone, the innovations of selected state variables do not have the ability in capturing average stock returns except IDIV, which might indicate that the FF factors totally capture the information of IDIV in explaining time-series stock returns.

Consistent with literature, we find innovation of term spread is related to B/P ratio, while inconsistently, we find no systematical relationship between innovation of default spread and firm size, instead, we find IDIV is related to size on CNAS stock market.

We conclude from the CSRs, the original FF factors (market beta and SMB) has ability in capturing the cross-sectional variation of excess stock returns and there are significant market risk premium and size premium during the period December 2006 to May 2015. Inconsistent with studies on U.S. stock market, in the presence of four innovations of state variables, FF factors do not lose their ability in capturing cross-sectional variations of excess stock returns on Chinese stock market. We find the information contained in the 114 innovation of aggregate dividend yields (IDIV) seems totally captured by the combination of market beta and size factor. FF factors might have played a limited role in capturing alternative investment opportunities proxied by innovations of the selected four state variables. We may conclude that the innovations of the selected four state variables are not an essential element when we try to understand the average return on Chinese stock market. Thus, we propose to consider other economic variables in this case or trying to find other explanations of the success of FF factors in China.

Write between chapter 2 and chapter 3

The study in chapter 2 is based on one of the three specific theories that are most discussed exposure to changes in economic variables in the context of ICAPM (the other two specific theories are distress risk, and asymmetric exposure to economic conditions). The three theories are not an exhaustive list of specific theoretical explanations for the performance of the FF3F Model. It represents three prominent theories that have empirical support.

As the results of chapter 2 suggested that FF factors do not lose their explanatory power in the presence of innovations of the four selected state variables (aggregate dividend yield, one-month T-bill rate, term spread and default spread) on CNAS stock market during the period December 2006 to May 2015. In other words, FF factors might not proxy for innovations of selected variables on CNAS stock market over the sample period.

In this case, we seek another theoretical explanation in the following chapter 3, which is the distress risk. Since one explanation for the persistent returns performance of high book-tomarket stocks is the risk of financial distress, which can be found in an extensive literature. For instance, [START_REF] Chan | Structural and return characteristics of small and large firms[END_REF] argued that distressed firms are more sensitive to changes in economic conditions and documented that distressed firms, as proxied by dividend reductions and leverage, earned relatively high returns. Thus, they were able to provide an explanation as to why small firms earn high returnsthese firms were more likely to have experienced dividend reductions and be highly leveraged. FF (1992) themselves showed that stocks with high book-to-market equity ratios earned relatively high returns, they proposed that this could be due to the decrease in market value associated with lower earnings prospects for those firms in distress. Furthermore, FF and other researchers continued to attribute the empirical evidence to distress risks in subsequent papers [START_REF] Fama | Size and book-to-market factors in earnings and returns[END_REF][START_REF] Fama | Multifactor explanations of asset pricing anomalies[END_REF]).

In addition, Firm's distress risk is an important indicator of a firm's performance and is also one of the most concerned characteristics by investors and firms. Measuring distress risk has been a hot research direction since the early 1930s FitzPatrick (1932). And two kinds of dominant models: accounting-based models that based on accounting ratios and market-based models that based on the market information are well developed and widely used in the massive of literature. The studies based on those predictive models are applied for investigating the relationship between distress risk and stock returns or comparing among the models. For instance, Dichev (1998), [START_REF] Griffin | Book-to-market equity, distress risk, and stock returns[END_REF], [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], [START_REF] Chava | Is Default Risk Negatively Related to Stock Returns?[END_REF]. all provide evidence that stock returns are related to distress risk (default risk).

One test of whether distress can explain why FF factors are priced risk factors was performed by [START_REF] Vassalou | Default Risk in Equity Returns[END_REF]. The researchers measured the default risk of individual stocks using a model developed by [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF]. Note that the risk of default is a relatively more extreme outcome of the risk of distress. The Merton's measure of default risk is the basis behind the credit ratings of Moody's KMV.

We carry out the following research and construct the distress risk factor using data of CNAS stock market during July 2005 to May 2015. To investigate whether FF factors proxy for distress risk on Chinese stock market, we augment FF3F Model with a mimicking distress risk factor. Furthermore, we implement both accounting-based and market-based model in estimating firms' distress risk to examine whether the different methods have effect on the empirical results. This chapter investigates the relationship between stock returns and distress risk, examine whether the size and value effects are related to distress risk on Chinese A-share stock market. Furthermore, we explore an augmented four-factor model by adding a distress risk factor in addition to Fama-French Three-Factor Model in order to examine whether Fama-French factors proxy for the distress risk.

Distress Risk Factor and Stock Returns on

To measure the financial distress risk and construct distress risk factor, we apply both accounting-based model and market-based model, the comparisons are performed between the results obtained from the two different methods. Then Fama-MacBeth two-stage approach and Errors-in-Variables adjusted method are implemented to perform the regressions.

Financial distress risk

Financial distress, also known as default risk, financial crisis or financial failure, is the situation that a company has certain kind of financial difficulties, generally, it is defined as "the likelihood that a levered firm will not be able to pay the contractual interest or principal on its debt obligations" [START_REF] Garlappi | Default risk, shareholder advantage, and stock returns[END_REF]. The worst situation of financial distress is bankruptcy, we say that the firm has gone into bankruptcy when a company reaches the point where it is unable to pay its debt and must stop its economic activity. [START_REF] Beaver | Financial ratios as predictors of failure[END_REF] defines the firm's failure as the inability of a firm to pay its obligations as they mature and points out that financial distress occurs when any of the following events comes up: bankruptcy, bond default, an overdrawn bank account, or nonpayment of a preferred stock dividend. [START_REF] Ross | Corporate Finance[END_REF] summarized previous studies and concluded that financial distress contains four conditions: (1) business failure, that is, a company cannot pay the outstanding debt after liquidation; (2) legal bankruptcy, namely, a company or its creditors applies to the court for a declaration of bankruptcy;

(3) technical bankruptcy, namely, a company cannot fulfill the contract on schedule to repay principal and interest; and (4) accounting bankruptcy, namely: a company's book net assets are negative 29 .

While in China and some other developing countries, financial distress is usually defined as the certain degree of financial deterioration ruled by the national security management institution. For example, in China, a listed firm is defined as 'Special Treatment' (ST) by China Securities Regulatory Commission if (1) a listed firm has negative net profits for two years consecutively, (2) the shareholders' equity of the company is lower than the registered capital, and (3) a firm's operations have stopped and there is no hope of restoring operations in the next three months due to natural disasters, serious accidents or law-suit and arbitration. According to the Chinese regulation, if an ST firm cannot improve its performance within the next three years, it is labeled as 'Particular Transfer' (PT) and may be delisted from the stock exchange market 30 .

None of the shareholders, creditors or investors is willing to witness the fail (bankruptcy) or deterioration of the firm since this situation make them suffer severe financial losses. So identifying firms that likely go into the deterioration situation in advance is of consequence.

In China, firm's default risk is also one of the most concerned characteristics by investors and firms, many policymakers and financial institutions needs to improve their understanding of distress risk of Chinese firms. It is important to develop an early warning 29 Sun et al. ( 2014) 30 Geng et al. (2015) 3.1 Financial distress risk 119 system for prediction of firms' financial distress, which have been a hot topic over the years in China.

Measurement of financial distress risk

The primary question of predicting distress risk is how to measure it, and the financial distress prediction, or called bankruptcy prediction, acts as an important role in the decision-making of various areas, including accounting, finance, business, and engineering etc. The prediction of distress risk has experienced from the qualitative analysis to quantitative analysis, and along with the development of computer technology, the ANNA (Artificial Nerve Network Analysis) Model which based on the statistics method and computer, seems to be the new generation of a prediction model for distress risk. Our research focuses on the quantitative models of measuring distress risk, which is still the dominant methods in the research field of financial distress risk.

Early in 1932, FitzPatrick (1932) analyzes and compare the financial ratios of successful industrial firms and those of failed firms, and he finds the significant difference between the financial ratios of the two kinds firms. In addition, the author also points out that financial ratios can not only reflect the financial condition but also the business performance of a firm, what's more, the financial ratio has predict ability for the firm's future. Thereafter, among numerous researches devote to predicting distress risk, the use of accounting ratios or market information are two dominant classifications. Later in recent years, there are models which consider both accounting and market information. Table 3.1 presents the dominating models in predicting financial distress since 1930'.

Accounting-based models

The accounting-based information is an important indicator of whether a company may encounter the financial distress or not, it can reflect a firm's financial conditions and business performance, and thus predict the future of the company. The early models to predict distress risk is mainly use accounting ratios.

The first study using a statistical approach to measure distress risk based on accounting information is [START_REF] Beaver | Financial ratios as predictors of failure[END_REF] univariate analysis of financial ratios which aims at predicting the corporate failure. Six groups 31 30 ratios are selected and tested on 79 failed firms and 79 sound firms during 1954 to 1964. He performs a dichotomous classification test of the predictive ability of the chosen accounting measures and identifies the six most powerful ratios: cash flow to total debt, net income to total assets, total debt to total assets, working capital to total assets, current ratio, and no-credit interval. He found that those indicators could discriminate between matched samples of failed and non-failed firms for as long as five years prior to failure. Beaver initiates 'The Univariate Discriminant Model' which make it easier for predicting finance distress using a simple model.

Despite the prominent step forward of Beaver in measuring and predicting default risk, the univariate model cannot comprehensively predict the distress risk of a firm, for instance, (1) single ratios calculated by Beaver do not capture time variation of financial ratios; (2) different accounting ratios may have different predicting ability and result in different consequences for the same firm;

(3) there are interaction effects among different accounting ratios, single ratio is not able to capture multidimensional interrelationships within the firm. So that the interpretation of a single ratio in isolation may be incorrect. The weaknesses of Beaver's univariate model have led to the development of the multiple discriminant analysis which will be the subject of the following section.

31 Cash-flow ratios, net-income ratios, debt to total-asset ratios, liquid-asset to total-asset ratios, liquid-asset to current debt ratios and turnover ratios 3.2 Measurement of financial distress risk 121

Altman's Z-score

To improve the accuracy of the assessment of distress risk from the univariate analysis, Altman (1968) apply a multiple discriminant analysis (MDA) to examine 66 manufacturing companies in the U.S., half of which filed bankruptcy while half of which are solvent between 1946 and 1965.

Similar as Beaver, 22 accounting ratios are selected on the basis of their popularity in the literature and their potential relevancy to the study, and are classified into five categories: liquidity, profitability, leverage, solvency, and activity. Finally, five variables are selected as doing the best job together to predict the corporate bankruptcy after applying the following processes:

(1) Observation of the statistical significance of various alternative functions including determination of the relative contributions of each independent variable; (2) evaluation of inter-correlations between the relevant variables;

(3) observation of the predictive accuracy of the various profiles; and (4) judgment of the analyst.

The five variables constitute the final discriminant function, which we call it Z-score: . . . . .

1 2 3 4 5 Z 0 012 X 0 014 X 0 033X 0 006 X 0 999 X      (3.1)
Where, Z is overall index (Z-score), 1 X is Working capital/Total assets, 2 X is Retained Earnings/Total assets, 3 X is Earnings before interest and taxes/Total assets, 4 X is Market value equity/Book value of total debts, 5 X is Sales/Total assets.

The lower a firm's Z-Score, the higher its default probability (DP). Altman proposes the "cut-off" point (critical point) so that to predict at what level to bankruptcy a firm is according to its Z-score. It is concluded that firms which have a Z-score below 1.81 are all bankrupt; the firms having Z-score between 1.81 to 2.675 are defined in a "gray area" or "zone of ignorance", which means the firms are in a situation that is not so clear, they have the probability to bankrupt; while firms having a Z-score bigger than 2.99 clearly are in the non-bankrupt condition. Still, it is uncertain about a firm whose Z-score is in the "zone of ignorance", Altman obtains a critical Z value 2.675, which is to tell from the bankrupt and non-bankrupt firms in this area. However, MDA has some well-known limitations. Such as (1) the statistical assumptions that predictors need to be normally distributed and the variance-covariance matrices of the predictors should be the same for both groups of firms (bankrupt and non-bankrupt); (2) the output of MDA model is a value (or score) which has little intuitive interpretation, since it is basically an ordinal ranking (discriminatory) device.

(3) the accuracy of Altman's model two or three year prior to default drops drastically than the accuracy one year prior to default, the reason maybe that deteriorate of some accounting ratios is just the appearance instead of the essence of bankruptcy. [START_REF] Ohlson | Financial ratios and the probabilistic prediction of bankruptcy[END_REF] criticizes the restrictive assumptions of Altman's MDA and comment that previous studies appear to have overstated the predictive power of models. To avoid the problem of MDA, Ohlson is the first who introduces the conditional logit analysis which is one of the conditional probability analysis to predict the probability of default and estimate firms' failure. The major advantage of the logit analysis is that 'no assumptions have to be made regarding prior probabilities of bankruptcy and/or the distribution of predictors'.

Ohlson's O-score

The logit model is based on the cumulative distribution function to maximize the joint probability of default for the distressed firms and the probability of non-failure for the healthy companies in the sample. Similar to the MDA, this method weights the independent variables and assigns a score, however, this method estimates the probabilities of default for each company in a sample.

Suppose P as the probability of default for any given firm, let i X denote the predictors for the i th observation, let i W be the parameters of i X , the expression of logit model is:

i 0 1 1 2 2 n n ( y ) ( W W X W X W X ) 11 P 1 e 1 e         (3.2)
Doing a little transformation and we will have:

nn i 0 1 1 2 2 n n i i i 0 i 1 P y ln( ) W W X W X W X W X 1P            (3.3) 3.2 Measurement of financial distress risk 123
The logit model supposes that ln( P / ( 1 P ))

 can be explained linearly by accounting ratios. P is the probability function which value is between 0 and 1 ( 0 P 1  ) 32 , the cutoff is 0.5, which means that if P bigger than 0.5, companies tend to have more probability of default, otherwise, the companies are healthy. Unlike the MDA which use a Z-score value to predict whether a firm is bankrupt or not, logit model uses a probability to measure the default risk, which makes it more accurate and reliable.

Ohlson chooses the sample that contains 105 firms which are bankrupt and 2058 nonbankrupt firms between the period 1970 and 1976, and all the firms are classified as an industrial. He constructs three logit models, model 1 predicts bankruptcy within one year, model 2 predicts bankruptcy within two years, and model 3 predicts bankruptcy within one or two years. The statistic "Percent Correctly Predicted" of the three models are 96.12%, 95.55%, 92.84% respectively.

He identifies four factors: the size of the company, a measure(s) of the financial structure, a measure(s) of performance and a measure(s) of current liquidity; which are statistically significant in affecting the probability of firm failure.

Finally, nine independent variables are employed to determine the probability of bankruptcy:

-SIZE = log (total assets / GNP price-level index) -TLTA = total liabilities / total assets -WCTA = working capital / total assets -CLCA = current liabilities / current assets -OENEG = 1 if total liabilities > total assets, 0 if otherwise -NITA = net income / total assets -FUTL = funds from operations / total liabilities -INTWO = 1 if a net loss for the last two years, 0 otherwise -CHIN = (

t t 1 net income -net income  ) / ( t t 1 net income net income   )
Assigning the corresponding weights to each variable and get the final O-score formula:

. .

log( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( )

O 1 32 0 407 SIZE 6 03 TLTA 1 43 WCTA 0 076 CLCA 1 72 OENEG 2 37 NITA 1 83 FUTL 0 285 INTWO 0 521 CHIN            (3.4)
In which, two of them are dummies (OENEG and INTWO). The use of qualitative variables is another advantage of the logit model compared to the discriminant analysis which is limited to the interpretation of quantitative ratios.

32 Refer to [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behavior[END_REF] for a comprehensive analysis of the logit model. Contrary to Altman's Z-score, the lower a firm's Z-Score, the more likely of a firm encounter default, the probability of default positively changes with Ohlson's O-score, which means the higher the O-score the higher the default risk.

Ohlson's logit model have several advantages: the predictors do not need to follow the normal distribution or the same variance-covariance matrices rule, and unlike Altman's MDA of which the output is a value, the logit model is based on the conditional probability analysis and measures the firm's probability of default. come to the conclusion that the logit model generally is superior to the MDA approach of Altman. Kleinert (2014) compares the performance of three accounting-based models in Belgium and Germany and draw the conclusion that Ohlson's logit model performs most accurate. In the Asian market, Wang and Campbell (2010a) studied listed Chinese companies during 2000 to 2008 and report a high accuracy rate (95%) of Ohlson's model. [START_REF] Pongsatat | Bankruptcy prediction for large and small firms in Asia: a comparison of Ohlson and Altman[END_REF] conclude that the Ohlson's logit model has a higher predictive ability in all three years preceding bankruptcy than that of Altman's MDA approach in Thailand.

Despite all the advantages, some critics are left on Ohlson's logit model: the use of maximum likelihood methodology to estimate the parameters makes the computational procedure complex. [START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF] argues that Ohlson's logit model fails by not including time varying changes. [START_REF] Grice | The limitations of bankruptcy prediction models: Some cautions for the researcher[END_REF] emphasizes that the relation between financial ratios and their effects on bankruptcy changes over industries and time.

Ohlson himself gives advice that the choice of different accounting ratios could improve the likelihood function. However, he also suggests that such non-accounting information as equity prices or their volatility might be most useful and should be examined in future research. The use of non-accounting information for predicting financial distress has led to the development of a special class of default-risk models based on the value of a firm set by the market.

Market-based models

Since the prevalent of accounting-based models in modeling the default risk, there follows some criticism about the decline performance and limitation of using accounting variables to predict distress risk33 .

125

Several reasons are listed below to query the distress risk measures which are based on accounting data:

-Default probability is a prediction about the likelihood of future events, though accounting information is backward-looking. Accounting models use information derived from the financial statements which aim to measure past performance and may not be very informative in predicting the future status of the firm. As [START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF] argue that since the accounting statements are prepared on a goingconcern basis, they are of limited utility in predicting bankruptcy by design.

-In addition, "the conservatism principle often causes asset values to be understated relative to their market values, particularly for fixed assets and intangibles. Downward-biased asset valuations will cause accounting-based leverage measures to be overstated." [START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF] -Financial ratios vary substantially across industries. Thus, accounting-based coefficients are specific to the industry and sample used and cannot be generalized with respect to all firms in the market.

-Accounting-ratio-based models are typically built by searching through a large number of accounting ratios with the ratio weightings estimated on a sample of failed and non-failed firms. Since the ratios and their weightings are derived from sample analysis, such models are likely to be sample specific. An additional point of critics has been that accounting models ignore economic idiosyncrasies and that data are collected over many years while leaving out market changes Mensah (1984).

-Most importantly, another deficiency is that accounting-based models do not incorporate a measure of asset volatility. Volatility is a crucial variable in analyzing and predicting bankruptcy because it captures the likelihood that the value of the firm's assets will decline to such an extent that the firm will be unable to repay its debts.

Those limitations of models using accounting variables in modeling default risk bring on the models that rely on market information. The equity market contains an alternative and potentially superior source of information about default probability because it assembles information from other sources in addition to the financial statements.

There are two classes of models that based on market data, specifically, structural models [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF] use option pricing methods to compute the default probability from the level and volatility of market value of assets, and reduced-form models 34 Shumway (2001) allow the default intensity to be extracted from debt or credit market securities. Since the vast majority of the market-based models are on the basis of option-pricing theory, we will mainly introduce the two popular model derived from option pricing theory and a model which belongs to the class of dynamic reduced-form models of default.

Black-Scholes and Merton (BSM) option-pricing model

Merton (1974) is the first who proposed a market-based model which applies the optionpricing methodology developed by [START_REF] Black | The pricing of options and corporate liabilities[END_REF] to relates the default risk to the capital structure of the company. In Merton's model, the equity (common stock) of a firm can be viewed as a standard European call option on the underlying firm's assets with a strike price equal to the book value of the firm's liabilities.

The limited liability feature of equity means that the equity holders have the right, but not the obligation, to pay off the debt holders and take over the remaining assets of the firm. That is, the holders of the other liabilities of the firm essentially own the firm until those liabilities are paid off in full by the equity holders. Thus, in the simplest case, equity is the same as a call option on the firm's assets with a strike price equal to the book value of the firm's liabilities [START_REF] Crosbie | Modeling default risk[END_REF].

The reason is that shareholders are residual claimants on the firm's assets after all other obligations have been met. According to Merton's theory, it is just as the shareholders sold the corporation to their creditors, they have the right, but not the obligation to pay off the creditors. The relation between equity value E V (y-axis) and firm's asset value A V (x-axis) is shown in Figure 3.1. At the maturity of the option, if the value of the firm's assets (take the point 2 V as example) is greater than the book value of liabilities X, the shareholders exercise their option on the assets, and the firm continues to exist. Otherwise, if the firm's asset value (take the point 1 V as example) is lower than the book value of liability X at maturity, the shareholders will choose not to exercise the option right and the value of equity is zero, which means the firm will default. Thus, the market value and volatility of the firm's underlying assets implied by the equity's market value are important to determine to what extent a firm will go bankruptcy. However, the market value and volatility of the firm's assets are usually cannot obtained directly. In 34 Jarrow and Turnbull (1995), [START_REF] Duffie | Modeling term structures of defaultable bonds[END_REF] 3.2 Measurement of financial distress risk 127 particular, Merton solves backward from the option price and option price volatility for the implied asset value and asset volatility. Besides, the BS model also assumes that the capital structure has only a single class of debt and a single class of equity.

Then, under these assumption and following Merton's theory, denote X as the book value of liability that maturing at T, the market value of firm's equity E V can be seen as a European call option on firm's underlying assets A V with has maturity equal to T, which is given by the BS formula for call options:

    rT E A 1 2 V V N d Xe N d   (3.6)
where,

  2 AA 1 A 1 ln V X r T 2 d= T       ,   2 AA 2 1 A A 1 ln V X r- T 2 d d T T           ,
N is the cumulative density function of the standard normal distribution, r is the risk-free rate, and rT Xe  is the present value of the promised debt payment.

Next, to solve the two unknown parameters

  A A E A E A A 1 A E E A E V V V V Nd V V V V               (3.7)
where the hedge ratio  equals to

E A V V  
which is the partial derivative of the equity value with respect to the asset value, and from BS formula of equation (3.6), it can be shown that the hedge ratio

E A V V   =   1 Nd .
Combines equation (3.6) and equation (3.7), asset value and its volatility are calculated.

The default probability t DP is the probability that the firm's assets value is less than the book value of the firm's liabilities, based on which, Merton derives the firm's probability of default (the details of derivation process are shown in Appendix E) in terms of the cumulative normal distribution:

2 A,t A t t A V 1 ln T X2 DP=N T                  (3.8)
Merton's distance-to-default (DD) is the number of standard deviations that the firm is away from default, which means that the higher the DD, the farther the firm is away from default (the lower probability of default), on the contrary, the lower the DD, the higher probability of the firm bankrupt.

  2 A,t t A A 1 ln V / X T 2 DD T        (3.9)   DP N DD  (3.10)
The major advantage of BSM option-pricing model in predicting default risk is that "they provide guidance about the theoretical determinants of bankruptcy risk and they supply the necessary structure to extract bankruptcy-related information" [START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF].

Unlike the accounting-based models that are constructed by comparing the characteristics of bankrupt and no bankrupt firms, using a statistical technique to derive the variables that best discriminate between the two groups of firms which are not grounded in theory, and distinguish firms of bankruptcy or no bankruptcy heavily dependent on the prior specification of firms. The equity of a firm can be viewed as a call option on the firm's assets leads to a measure of default risk that is derived from theory and is economically justifiable.

Furthermore, compared with the conventional accounting-based models, it is more forwardlooking, dynamic and easier for using because it is calculated based on the market prices which reflect future expected cash flows (the accounting-based models, on the contrary, reflect the past performance of the firms), and contain the information comes from financial statements plus other information not included in the financial statements.

Among plenty researches that implement BSM model, one of the most popular and commonly used is KMV model, which will present in the next section.

KMV model

KMV model was first introduced by Oldrich Vasicek and Stephen Kealhofer Vasicek (1984) also as an extension of BSM model. In 1989, Kealhofer, McQuown, and Vasicek set up the KMV Company which is named by the founder's names and later in 2002 was bought by the company Moodyś. Then KMV is set to the successful practical model that estimated the default risk of firms.

Though BSM option-pricing model is the genesis for understanding the link between the market value of the firm's assets and its equity, and is widely understood and provides a useful framework to estimate firm's DP. KMV model assumes "the firm's equity is a perpetual option with the default point acting as the absorbing barrier for the firm's asset value" [START_REF] Crosbie | Modeling default risk[END_REF], the firm is assumed to default when the asset value hits the default point. Unlike BSM model, allows only two types of liabilities, a single class of debt and a single class of equity, KMV model takes multiple classes including short-term liabilities, long-term liabilities, convertible debt, preferred equity, and common equity of liabilities into consideration.

There are three main steps to determine default probability of KMV model, we will present precisely the differences from BSM model in each step.

-

Step 1 Estimate firm's asset value and its volatility

The BSM model applies the method called "simultaneous equations method" to solve firm's asset value and volatility, that is solving the combination of tow equations (3.6) and (3.7) to obtain two unknown parameters. However, the model which presents the links between asset value and volatility given by equation (3.7) holds instantaneously. [START_REF] Crosbie | Modeling default risk[END_REF] emphasize that "In practice the market leverage moves around far too much for equation (3.7) to provide reasonable results. Worse yet, the model biases the probabilities in precisely the wrong direction". For instance, in equation (3.7), if the market leverage ( AE V / V ) decreases then the asset volatility E  will tend to be overestimated and thus the default probability will be overstated as the firm's credit risk improves. On the conversely, if the market leverage increases the asset volatility E  will be underestimated and the default probability will be understated.

Instead of using instantaneous relationship in equation (3.7) and "simultaneous equations method" to solve the two unknown parameters of the Merton' option pricing formula (3.6), KMV model [START_REF] Crosbie | Modeling default risk[END_REF] resolve the problem by using a complex iterative procedure to find value of firm's asset and volatility. The procedure uses an initial guess of firm's asset volatility A  and then solve the equation (3.6) to determine a set of the firm's asset value A V and thus obtain the asset returns. Then the volatility of the resulting returns is used for the next iteration to determine a new set of A V and therefore a new series of asset returns. The procedure continues like this until the results converge.

-Step 2 Calculate the default point and distance-to-default

To calculate the DD of Moody's KMV, an important concept is default point. A firm default if the market value of assets falls below a certain value which is called the default 3.2 Measurement of financial distress risk 131 point, and it is generally accepted that the firm reaches the default point when the value of asset less than its total liabilities. However, [START_REF] Crosbie | Modeling default risk[END_REF] find in general this is not the case, the default commonly occurs when the market value of firm's asset locates between the total liabilities or total debt and the short-term (current) liabilities (debt). In KMV model, the default point is calculated as short-term debts (STD) plus one-half of long-term debts (LTD).

1 Default Point= STD+ LTD 2 (3.11)
Moody's KMV argues that in fact, the distribution of the DD is difficult to measure, so the assumption of normal or lognormal distribution such as BSM model is not appropriate to use in practice. KMV model proposes the DD which "compares the market net worth to the size of a one standard deviation move in the asset value":

A KMV AA V Default Point DD = V   (3.12)
where A V is the market value of firm's assets and A  is asset volatility. The numerator in the formula is the firm's market net worth which equals to the value of assets minus the default point, a firm will default when its market net worth reaches zero.

-Step 3 Calculate the Expected Default Frequency based on the empirical distribution of the DD BSM model calculates the DP (default probability) as the normal distribution of negative DD, whereas, [START_REF] Crosbie | Modeling default risk[END_REF] point out that in practice the normal distribution is a very poor choice to define the probability of default, because Moody's-KMV observe that defaulted firms have a leptokurtic distribution and the normal distribution underlying the BSM model leads to underestimation of the true value of firm's DP.

To avoid this effect of using the normal distribution, after calculating the distance-todefault, the KMV use their own large default database36 which collected over 20 years, to derive an empirical distribution relating the DD to the DP. The empirical distribution obtained from the KMV's proprietary database has much wider tails than the normal distribution.

This DP is well known as Expected Default Frequency (EDF), which is the market-based credit measure developed by Moody's KMV. The EDF is nothing but the probability that a given firm will default within 1 year according to the KMV methodology. The formula of EDF is similar as BSM's DP of equation (3.10), the normal distribution N is replaced by the empirical distribution of KMV which we can denote KMV Ñ :

EDF = KMV Ñ   KMV DD (3.13)
Moody's KMV has also a software product which is called 'Credit Monitor' to analyze the EDF credit measures, one can calculate the EDF values for one to five years through Credit Monitor.

Many researchers go for KMV's claim and argue that it is inconsistent to derive a formula for calculating DP based on an underlying normal distribution and then depart from KMV's empirical distribution in the final calculation of the DP. A large number of world financial institutions are subscribers of the KMV model.

From a purely theoretical point of view, the differences between KMV and Merton's models are not dramatic. The KMV model, however, relies on an extensive empirical testing and it is implemented using a very large proprietary database. [START_REF] Shumway | Forecasting bankruptcy more accurately: A simple hazard model*[END_REF] find that many accounting ratios used in previous models [START_REF] Altman | Financial ratios, discriminant analysis and the prediction of corporate bankruptcy[END_REF]Zmijewski (1984) for estimating default probability are not statistically significant, instead, the market size, past stock returns and idiosyncratic standard deviation of stock returns are all strongly related to the firm's bankruptcy. The author argues that the static models do not consider the time-changing characteristics of firms and propose a discretetime hazard model to predict bankruptcy by using both accounting ratios and market variables, which is a better predictor of bankruptcy than alternative models. [START_REF] Chava | Bankruptcy prediction with industry effects[END_REF] prove that the prediction ability for the bankruptcy of Shumway's hazard model is superior to accounting-based models [START_REF] Altman | Financial ratios, discriminant analysis and the prediction of corporate bankruptcy[END_REF] and Zmijewski (1984)), in addition, they find that "accounting variables add little predictive power when market variables are already included in the bankruptcy model". [START_REF] Campbell | In search of distress risk[END_REF] also develop a dynamic hazard model to estimate the default probabilities and study the determinants of corporate bankruptcy and the pricing of distressed stocks. They declare that their best model includes additional variables and has greater explanatory power than the existing models estimated by [START_REF] Shumway | Forecasting bankruptcy more accurately: A simple hazard model*[END_REF] and [START_REF] Chava | Bankruptcy prediction with industry effects[END_REF].

Hazard model

Comparing Accounting-based models and market-based models

In summary, the market-based models overcome the main shortcomings we mentioned at the beginning of the section 3.2.2 about accounting-based models: 134 -The most importantly, market-based models employ BS option-pricing theory provide the theoretical basis for predicting firm's default risk or distress risk. While the accounting-based models are not grounded on the economic theory.

-Dissimilar accounting-based models that use information derived from financial statements which reflect the past performance of the firms, market-based model such as BSM model, depend on the market prices which reflect investors' expectations about the firm's future performance, thus the market-based models are better for calculating the probability of default in the future. Furthermore, the market prices contain the information in financial statements and other information which is not included in the financial statement.

-Market-based variables provide the direct estimation of volatility, which is a powerful predictor of firm's default risk and is not contained in the accountingbased model. Despite the popularity and the advantages of market-based models to predict firm's default risk, there are still some critics left for market-based models, such as the models based on the underlying option-pricing theory require the assumption of normality of stock returns and the models do not distinguish between different types of debt and assume that the firms only have a single zero coupon loan 38 . Many researchers give the evidence that accountingbased models are still indispensable in predicting distress risk.

Using a hazard model with a longer time period, [START_REF] Beaver | Have financial statements become less informative? Evidence from the ability of financial ratios to predict bankruptcy[END_REF] finds that the ability of accounting ratios to predict bankruptcy remains. Their findings indicate that the market variables complement accounting variables and that the use of market variables causes only a slight reduction of predictive power of the accounting variables in certain sub-periods. [START_REF] Agarwal | Comparing the performance of market-based and accounting-based bankruptcy prediction models[END_REF] find out that there is little difference between market-based models and Altman's model in predicting firms' distress risk in the UK, and the accounting-based model even produces significant economic benefit over the market-based models. In the paper of [START_REF] Reisz | A market-based framework for bankruptcy prediction[END_REF], they estimate the default probability for 38 [START_REF] Allen | Credit Risk Measurement. New Approaches to Value at Risk and Other Paradigms[END_REF] 3.2 Measurement of financial distress risk 135 5784 industrial firms and conclude that Altman's Z-score model better predict firm's bankruptcy over a one-year horizon. Moreover, [START_REF] Campbell | In search of distress risk[END_REF] find that marketbased models have little forecasting power after controlling for other variables.

To conclude, when comparing the two mainstream distress risk prediction models: accounting-based models and market-based models, we can say that both imply advantages and disadvantages.

Financial distress risk and equity returns

In the asset pricing area, as we all know that the market risk cannot explain all the variation of average stock returns, researchers have been committed to exploit the anomalies which have additional explanatory power. One of the anomalies that researchers are interested in is the firm's distress risk, the cross-sectional relation between default risk and stock returns, the so-called default risk premium, has been a subject of intense debate in the literature. numerous studies apply the models for measuring distress risk and try to find the relation between expected stock returns and firm's distress risk.

Since a number of empirical studies investigating the relationship between financial distress risk and equity returns find that the distress risk is related to firm's B/M ratio, especially after FF3F model achieves huge empirical success, considerable researchers regard financial distress risk as a factor and examine whether distress risk factor can be explained (proxy) by FF factors.

Literature reviews on developed markets

Distress risk and expected stock returns

In order to find out the relation between distress risk and equity returns, it is important to have a correct proxy for distress risk, and "the risk of bankruptcy appears to be one natural measure of firm distress [START_REF] Dichev | Is the risk of bankruptcy a systematic risk?[END_REF], thus the diverse models of measuring firm's default probability provide the rational proxies for distress risk. The empirical studies on the distress premium mainly apply either the traditional accounting-based models such as Altman's Z-score and Ohlson's O-score 39 or the market-based models such as Merton's option-pricing model and Moody's KMV model 40 to estimate distress risk (default risk/probability). A few researchers also apply the dynamic reduced-form model such as Shumway's hazard model as a proxy for distress risk.

Dichev (1998) is the first who carries out researches on the relationship between default risk and stock returns, by applying Altman's Z-score and Ohlson's O-score as proxies for default risk. Dichev examines whether bankruptcy risk is a systematic risk and the relation of distress risk factor to size and B/M effects on U.S. market during the period 1981 to 1995. His findings reveal that the risk of bankruptcy is not a systematic risk and there is a negative relationship between bankruptcy risk and stock returns, firms with higher default risk are rewarded by lower average returns instead of higher returns, which is inconsistent with the risk-based explanation for distress, this puzzling relation between distress risk and stock returns is often called the "distress anomaly. Furthermore, inconsistent with some studies 41 which suggest that the size and B/M effects may the proxies of the distress risk factor, his results demonstrate that the relationship between bankruptcy risk and B/M equity ratio is not monotonic, thus "a return premium related to bankruptcy risk cannot fully explain the B/M effect", and there is no size effect during his research period.

Dichev's conclusion is confirmed by [START_REF] Griffin | Book-to-market equity, distress risk, and stock returns[END_REF] who examines the relationship between B/M equity, distress risk and stock returns using Ohlson's O-score as a proxy for firm's distress risk. Similarly, they find that firms with high B/M equity ratio earn significantly lower returns as a premium for distress risk than those of low B/M firms and they come to a conclusion that the B/M effect must be due to mispricing.

Numerous researches following obtain the negative relationship as Dichev, Campbell et al. (2008) and [START_REF] Campbell | Predicting financial distress and the performance of distressed stocks[END_REF] implement a dynamic hazard model for predicting firm's distress risk by combining both accounting information and market-based measures over the period 1981 to 2003, and they document that the default probability is significantly negatively related to stock returns, which becomes even more stronger after controlling for size. They give some possible explanation for the distress anomaly: the stocks of firms with higher distress risk are overestimated by investors, and "distressed stocks have characteristics that appeal to certain investors, such as increased opportunities to extract private benefits of control or positive skewness of returns". Likewise, [START_REF] George | A resolution of the distress risk and leverage puzzles in the cross section of stock returns[END_REF] also report a negative relation between stock returns and default risk measured by the O-score.

However, there are a few researchers find the positive relationship between distress risk and stock returns, such as [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] which is the first study that examines 40 Vassalou and Xing (2004), Garlappi andYan (2011) Gharghori et al. (2009), etc. 41 Fama and French (1992), K. C. [START_REF] Chan | An exploratory investigation of the firm size effect[END_REF], [START_REF] Chan | Structural and return characteristics of small and large firms[END_REF], etc.

3.4 Construct distress risk factor and portfolios on Chinese stock market 137 default risk in the context of the Fama-French model by extracting default risk estimated from Merton's option pricing model. Inconsistent with Dichev, they point out that the default risk is a systematic risk, and the default risk is closely related to the firm size and B/M equity ratio, there exist size and B/M effects but only within the highest default risk portfolios. Moreover, contrary to the previous empirical studies, firms with higher default risk earn higher returns than low default risk firms, however, this finding only lies in the small size and high B/M portfolios. They attribute these conflicting results to the measurement for estimating default risk. [START_REF] Chava | Is Default Risk Negatively Related to Stock Returns?[END_REF] also document a positive and stable cross-sectional relation between default risk and expected stock returns throughout their research period. They argue that the negative relation between distress risk and expected returns is due to "the use of noisy ex-post realized return by the prior studies to estimate the ex-ante expected return".

Then the implied cost of capital (ICC) is applied to estimate the expected stock returns, and the two measures to predict firms' default risk are EDF of KMV model and Shumway's hazard model.

Recently, apart from using accounting-based models or market-based models as proxy of distress risk, [START_REF] Friewald | The Cross-Section of Credit Risk Premia and Equity Returns[END_REF] examine the relation between expected stock returns and credit risk premium estimated from credit default swaps (CDS) spreads, as they claim that "sorting firms into portfolios using only physical or risk-neutral default probabilities may not be sufficiently informative about expected stock returns". Their results indicate a positive relationship between the expected excess stock returns and default probabilities, the stock returns increase with credit risk premium. Their findings are conflictive with [START_REF] Avramov | Momentum and credit rating[END_REF] who use credit ratings to measure financial distress, show that stock returns significantly increase with S&P senior debt credit ratings, which implies a negative relationship between returns and default risk. show that most of the negative return for high default risk stocks is concentrated around rating downgrades.

The literature generally has the conclusions that there exist negative or positive or no relationship between stock returns and distress risk. Nonetheless [START_REF] Garlappi | Default risk, shareholder advantage, and stock returns[END_REF] and [START_REF] Garlappi | Financial distress and the cross-section of equity returns[END_REF] document particularly a hump-shaped relationship using marketbased default probability estimates from Moody's KMV model. The results demonstrate that the higher distress risk not always associated with higher expected stock returns. Furthermore, they emphasize the important role of the 'shareholder advantage' in determining the equity returns, the higher shareholder advantage the lower expected equity returns as the default probability increases, and lower shareholder advantage which implies a higher expected equity returns is positively related to default risk. As they expressed "the trade-off between the risk of default to equity and the likelihood of bargaining gains in Out of U.S. market, [START_REF] Gharghori | Default risk and equity returns: Australian evidence[END_REF] test the relationship between default risk and equity returns in Australia using option-based models as proxy for distress risk. Their results show that there is a negative relationship between default probability and stock returns, what's more, they also suggest that the negative relationship is not because of a leverage, volatility or momentum effect. [START_REF] Aretz | Do Stock Returns Really Decrease with Default Risk? New International Evidence[END_REF] provide the evidence on the cross-sectional relation between default risk and stock returns for non-U.S. firms in 14 developed markets using the approach of [START_REF] Campbell | In search of distress risk[END_REF][START_REF] Campbell | Predicting financial distress and the performance of distressed stocks[END_REF]. Their results demonstrate a statistically significant positive default risk premium in the 14 international markets, the firms with higher default risk outperform those with lower default risk. In addition, their results also indicate that "the magnitude of the default risk premium is contingent upon several firm characteristics". [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] point out that their default probability (DP) estimated using Merton's model is not the real DP, instead, the DP calculated based on the empirical distribution by Moody's KMV model is the actual DP. Thus they call their measure of DP default likelihood indicator (DLI). In order to construct the distress risk factor, they proceed following steps: first state the aggregate default likelihood measure P(D) which is the simple average of the DLI of all firms; then define the aggregate survival rate SV equals to 1-P(D); finally, the distress risk factor is defined as the change of SV: is different from that captured by those default spreads. 42 Default return spread, which is defined as the return difference between Moody's BAA rating bonds and AAA rating bonds. Default yield spread, which is defined as the yield difference between Moody's BAA bonds and AAA bonds. The change in default spread from [START_REF] Hahn | An Empirical Investigation of Risk and Return under Capital Market Imperfections[END_REF], which is defined as the change of the difference in the yields between Moody's BAA bonds and 100-year government bonds.

Distress risk factor

  t t 1 SV SV SV     (3.17
3.4 Construct distress risk factor and portfolios on Chinese stock market 139 Another distress risk factor proposed by [START_REF] Gharghori | Are the Fama-French factors proxying default risk?[END_REF] is a mimicking portfolio which measures the difference in returns between high default risk firms and low default risk firms. They also apply Merton's option-pricing model to calculate firms' default probability, and similar as Vassalou and Xing, they augment FF3F model with their distress risk factor to test whether FF factors SMB and HML can proxy for distress risk. We will follow the later method to construct our distress risk factor on CNAS stock market.

Empirical studies of distress risk on Chinese stock market

To the best of our knowledge, the research on Chinese market mainly focuses on testing the predictive accuracy of commonly used models in estimating distress risk using data of Chinese listed firms and measuring default risk of Chinese companies without considering the relationship between default risk and stock returns. Wang and Campbell (2010b) investigate the prediction accuracy of Altman's Z-score in estimating Chinese firms' failure using data from 2000 to 2008, and point out that Z-score has high accuracy in predicting firms' failure in China. In the same year, they Wang and Campbell (2010a) publish an article that examines the predictive ability of another leading accounting-based model (Ohlson's O-score) for Chinese listed firms, in which the prediction accuracy rate is testified above 95% in general. Likewise, [START_REF] Ni | The determinants of bankruptcy for Chinese firms[END_REF] show that accounting-based models (Altman's Z-score and Ohlson's O-score) perform reasonably well in determining business failures of Chinese firms. [START_REF] Huang | Value premium in the Chinese stock market: free lunch or paid lunch?[END_REF] use Altman's Z-score and Ohlson's O-score to measure the financial distress risk of all nonfinancial firms of A-share stock market for the period 1997 to 2008, trying to test whether there exist value or size effect. Their results show that firms with small size have higher distress probability than firms with big size, while there is no significant difference in distress probability for firms with different B/M equity ratio. In addition, when the distress risk factor is added into their conditional regressions, the size factor SMB of FF3F model lose more than half of explanatory power, however, "the proxy for distress risk itself does not show incremental explanatory power when competing with the three Fama-French factors". Overall, they conclude that the size factor is better than distress risk factor in explaining variations of expected stock returns on Chinese stock market.

Apart from the literature that tests the accounting-based models in China, there are researchers examine the practicability of the market-based model (Merton's model and Moody's KMV model) in predicting distress risk of Chinese listed firms. Such as [START_REF] Lu | Empirical Research on Credit Condition of Chinese Listed Corporation with KMV Default Model[END_REF], [START_REF] Zhou | Using the Distance to Default to Identify Credit Risks: An Empirical Study[END_REF], Xiaohong Chen et al. (2010) and [START_REF] Chen | Estimation of Default Risk Based on KMV Model-An Empirical Study for Chinese Real Estate Companies[END_REF], who apply KMV model to estimate distress risk; [START_REF] Liang | An empirical estimation of the default risk of Chinese listed company based on the Merton-KMV Model[END_REF] and [START_REF] Law | Assessing Default Risks for Chinese Firms: A Lost Cause?[END_REF], who calculate firms' distress risk using models based on Merton's theory.

Particularly worth mentioning, most of the literature using KMV model to measure distress risk of Chinese firms have discussed that it is not appropriate to apply KMV's EDF in calculating firms' default probability, since KMV model use an empirical distribution derived based on the database of U.S. market. At present, as stated by Xiaohong Chen et al. (2010), "there is no similar database in Chinese credit market, which means no EDF statistics is available", so researchers use DD of KMV model instead of the DP as the measure of distress risk in China.

Xiaohong Chen et al. (2010) measure credit risk of listed firms of Small Medium Enterprise Board (SME) in China using KMV's DD and evidence indicates the high credit risk of listed firms in SME. Moreover, they find firms' size has a significant impact on credit risk, the small size firms tend to have higher default probability than medium and large size firms. [START_REF] Chen | Estimation of Default Risk Based on KMV Model-An Empirical Study for Chinese Real Estate Companies[END_REF] implement an empirical research for the default risk of Chinese real estate firms during the period 2007 to 2012. They implement KMV model as proxy for distress risk and contrary to Xiaohong Chen et al. (2010) that they find big size firms face higher default risk than small size firms.

Liang (2012) tests the predictive ability of DLI [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] More recently, [START_REF] Law | Assessing Default Risks for Chinese Firms: A Lost Cause?[END_REF] assess Chinese firms' distress risk using a variant of Merton's model and link the default risk with firm-specific and economic variables to test whether they have an influence on firms' default probabilities. Furthermore, the authors compare the result with that obtained from a model using borrowing cost as a measurement of default probability. They conclude that the distress risk measured by the market-based model is affected by firms' fundamentals, and that market-based model better estimates the stand-alone 1-year probability of default for individual firms in China.

Several researchers exploit distress predictive models themselves depending on the data of Chinese firms, such as [START_REF] Geng | Prediction of financial distress: An empirical study of listed Chinese companies using data mining[END_REF], who build financial distress warning model based on 32 financial indicators of 107 Chinese firms which are 'special treatment' (ST) 43 . And some other researchers such as [START_REF] Bhattacharjee | Financial distress of Chinese firms: Microeconomic, macroeconomic and institutional influences[END_REF] and [START_REF] Liu | Corporate Failure Prediction Models for Advanced Research in China: Identifying the Optimal Cut Off Point[END_REF] trying to find the impact of some macroeconomic, firm-specific variables and the cutoff point on the financial distress risk of Chinese listed firms. [START_REF] Lin | Is default risk a systematic risk of Chinese stock markets?[END_REF] is one of the few studies that investigate the relationship between distress risk and expected stock returns on Chinese stock market. They examine whether default risk is a systematic risk in China and related to expected stock returns using data of Chinese stock market from 2000 to 2006 by applying Vassalou and Xing's DLI to calculate firms' default probabilities. The empirical evidence demonstrates that the default risk is not a systematic risk and there is no significant relationship between the expected stock returns and the implied default risk, even controlling for size and B/M equity ratio.

Our research does not aim to find a better distress predictive model or to examine the predictive accuracy of existing models on Chinese stock market. Since the lack of literatures that discuss the relation between distress risk and expected stock returns in China, we devote ourselves to explore the relationship based on the framework of Fama-French Three-Factor Model and examine whether FF factors can proxy for distress risk calculated through the most popular and commonly used models which have been proved able to predict distress risk on Chinese stock market, in addition, whether an augmented four-factor model with distress risk factor can explain expected excess stock returns better on CNAS stock market.

Construct distress risk factor and portfolios on Chinese stock market

Data

All the data needed in this study during the period July 2005 to May 2015 (119 months) is collected from Bloomberg, and in research of both methods, we exclude the financial firms, the capital structure of which is distinguished from that of common ones, and the firms with negative B/P ratios also removed from the sample as Chapter 1. Since our research focuses on the healthy firms, the firms which labeled as 'ST' and 'PT' are also out of our 43 China Securities Regulatory Commission carries out a 'Special Treatment' (ST) warning mechanism to indicate abnormalities in a listed companies' financial status [START_REF] Geng | Prediction of financial distress: An empirical study of listed Chinese companies using data mining[END_REF], firms will labeled as ST if they have negative profits for two consecutive years and the equity of shareholders is less than the registered capital, even may be delisted from the stock market if their performance will not improve within next three years. consideration. We exclude the firm if one has incomplete data at certain months. To proceed our research and to perform the comparison, first of all, we calculate the default probability using accounting-based model (Ohlson's O-score) and market-based model (Merton's option-pricing theory) separately. These default probabilities are then used as a basic criterion for the distinction of firms' distress risk.

Calculate default probability by O-score and DLI

-O-score as proxy of distress risk Due to the limitations of Altman's Z-score, such as the strict statistical assumption of MDA, especially, the Z-score is rather a value measuring of financial strength with little intuitive interpretation. We choose Ohlson's O-score which measures the probability of financial distress.

To be included in our sample, a firm must have two-year ahead data of net profitability for the purpose to calculate the O-score and at least 12-month data of returns. We calculate the O-score of stocks formula (3.4) with our database at the end of each December during the research period July 2005 to May 2015. Particularly, consistent with Dichev (1998), we do not adjust for the 'GNP price-level index' of the first 'SIZE' variable in formula (3.4) because the tests in this study employ monthly data, within which the index is fixed. Thus the 'SIZE' in the formula (3.4) equals to log (total assets).

-DLI as proxy of distress risk Following [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], we compute DLI (equation (3.8)) by applying the methodology developed by [START_REF] Black | The pricing of options and corporate liabilities[END_REF] and extended by [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF] to estimate default probabilities of the individual firms on CNAS stock market. There are two main reasons why we use Merton's theory instead of using EDF of KMV model to calculate distress risk in China: Firstly, as many researches emphasize that the empirical distribution of KMV is deduced based on database of U.S. market, while there is not such a distribution in China, it is not correct to apply EDF to estimate distress risk on Chinese stock market; secondly, after empirical analysis of defaults, KMV has found that firms most frequently reach the default point when the firm's value approximately equals to short-term (current) liabilities plus 50 percent of long-term liabilities. However, whether the default point is the same on the Chinese stock market is still a question, it is not a responsible way to calculate KMV's DD based on their default point.

To calculate DLI, we need to solve Black-Scholes formula (3.8) and obtain two unknown variables A V (asset value) and A  (asset volatility), with input value of equity E V (market 3.4 Construct distress risk factor and portfolios on Chinese stock market 143 capitalization, equals to share price times the shares outstanding), strike price X which is the book value of liability, risk-free interest rate r and maturity T. We follow the approach of Moody's KMV [START_REF] Crosbie | Modeling default risk[END_REF] and [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], applying a more complex iterative procedure to solve for the asset volatility A  and value of firm's asset A V :

-

Step 1, at the end of each year, we calculate the daily returns of firms' equity from the past 12 months to obtain the volatility of equity E  , which is as the initial estimate of A  .

-

Step 2, then we use daily E V and this initial estimation A  to solve the Black- Scholes formula on each trading day for the past year to get daily estimates A V .

-Step 3, we next take the standard deviation of those A V s as the new estimate of A  , which is used for the following iteration procedure.

Step 2 and 3 above are repeated until the value of A  from two consecutive iterations converge with the tolerance level 0.001. Once we obtain the converged value of A  , we use it to find out our final estimation A V . Then we calculate DD using equation (3.9) at each year-end over our sample period, DLI is then denoted by the cumulative density function of the standard normal distribution of subtractive DD (equation (3.10)).

Furthermore, we always calculate default probability with a one-year horizon. The risk-free rate also needs to be a yearly rate, here we use one-year fixed deposit rate which is officially determined by the People's Bank of China. There are at least three reasons why the time to maturity is set to one year: first, choosing one year permits comparability with prior research such as [START_REF] Griffin | Book-to-market equity, distress risk, and stock returns[END_REF], [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] and [START_REF] Lin | Is default risk a systematic risk of Chinese stock markets?[END_REF]; second, a maturity of greater than one year is difficult to justify as there are too many factors (firm specific and economy-wide) that may affect a firm's DP over time; third, one-year maturity represents a reasonable balance between the weight placed on market leverage, asset volatility, and asset growth rate in the construction of the DPs [START_REF] Gharghori | Investigating the performance of alternative default-risk models: Option-based versus accounting-based approaches[END_REF]. The

Summary description of O-score and DLI

Portfolios construction using O-score and DLI as proxy of distress risk

In Chapter 1, we sort stocks both into 6 (2x3) and 25(5x5) Size-B/P portfolios and we find that the different sorts of portfolios do not affect the empirical results. In this chapter, we construct 18 (2x3x3) Size-B/P-O-score (SBPO) portfolios as follows:

Similarly, like FF six portfolios, we sort stocks into two size portfolios (Small and Big) and three B/P portfolios (Low, Medium and High). The size breakpoint for year t is the median CNAS market capitalization at the end of June of year t. B/P ratio for June of year t is the book value of equity for the last fiscal year end in t-1 divided by the price for December of t-1, the breakpoints are the 30th and 70th CNAS percentiles. At the end of each year t-1, Oscore for year t is calculated using Ohlson's formula (3.4) for each stock, then stocks are sorted into 3 distress risk (DR) groups (O1, O2 and O3, which represent the low, medium and high O-score groups, separately) according to their O-score with the breakpoint 30th and 70th percentiles.

The 18 portfolios which are constructed at the end of each June of year t, are the intersection of two size portfolios, three B/P portfolios, and three O-score portfolios, we denote the portfolio which has small size, low B/P ratio and low DR as SL1, the portfolio which has small size, low B/P ratio and medium DR as SL2, and so on the 18 portfolios are denoted by SL1, SL2, SL3, SM1, SM2, SM3, SH1, SH2, SH3, BL1, BL2, BL3, BM1, BM2, BM3, BH1, BH2, and BH3. Portfolios are reconstructed in June of each year. The distress risk factor DRF is the difference between average returns of high O-score portfolios and low O-score portfolios.

Following exactly the same process, we construct 18 Size-B/P-DLI (SBPD) portfolios with two size portfolios, three B/P portfolios and three DLI portfolios (D1, D2, D3 are the low DLI portfolio, medium DLI portfolio, and high DLI portfolio, respectively). The three DLI portfolios are constructed in the same way that three O-score portfolios are done above, except that the basis criterion for distinguishing firms' distress risk is DLI instead of Oscore.

Construction of distress risk factor

The proxies of distress risk we use are the DP calculated by O-score and DLI stated in the previous section. At the end of each June of year t, we sort stocks according to their Oscore (or DLI) of the end of year t-1 into three groups, denoted as O1, O2 and O3 (or DLI1, DLI2, DLI3) from low to high default probabilities. The breakpoints are 30% and 70% percentiles of the O-score (or DLI) of the sample firms. The portfolios remain unchangeable from July of year t to June of year t+1, and portfolios are reformed at the end of June of year t+1, and so forth for the whole sample period. The mimicking portfolio DRF is the distress risk factor, which measures the return difference between the high-DP portfolio (O3 or DLI3) and the low-DP portfolio.

Distress risk, size and B/P ratio of Chinese stock market

Numerous studies suggest that a firm distress risk factor could be behind the size and the value effects. For instance, [START_REF] Griffin | Book-to-market equity, distress risk, and stock returns[END_REF] and [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] both show that the B/M and size effects are concentrated in high default risk firms, thus leding to the conjecture that the value and size effects are closely related to distress risk.

We aim to investigate whether there exist size and value effects on CNAS stock market related to the distress risk in this section. In order to compare whether different methods of measuring distress risk have different impact to our empirical results, we apply both of the leading models, accounting-based model of Ohlson's O-score and market-based model according to Merton's option-pricing theory, to estimate the distress risk of Chinese listed firms on A-share stock market.

3.5 Distress risk, size and B/P ratio of Chinese stock market 147

Distress risk and variation of stock returns

Following [START_REF] Griffin | Book-to-market equity, distress risk, and stock returns[END_REF] and [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], stocks are ranked each June of year t according to their previous December O-score or DLI. To analyze the relation between distress risk (DR) and stock returns, and whether there exist size and value effects on CNAS stock market, the stocks are sorted separately into quintile and decile according to their O-score and DLI (proxies of distress risk), we then examine whether the portfolios with different distress risk provide significantly different returns. A significant difference in the returns would indicate that default risk may be important for the pricing of equities [START_REF] Vassalou | Default Risk in Equity Returns[END_REF].

The simple sorts of stocks based on their O-score and DLI are presented in Panel A and Panel B of Table 3.3, respectively. In each panel, stocks are firstly divided into five portfolios according to their O-score or DLI, the returns, size, and B/P ratio of portfolios are also shown in the table. Independently, we also sort stocks into 10 portfolios by their Oscore or DLI. In Panel A, no matter for the five or the ten O-score portfolios, the results are similar. We find no obvious differences in average returns across the portfolios, and the return difference between the highest DR portfolio and the lowest distress risk portfolio is not statistically significant (0.0029 for the five portfolios with t-stats -1.0688 and 0.0037 for the ten portfolios with t-stats 0.9706). However, it seems that the firm size is negatively related to the distress risk, the higher DR portfolios have smaller size. B/P ratios do not show much differences across the DR quintile or decile except for the highest DR portfolios which have lowest B/P ratio among other DR portfolios.

In Panel B, there is neither significant return difference among the five portfolios, nor the ten portfolios sorted by DLI (-0.0028 for the five DLI-sorted portfolios with t-stats -0.7907 and -0.0038 for the ten DLI-sorted portfolios with t-stats -0.9025). Different from portfolios that sorted by O-score, the trend of size-change is ruleless, but consistent with the results of [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], the B/P ratio of portfolios increases for both sorts with their default probability (proxy by DLI) increases.

Since the non-significant return differences among the portfolios sorted by both O-score and DLI, we cannot confirm that distress risk has an impact on average stock returns. However, the results reveal that there exist probably size or value effect associated with DR.

Size effect

In order to examine whether there exists size effect across the distress risk groups, we implement the two-way sorts the way [START_REF] Vassalou | Default Risk in Equity Returns[END_REF] do, stocks are first sorted into five quintiles based on their O-score or DLI (distress risk), then within each DR groups, stocks are sorted into five size groups according to their total market capitalization. Furthermore, we also examine the size effect across the whole sample by sorting all stocks into five size quintiles.

The results of the 25 O-score/Size portfolios are presented in Table 3.4, across the columns are the five DR quintiles, and across the rows are the five size quintiles. The average portfolio returns, size, B/P ratio and O-score are displayed respectively in Panel A, B, C and D. The results in Panel A suggest that there are significant size effects across each DR quintile, the strongest effect is in the group of highest DR with return difference between small and big size portfolios of 0.0194 (with t-stats 3.7498 at 5% confidence level). And we also find the size effect across our whole sample with return difference of 0.0159 (t-stats 3.1086).

The results in Panel B show that across each size quintile, the DR of firms increases with the size decreases apart from the lowest O-score portfolios, consistent with our findings in Table 3.3, the smaller size firms tend to have higher default probabilities. From Panel D, we cannot tell obvious variations within the DR quintiles; only within the highest DR quintile, the smallest size portfolio has the highest O-score, while the biggest size portfolio has the lowest O-score. Panel C indicates that within each size quintile, portfolios with highest DR tend to have lower B/P ratio at least for the three smaller size quintiles, but it is not clear that whether B/P ratio is related to DR directly from this analysis, we will carry out the analysis of value effect subsequently.

To examine whether the size effect controlled by distress risk which estimated using market-based method (DLI) is distinct from that controlled by O-score, we proceed the same steps above except the stocks are first sorted into five portfolios based on their DLI instead of O-score, then within each DLI quintiles stocks are sorted into five size groups, the results are shown in Table 3.5. The same results are found in Panel A that across each DR quintiles, average return of portfolio decreases as the firm size increases, and there exist strong size effect across each DR quintile (the return differences are all statistically significant at 5% confidence level). The strongest effect still is in the highest DR groups (return difference is 0.0180 with t-stats 3.3040). The relationship between DR and size seems chaotic (Panel B) except the two small size quintiles, within which the size increases as DR increases. Panel C of Table 3.5 shows no explicit relationship between B/P ratio and distress risk, but within each size quintile, the portfolio with highest DR seems has the higher B/P ratio. The most obvious variation is across the highest DR group in panel D, the highest distress risk belongs to the big size portfolio (Big-5). Overall, average returns are closely related to firm size in both Table 3.4 and Table 3.5. it appears that there exists strong size effect across DR group and in the whole sample as well, no matter the proxy for DR is O-score or DLI. This finding is consistent with our empirical results in Chapter 1. However, the relation between size (or B/P ratio) and DR is kind of chaotic and not easy to distinguish from the size effect tests controlled by DR.

Value effect

Similar to the analysis of size effect, to examine the value effect across the DR groups, stocks are first sorted into five DR quintiles and within each DR quintile, the stocks are sorted into five B/P groups. Across the rows of Table 3.6 are the five B/P quintiles and across the columns are the five O-score quintiles. In Panel A, we find the return difference between the highest B/P quintile and the lowest B/P quintile neither significant for all of the five DR portfolios nor significant across the whole sample, which indicates that there exists probability no value effect controlled by distress risk on CNAS stock market during the research period.

In Panel B, the relationship between B/P ratio and DR is not clear. The DR is negatively related to firm size within the lowest B/P quintile (Panel C). In Panel D, across each DR quintile, the relationship between O-score and B/P ratio is not clear except for the lowest and highest DR portfolios. Across the lowest DR quintile, it seems that with tiny change of O-scores, higher B/P ratio associated with higher O-score; but across the quintile which has the highest DR, the higher the B/P ratio the lower O-score of portfolios, exceptionally, the portfolio with lowest B/P ratio has the highest DR (with O-score 3.1856).

The results of value effect controlled by distress risk which is proxy by DLI are displayed in Table 3.7. Notice that in Panel A, same as Table 3.6, none of the return difference across the five DLI quintile is significant. In Panel B, within each B/P quintile, higher DLI (DR) portfolios tend to have higher B/P ratio. In panel D, the DLI of portfolio increases as the B/P ratio increase in the highest DR quintile except for the lowest B/P portfolio. We summarize that there exists strong size effect but no value effect, however, the robust size effect and lack of value effect are robust when controlled by distress risk as well as for the whole sample on CNAS stock market from 2005 to 2014. And the effects are also robust to the different proxies for distress risk. Nevertheless, the relationship between size and DR, and B/P ratio and DR are quite confusing. The most distinct is that B/P ratio is positively related to DR that use DLI as proxy (Panel B of Table 3.7), portfolios with higher DLI have higher B/P ratio.

Augmented four-factor model and empirical evidence

In order to investigate whether FF three factors are proxies for distress risk, we examine an augmented four-factor model, which include market factor (market premium), size factor (SMB), value factor (HML) and distress risk factor (DRF). If all the priced information in SMB and HML is related to financial distress risk, we would expect to find that in the presence of DRF, SMB and HML lose all their ability to explain equity returns 44 . In particular, we use both accounting-based model and market-based model as proxy for distress risk to investigate whether different methods of estimating default probability cause different results.

Augmented four-factor model

We add a distress risk factor on the basis of FF3F model to form the augmented four-factor model:

         i ,t f i i M ,t f i i i i ,t R R a b ( R R ) s SMB h HML d DRF (3.18)
where DRF is our mimicking portfolio, distress risk factor, i d is the regression coefficient of DRF, and  i ,t is the error term for portfolio i at time t. DRF is constructed separately using O-score and DLI as proxy for distress risk, denoted as HML are highly positive correlated, the component of equity returns that each factor explains may be similar.

Time-series regressions analysis

We carry out the TSRs of the augmented four-factor model on CNAS stock market in this section. To construct distress risk factor, we apply both accounting-based model and market-based model to estimating default probability of stocks.

3.6 Augmented four-factor model and empirical evidence 157

Accounting-based distress risk factor and regression results

Table 3.8 shows the summary statistics of 18 portfolios sorted on Size, B/P and O-score. For all the 18 portfolios, the average excess returns are lower for small size portfolios while higher for big size portfolios, which is consistent with the size effect conclusion that equity return is negatively related to firm size, the big size portfolios tend to have lower average returns. However, we find no obvious relationship between average excess returns and B/P ratio or distress risk proxy by O-score, except the highest B/P portfolios with small size (across the highest B/P group, the higher DR portfolio tends to have higher average excess return) and the lowest DR portfolios with small size (across the lowest DR portfolios, higher B/P portfolio tends to have lower average excess return, which is inconsistent with FF's findings that average stock returns are positively related to B/M ratio). The results of Table 3.9 also reveal that distress risk is related to firm size, regarding to the size parts, the higher DR portfolios always have smaller size (except the portfolio SH1), meanwhile, regarding to the O-score parts, the big size portfolios have lower O-score than the small size portfolios excluding the lowest DR groups. Whereas, it is not easy to tell the relationship between B/P ratio and O-score from the analysis so far.

To investigate how the four factors, explain average excess returns of 18 SBPO sorted portfolios, we following perform the TSRs and the results are presented in Table 3.9. The left-hand part presents the regression coefficients and adjusted R-squares, while the righthand part presents the corresponding t-statistics corrected for heteroscedasticity and autocorrelation using Newey-West estimator with five lags and the residual standard error.

As always, the coefficients of excess market return and SMB are all highly significant at 5% confidence level, and there exists size effect. Regression coefficients β(h) increase as B/P ratio increase, but the loadings on HML seem only to be significant within the highest B/P groups (for small size portfolios and big size portfolios) and the lowest B/P group (for big size portfolios). Loadings on DRF β(d) increase as O-score increase except for the portfolio group with small size and medium B/P ratio, but the significant coefficients mainly exist in the lowest (for big size portfolios) and highest (for small size and big size portfolios) Oscore groups. Comparing with the regressions on FF3F model of the same 18 portfolios (Appendix F), the TSR coefficients of FF three factors do not have a noteworthy difference with or without an augmented factor DRF in addition to FF3F model. Adding a DRF factor (with averaged adjusted R-square 0.8990) does not change markedly the time-series explanatory power of FF three factors (with averaged adjusted R-square 0.8939). This table reports the time-series regression results for 18 portfolios formed on size, B/P ratio and O-score. The stocks are divided into two size groups based on the breakpoint of median market capitalization, and the breakpoints for the three B/P groups are the top 30%, median 40% and bottom 30% of B/P ratio, similarly as B/P groups, the stocks are divided into three groups based on their O-score (O1, O2 and O3, represent the low, medium and high O-score separately). The intersection of two size groups, three B/P groups and O-score groups form 18 portfolios. The left part of the table is the coefficients of time-series regressions and adjusted R-square, the right part is the corresponding t-stats corrected for heteroscedasticity and autocorrelation using Newey-West estimator and residual standard error, and the numbers in bold are significant at 5% confidence level. Regression: Thus we conclude that there exists distress risk effect, since portfolios with higher O-score associated with higher return. The DRF constructed using O-score as proxy for DR has explanatory power in time-series stock returns only for the portfolios with extreme DR (lowest DR or highest DR). Whereas, the augmented DRF add limited explanatory power in explaining stock returns, and FF factors are not proxy for distress risk in explaining timeseries variations of average stock returns, at least when the DRF is constructed using Oscore to estimate financial distress risk. We then perform the same TSRs using DLI as proxy for DR.

         i ,t f i i M ,t f i i i O-score i ,t R R a b ( R R ) s SMB h HML d DRF
3.6 Augmented four-factor model and empirical evidence 161

Market-based distress risk factor and regression results

In order to test whether different methods for predicting distress risk affect the empirical results, we proceed the Merton's option-pricing model (market-based model) in predicting default probability, which is later applied by [START_REF] Vassalou | Default Risk in Equity Returns[END_REF]. Vassalou and Xing denote Merton's default probability as DLI (Default Likelihood Indicator), follow which we calculate the default probability of CNAS stocks.

Table 3.10 displays the summary statistics of 18 SBPD sorted portfolios, the structure of the table is similar to Table 3.8 except the proxy for distress risk is DLI instead of O-score. Not surprisingly that average excess returns are negatively related to firm size, however, the relationship between average excess return and B/P ratio or DLI is chaotic. The relationship between size and DLI is not as clear as that between size and O-score, while it seems that B/P ratio increases as DLI increases except the portfolio SL1. Next, we will implement the TSRs to investigate how the four factors explain average excess returns and to figure out the relationship among stock returns, size, B/P ratio and distress risk.

The TSRs' results on the augmented four-factor model of 18 SBPD sorted portfolios are reported in Table 3.11. It shows pretty much the same results as that of 18 SBPO sorted portfolios in Table 3.9. All the regression coefficients for excess market return and SMB are highly significant, and excess stock returns are negatively related to firm size. Exceptionally, β(d), the coefficients of DLI DRF , are significant for both the lowest DLI portfolios (with negative loadings) and the highest DLI portfolios (with positive loadings), consistent with [START_REF] Vassalou | Default Risk in Equity Returns[END_REF], we find positive relationship between excess stock returns and distress risk on Chinese market, but only in the lowest or (and) highest DR (DLI) portfolios. Our results are contrary to some literature 45 that conclude the high default risk is not rewarded by higher returns. Comparing with the TSRs on FF3F model of the same 18 SBPD portfolios (Appendix F), in the presence of augmented DRF (DLI as proxy for DR), FF factors do not lose their explanatory power, however, the four-factor model indeed capture slightly more variation of the 18 SBPD sorted portfolios' return (with average adjusted R-square 0.9027) than the original FF3F Model (with average adjusted Rsquare 0.8980).

We can conclude that the excess market returns and size factor SMB are always highly positively related to excess average stock returns, and big size stocks always have lower average returns. The value factor HML also has explanatory power in explaining the timeseries average stock returns, but only exist in the extreme (lowest or highest) B/P groups. In addition, there exists significant distress risk effect on CNAS stock market over the sample In this table, the time-series regressions' results for 18 portfolios formed on size, B/P ratio and DLI are presented. The stocks are divided into two size groups based on the breakpoint of median market capitalization, and the breakpoints for the three B/P groups are the top 30%, median 40% and bottom 30% of B/P ratio (named Low, Medium and High), similarly as B/P groups, the stocks are divided into three groups based on their DLI (named D1, D2, and D3, represent the low, medium and high DLI separately). The intersection of two size groups, three B/P groups and DLI groups form 18 portfolios. The left part of the table is the coefficients of time-series regressions and adjusted R-square, the right part is the relative t-statistics corrected for heteroscedasticity and autocorrelation using Newey-West estimator and residual standard error, and the numbers in bold are significant at 5% confidence level. Regression: period, the explanatory power of DRF exists in the extreme top (highest DR) and bottom (lowest DR) portfolio groups. FF factors cannot proxy for DRF, instead, DRF explains average stock returns in combination with FF factors on CNAS stock market. However, the additional explanatory power of DRF is limited. Besides, the distress risk factor constructed based on DLI seems performs better than that constructed based on O-score.

         i ,t f i i M ,t f i i i DLI i ,t R R a b ( R R ) s SMB h

Cross-sectional regressions of the augmented four-factor model

Furthermore, we also conduct the CSRs using FM two-stage approach to examine whether the augmented four-factor model is able of capturing the variation of the cross-sectional average excess stock returns. The CSR formula is as follows: The empirical results are reported in Table 3.12, in Panel A, the DR is estimated by O-score, while in Panel B, the DR is measured by DLI. Each panel contains three parts, which report respectively the CSR results of the three kinds of regressions (denoted as R1, R2 and R3) mentioned above. The first row in each part is the average of 119 CSR coefficients, and the corresponding FM t-stats and EIV adjusted t-stats (SH t-stats) are reported in the bracket below the coefficients. The averaged adjusted R-squares are reported in the last columns in percentage values.

             i ,
The results in both Panel A and Panel B are much the same. No matter regressing the 18 portfolios on only market factor (R3) and DRF (both constructed based on O-score and DLI) or on FF3F Model (R2), loadings on DRF is never an important determinant of average returns. Furthermore, comparing the first two regressions (R1 and R2), FF factors (market beta and SMB of Panel A, SMB of Panel B) do not lose their explanatory power in the presence of DRF. We might conclude that though DRF is a priced factor in determining time-series average returns, it is not the case in determining cross-sectional average returns on CNAS stock market over the sample period.

The results also indicate that no matter the DRF is constructed using O-score or DLI as proxy, neither value factor HML and distress risk factor DRF is able to capture the crosssectional variation in average stock returns. The evidence again proves the existence of size premium on CNAS stock market.

Conclusions

We use both accounting-based model (O-score) and market-based model (DLI) to estimate distress risk and construct a mimicking distress risk factor on CNAS stock market. We first examine whether there exist size effect and value effect controlled by default risk or in the whole sample during our research period in China. The results suggest that there only exists size effect but this effect seems not related to distress risk, and this effect do not depend on the method we use to estimate the distress risk.

Following literature such as Vassalou and Xing that investigate whether the Fama-French factors can be proxy by distress risk factor, we augment FF3F model by adding a mimicking distress risk portfolio (DRF). We examine the variation of excess average returns of 18 Size-B/P-DR sorted portfolios explained by the augmented four-factor model both through time-series and CSRs. From the TSRs, we conclude that the explanatory power of FF three factors do not has significant change with or without the DRF is presented in the model. FF factors cannot proxy for DRF, instead, DRF explains time-series average stock returns combining with FF factors on CNAS stock market; most contributions to the excess average returns of value factor HML and distress risk factor DRF are concentrated in the extreme top or bottom portfolios, and the average returns are positively related to the distress risk. However, the additional explanatory power of DRF is limited. Comparing the regression results by using O-score and DLI as proxy of distress risk, the distress risk factor constructed based on DLI seems performs slightly better than that constructed based on O-score.

We provide evidence from the CSRs that no matter the DRF is constructed using O-score or DLI as proxy, there exists robust size premium (robust market premium when DR is Chapter 3 Distress Risk Factor and Stock Returns on Chinese A-Share Stock Market 168 estimated using O-score), neither value factor HML and distress risk factor DRF is able to capture the cross-sectional variation in average stock returns. Thus, FF factors cannot proxy as DRF in the cross-section on CNAS stock market over the sample period.

General conclusions

The main objective of this dissertation is to explore the risk factors and factor models on CNAS stock market based on the context of FF3F Model.

The main results of this dissertation are presented as follows:

-First of all, we re-examine the applicability of FF3F Model considering several special features of Chinese stock market during July 2004 to May 2015. The empirical results show that FF3F Model can explain a majority of time-series variation of the CNAS stock returns during the research period, when using tradable market value to weight the portfolios, total market capitalization to decide the size breakpoint and B/P ratio instead of B/M ratio. The CSRs results are consistent with most of the previous studies on Chinese stock market, market beta and SMB are important determinants in explaining the cross-sectional variation in the average stock returns over the sample period. There exists negative market premium and positive size premium on CNAS stock market, however, we find no value premium during the sample period. Those findings are robust with EIV adjustment and are independent of research interval.

-We also investigate the applicability of the latest FF5F Model on CNAS stock market during the period July 2010 to May 2015. To proceed with this examination, we construct three sets of portfolios, six value-weighted Size-B/P portfolios, six value-weighted Size-OP portfolios and six value-weighted Size-Inv portfolios. For all the three sets of portfolios, the original three factors -market factor, size factor and value factorstill have strong time-series explanatory power for the expected excess returns in the presence of profitability and investment factors. There always exists size effect in all three sets of portfolios and the excess returns are negatively related to firm size; there exists value effect in SBP portfolios, profitability effect in Size-OP portfolios and investment effect in Size-Inv portfolios. The explanatory power of RMW factor only exists in the six Size-OP portfolios. CMA factor explains the average return of portfolios that only in the extreme OP or Inv groups (such as the weak OP group, robust OP group, the aggressive and conservative Inv groups); while the significant loadings on CMA for the Size-B/P portfolios are relatively dispersive.

-Comparing the performance of both FF3F Model and FF5F Model on CNAS stock market, in the presence of profitability and investment factors, FF5F Model seems not capture more variations of expected stock returns than the three-factor model except the six value-weighted portfolios formed on size and operating profitability (though the improvement is limited) on CNAS stock market during the research period July 2010 to May 2015. However, the research period is relatively short in this study, we suggest to apply the examination with longer time interval for the FF5F Model on Chinese stock market in the future.

-We examine in chapter 2 whether FF factors SMB and HML proxy for the innovations of selected state variables (aggregate dividend yield, one-month T-bill rate, term spread and default spread) that describe future investment opportunities on CNAS stock market during the period December 2006 to May 2015. Both timeseries and CSRs are performed on five comparative models. The empirical results indicate that FF factors don't lose their explanatory power with or without the presence of the innovations of selected four state variables in both the time-series and cross-sectional examinations on CNAS stock market over the research period.

Evidence from the CSRs also reveals that there are significant market risk premium and size premium. We find the information contained in the innovation of aggregate dividend yields (IDIV) seems totally captured by the combination of market beta and size factor. FF factors might have played a limited role in capturing alternative investment opportunities proxied by innovations of the selected four state variables.

-Since we find that FF factors cannot proxy for innovations of selected state variables on CNAS stock market, for the sake of the meaning behind them, we examine whether FF factors proxy for distress risk factor and compare whether different methods of constructing factors result in the different outcomes. The empirical results suggest that there is no significant evidence that FF factors are proxying for distress risk on CNAS stock market. The presence of DRF has little effect on the time-series explanatory power of FF three factors, instead, DRF can explain partially the time-series excess average stock returns combining with FF three factors. Comparing the TSR results by using two different methods as proxy of distress risk, the distress risk factor constructed based on DLI seems performs slightly better than that constructed based on O-score in capturing time-series average returns. However, DRF is not an important determinant of cross-sectional average returns, and FF factors cannot proxy as DRF in the cross-section on CNAS stock market during our research period July 2005 to May 2015.

Moreover, our studies on the risk factors in China presented in this dissertation have also provided new implications in practice on Chinese stock market:

First of all, considering several special features of Chinese stock market, our results indicate that the market beta and size factor SMB are important determinants of crosssectional average stock returns. And the existence of size premium and lack of value premium on CNAS stock market seem independent of the research period. Based on those findings of FF3F Model on Chinese stock market, such as asset managers, they can build portfolios that tilt towards the size factor SMB but not the value factor HML so that to gain the size premium. Furthermore, asset managers or the individual investors are able to assess the potential performance of a portfolio relative to the FF3F Model as a benchmark.

Then from the results of examination of FF5F Model on CNAS stock market, we conclude that the profitability and investment factors have limited additional explanatory power, and Fama-French Five-Factor Model does not have significant improvement in explaining average excess stock returns comparing with the original three-factor model on CNAS stock market, which is inconsistent with the findings on U.S. stock market. Similarly, if investors want to invest in Chinese stock market, it's better and easier to select the portfolios that constructed based on FF3F instead of FF5F Model. However, if investors invest on U.S. stock market, it is wiser to choose their portfolios that constructed based on FF5F Model, since FF5F Model performs better than FF3F Model on U.S. stock market.

In addition, our attempts to find the economic explanation of FF factors on Chinese stock market suggest that FF factors don't lose their explanatory power in the presence of the innovations of selected state variables in both time-series and CSRs on CNAS stock market over the research period, and the presence of innovations of state variables do capture more variation of average returns than original FF3F Model. The findings indicate that on Chinese stock market, constructing portfolios tilt towards the innovations of the four economic variables cannot gain extra risk premium in addition to the FF factors. FF3F Model seems to be the best choice in practice so far on Chinese stock market.

Finally, our findings in the last chapter suggest that FF factors are not proxy of distress risk on CNAS stock market, instead, the distress risk factor explains the time-series excess average stock returns combining with FF three factors. The augmented four-factor model explains the time-series variation of average excess stock returns slightly better than FF3F Model on CNAS stock market. In this case, for example, if constructing portfolios tilt towards our mimicking distress risk factor in addition to FF factors, one can expect more average returns than constructing portfolios only based on the original FF factors. However, the extra benefit comes from distress risk factor is limited. Moreover, for instance, our findings are also can be implemented by companies to estimate the cost of equity; by investors to evaluate the inherent value of equities and to make their decisions.

All in all, in order to keep up with the pace of China's reforms and the globalization of its economy, the Chinese stock market has experienced fast development and overall institutional reforms. Considering the special features, the asset returns and its determinants might be different between Chinese stock market and those of developed stock markets such as U.S. and European markets. Our present research fails to find the economic explanation for the success of FF factors on CNAS stock market, therefore, we propose to consider the risk factors which feature the special characteristics of the Chinese stock market or other economic variables that related to stock returns in further researches. This table presents the time-series regressions results of FF5F model. In each panel, the regression intercept a , the regression coefficients b , s , h , r and c of market factor, size factor, value factor, profitability factor and investment factor, adjusted R square are respectively presented in the left part of the table, the corresponding t-statistics corrected for heteroscedasticity and autocorrelation using the Newey-West estimator and residual standard error are presented in the right part. Panel A is the regressions on six Size-B/M portfolios, across the columns are the two size groups (Small and Big) and across the rows are the three B/M groups (Low, Medium, and High). Panel B is the regression results of six Size-OP portfolios, same as Panel A, across the columns are the two size groups and across the rows are the three OP groups (Weak, Neutral and Robust). Panel C is the regression results of six Size-Inv portfolios, across the columns are the two size groups and across the rows are the three Investment groups (Aggressive, Neutral and Conservative). Numbers in bold are the t-stats which are significant at 5% confidence level.

Regression:

  (period: July 2004-May 2015) ............................................................................................. 41 Table 1.4 Summary statistics of Fama-French three factors and correlation coefficients among variables (July 2004-May 2015) .............................................................................. 42 Table 1.5 Descriptive statistic of Fama-French 25 Size-B/P portfolios (July 2004-May 2015) ..................................................................................................................................... 43 Table 1.6 Time-series regression of six value-weighted Size-B/P portfolios on Chinese Ashare stock market (July 2004-May 2015, 131 months) ..................................................... 45 Table 1.7 Time-series regressions of 25 value-weighted Size-B/P portfolios on FF3F Model, Chinese A-share stock market (July 2004 -May 2015; 131 months) .................................. 46 Table 1.8 Cross-sectional regressions of six value-weighted Size-B/P portfolios and 25 value-weighted Size-B/P portfolios, Chinese A-share stock market (July 2004-May 2015) .............................................................................................................................................. 51

(

  2010-2014) .......................................................................................................................... 55

  and Size-Inv (July 2010-May 2015, 59 months) .................................................................. 58 List of Tables viii

  Figure 1.1 SHASHR Index and SZASHR Index (1992-2015) .............................................

  Figure 1.1 SHASHR Index and SZASHR Index (1992-2015) .............................................

Figure 1

 1 Figure 1.2 SHASHR Index and NYSE Composite Index (1992-2015) ...............................

Figure 1 . 3

 13 Figure 1.3 Total listed firms and that of SSE and SZSE, listed stocks of A-share stock market (1990-2014) ..............................................................................................................

Figure 1 . 4

 14 Figure 1.4 Total market capitalization and that of A-share and B-share stock market (unit:100 million yuan; 1992-2014) .....................................................................................

Figure 1 . 5

 15 Figure 1.5 Loadings of 25 Size-B/P portfolios on FF3F ......................................................

Figure 1 . 6

 16 Figure 1.6 Annual number of firms that has available data of OP and Inv ..........................

Figure 3 . 1

 31 Figure 3.1 Equity as a European call option on the firm ....................................................

Figure 3 . 2

 32 Figure 3.2 Annual aggregate O-score (2005-2014) ............................................................

Figure 3 . 3

 33 Figure 3.3 Annual aggregate DLI (2005-2014) ..................................................................

  ), 'Long-run Return Performance following Listed Rights Issue: Based on the Improved Three-factor Model', Journal of Financial Research 5: 114-129 (in Chinese). 10 Liao, L. and Shen, H-B. (2008), 'Fama-French Three Factors Model and the Effect of the Splitshare Structure Reform', The Journal of Quantitative and Technical Economics 9: 117-125 (in Chinese) 11 Liu, G-M. and Yang, C. (2010), 'Application of Fama-French Multi-Factor Model in China's Bond Market during Recent Financial Crisis', Journal of Zhejiang University (Science Edition) 4: 396-400 (in Chinese).

Figure 1 .

 1 Figure 1.1 14 shows the performance of both Shanghai Stock Exchange A-Share (SHASHR) Index and Shenzhen Stock Exchange A-Share (SZASHR) Index from 1992 to 2015. It contains two parts, index point (white for SHASHR Index and green for SZASHR) and volume (grey for SHASHR and rose red for SZASHR). SHASHR Index has averaged 1921.11 index points from 1992 until 2015, reaching the highest 6395.76 index points in October of 2007 and a record low of 293.75 index points in January of 1992. SZASHR Index reaches the record high also in 2007 (2015 not included), a record low of 95.26 in July 1994, and has averaged 681.16 index points from 1991-2015. Both indexes have the volume increased before 2007 and change unstable after, until 2014 and 2015, both indexes have a remarkable growth. Figure 1.2 shows the performance of both SHASHR Index and NYSE Composite (NYA) Index in U.S., in the upper part, the white line is SHASHR Index

Figure

  Figure 1.1 SHASHR Index and SZASHR Index (1992-2015)

Figure

  Figure 1.2 SHASHR Index and NYSE Composite Index (1992-2015)

  .4, it is obvious that the Chinese stock market has undergone a dramatic growth since its establishment in 1990. The total listed firms increase sharply during 25 years (from 10 total listed firms in 1990 to 1088 in 2000, and 2613 total listed firms in the year 2014), and total market capitalization from RMB 104.8 billion (year 1992) to 37 254.7 billion (year 2014). The total listed stocks in A-share stock market increased from 53 (year 1992) to 2592 (year 2014) with a combined market capitalization of RMB 97.8 billion in 1992 to 37 082.3 billion in 2014.

Figure 1 . 3 Figure 1 . 4

 1314 Figure 1.3 Total listed firms and that of SSE and SZSE, listed stocks of A-share stock market (1990-2014)

Figure 1 . 5

 15 Figure 1.5 Loadings of 25 Size-B/P portfolios on FF3FThis figure represents the time-series regressions loadings on FF three factors of 25 value-weighted Size-B/P portfoliosb, s, h, separately. On the x-axis are the 25 portfolios from S1H1 (smallest size and lowest B/P ratio) to S5H5(biggest size and highest B/P ratio), noting that in the middle panel, five portfolios of the same B/P quintile are grouped together in the order of increasing size, whereas in other two panels, five portfolios of the same size quintile are grouped together in the order of increasing B/P ratio.Regression: i ,t

Figure

  Figure 1.5 Continued

Figure 1 . 6

 16 Figure 1.6 Annual number of firms that has available data of OP and Inv

1. 5

 5 Construction of profitability and investment factors and empirical results of FF5F

  and a new wave was formed in the development field of financial theories with the aim of explaining the causes of these special consequences.

  2 Fama-French Factors and Innovations in State Variables on Chinese A

Model

  Model 4 with Model 1 and Model 5 with Model 2, including innovations of state variables or not in the regression model do not change the performance of FF factors (innovations of FF factors) in capturing time-series variation of expected stock returns. The innovations of state variables that describe time variation in investment opportunities have little or marginal effect when adding them into FF3F Model or model with innovations of FF factors as independent variables. Comparing Model 4 and Model 5, the results prove again the high correlation between FF factors and their innovations, since the regressions results are much alike from both models.We can conclude that FF factors (or innovations of FF factors) explain the time-series variation of expected stock returns well, with or without the innovations of state variables are included in the model. When the four innovations of state variables are regressed alone,

Model

  ........................................................................................... 3.2 Measurement of financial distress risk ................................................................ 3.3 Financial distress risk and equity returns ............................................................. 3.4 Construct distress risk factor and portfolios on Chinese stock market ................ 3.5 Distress risk, size and B/P ratio of Chinese stock market ................................... 3.6 Augmented four-factor model and empirical evidence ....................................... 3.7 Conclusions ..........................................................................................................

Chapter 3

 3 Distress Risk Factor and Stock Returns on Chinese A-Share Stock Market 124

Figure 3 . 1

 31 Figure 3.1 Equity as a European call option on the firm



  in equation (3.6) which implies that the equity value can be represented as a function of the asset value, Merton applies Ito's Lemma 35 to determine an instantaneous standard deviation of equity that can be otherwise estimated from the historical share prices.Follows from Ito's lemma, the relation between equity value volatility E  and the asset value volatility A  is as follows:

  [START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF] compare the performance of two accounting-based models (Altman's Z-score and Ohlson's O-score) and the market-based model (BSM optionpricing model), and their results demonstrate that BSM model provides significantly more information of bankruptcy probability than both accounting-based models. They recommend researchers to apply BSM model instead of Z-score and O-score proceeding the research.

  ) Equation (3.17) represents the change in aggregate survival rate   SV  at time t. The authors also examine the correlation between   SV  and several commonly used default spreads 42 , the low correlations indicate that the information captured by their   SV 

  by using data of Chinese listed firms during 2000 to 2010, and the results reveal that the DLI based on Merton's model is a significant model for predicting distress risk on Chinese stock market. What's more, the author augments the original Merton-KMV model with financial ratios (profitability, leverage, and liquidity) and compare the augmented model with Merton-KMV model and accounting-based model. The evidence shows that the original Merton-KMV model can be improved by an augmented model and the accounting-based model is the weakest one in measuring default risk on Chinese stock market.

  annual aggregate O-score and aggregate DLI from 2005 to 2014 are presented in Figure 3.2 and Figure 3.3 respectively, from which we could see that the tendency of both figures is similar. Both the aggregate O-score and aggregate DLI increase dramatically from 2008 to 2009, the period which is well known as the recession period because of the worldwide financial crisis, while the aggregate default probability decreases sharply (2009-2010) during the period of economic recovery.

Figure

  Figure 3.2 Annual aggregate O-score (2005-2014)

  summary statistics of four factors are shown in Table3.8 Panel A presents the statistic description of four factors, the time-series mean of market premium (0.0024), SMB (0.0119) and O score DRF  (0.0010) are positive, while that of HML(-0.0020)



  estimated coefficients of the market factor, size factor SMB, value factor HML and distress risk factor DRF obtained from TSRs; DRF are the coefficients of CSRs.Following equation (3.19), the CSRs are performed each month (119 months, July 2005 to May 2015) by regressing the excess returns of 18 Size-B/P-DR sorted portfolios on the coefficients obtained from the TSRs, thus we have 119 sets of CSR coefficients. The gammas are then calculated by taking the simple average of the 119 sets of CSR coefficients. Similarly, we also report both the FM t-stats and the EIV adjusted t-stats as in previous chapters. And we also examine the four-factor model with DRF estimated based on O-score and DLI, respectively.In order to examine whether FF factors proxy for DRF in capturing the cross-sectional variation of average stock returns, we perform three kinds of regressions on (1) the augmented four-factor model as presented in equation (3.19); (2) the original FF3F Model; and (3) only excess market return and DRF using 18 Size-B/P-DR (O-score or DLI) portfolios.

Table 1 .

 1 1 Summary of Chinese stock market 1990-2014 .................................................... 34 Table 1.2 Annual average available number of firms that have required data (2001-2014) 40 Table 1.3 Descriptive statistic of Fama-French six value-weighted Size-B/P portfolios

  ........ 54 Table 1.10 Annual number of stocks in 25 Size-OP portfolios and 25 Size-Inv portfolios

Table 1 .

 1 11 Annual number of stocks in six Size-OP portfolios and six Size-Inv portfolios 56 Table 1.12 Summary statistics of Fama-French five factors (July 2010-May 2015) ........... 57 Table 1.13 Average monthly excess returns for portfolios formed on Size-B/M, Size-OP

La mé diane de la capitalisation boursiè re

				Petit Bas	Grand Bas
			30e percentil B/P
			Petit Moyen	Grand Moyen
			70e percentil B/P
				Petit Haut	Grand Haut
	Les facteurs SMB et HML est construit comme suit:
	SMB	 	1 3 3 ( Petit Bas+Petit Moyen+Petit Haut) 1 ( Grand Bas+Grand Moyen+Grand Haut )	(4)
	HML	11 ( Petit Haut+Grand Haut ) 22 	( Petit Bas+Grand Bas )

Chapitre 3 Facteur de Risque de Dé tresse et Rentabilité s des Actions sur le Marché Boursier Chinois Objectif

  13) Le modè le 1 repré sente les ré gressions chronologique sur la rentabilité excé dentaire du marché , les innovations des variables d'é tat et les innovations des facteurs FF SMB et HML (ISMB et IHML). Le modè le 2 repré sente les ré gressions chronologiques sur la rentabilité excé dentaire du marché , les innovations des variables d'é tat et les facteurs FF initiaux SMB et HML. Les variables indé pendantes dans le modè le 3 sont les rentabilité s excé dentaire du marché et quatre innovations des variables d'é tat. Dans le modè le 4, les variables indé pendantes sont les rentabilité s excé dentaire du marché et les innovations de SMB et HML. Le modè le 5 n'est que le Modè le FF3F original.Nous pouvons conclure que les facteurs FF (ou les innovations des facteurs FF) expliquent bien la variation des sé ries chronologiques des rentabilité s attendus des actions, avec ou sans les innovations des variables d'é tat dans le modè le. Lorsque les quatre innovations des variables d'é tat sont respectivement ré gressé es, seulement IDIV a un pouvoir explicatif pour la rentabilité moyenne; en pré sence de facteurs FF (ou des innovations des facteurs FF), IDIV perd sa capacité à capturer les variations des rentabilité s chronologiques attendus.La pré sence des quatre innovations de variables d'é tat qui pré voient des opportunité s d'investissement futures ne expulse pas les facteurs FF. L'information contenue dans l'innovation des rendements de dividende IDIV semble totalement capturé e par la tudie la relation entre les rentabilites des actions et le risque de dé tresse, et aussi examine si l'effet de taille et l'effet de valeur sont lié s au risque de dé tresse sur le marché boursier chinois A-share. De plus, nous explorons un modè le à quatre facteurs en ajoutant un facteur de risque de dé tresse en plus des trois facteurs FF afin d'examiner si facteurs FF sont des proxys de facteurs de risque de dé tresse. Nous examinons si diffé rentes mé thodes de construction des facteurs entraî nent des ré sultats diffé rents.

	La
	Modè le 5
	 R R i ,t	f	  i  	i ,m	M ,t ( R		f R )			i ,SMB	SMB			i ,HML	 HML e i ,t	(14)

Nous ré alisons les sé ries chronologiques suivant les cinq modè les ci-dessus et ré alisons é galement les ré gressions transversales correspondant aux cinq modè les comparatifs. Ré sumé de la thè se en franç ais xxx Ré sultats et conclusions combinaison du marché bê ta et le SMB (ou ISMB). Bien que le modè le comporte à la fois des facteurs FF et des innovations de variables d'é tat (comme les facteurs de risque) effectue lé gè rement meilleurs que le Modè le FF3F original (compte tenu de R-carré moyenné ajusté ), les FF facteurs ont pu jouer un rôle limité en capturant d'opportunité s d'investissement alternatives repré senté es par les innovations des variables d'é tat.

L'é tude du chapitre 2 est basé e sur l'une des trois thé ories spé cifiques les plus discuté es: l'exposition aux changements dans les variables é conomiques dans le contexte de l'ICAPM (les deux autres thé ories spé cifiques sont le risque de dé tresse et l'exposition asymé trique aux conditions é conomiques). Les ré sultats dé montrent que les facteurs FF ne repré senter pas les innovations des quatre variables sé lectionné es sur le marché boursier chinois Ashare pendant la pé riode de dé cembre 2006 à mai 2015. Une autre explication thé orique, le risque de dé tresse, est é tudié dans ce chapitre. Puisque une explication de la performance des rentabilité persistants des hauts B/M actions est le risque de dé tresse financiè re.

xxxi Ce chapitre é

mesure de risque de dé tresse financiè re

  Parmi les mé thodes de pré vision du risque de dé tresse, l'utilisation de ratios comptables et d'informations sur le marché sont deux classifications dominantes. Les modè les qui

utilisent des ratios comptables pour estimer le risque de dé tresse s'appellent les modè les basé s sur la comptabilité , par exemple, le 'Z-score' de

[START_REF] Altman | Financial ratios, discriminant analysis and the prediction of corporate bankruptcy[END_REF]

et le 'O-score' de

  Tout d'abord, nous trouvons qu'il existe un effet de taille fort, mais aucun effet de valeur. L'effet de taille et le manque d'effet de valeur sont robustes lorsqu'ils sont contrôlé s par le risque de dé tresse ainsi que sur l'ensemble de l'é chantillon du marché boursier chinois. Et les effets sont é galement solides pour les proxys diffé rentes du risque de dé tresse.À partir des ré gressions chronologique, nous trouvons qu'il existe un effet de risque de dé tresse significatif, les portefeuilles qui ont le risque de dé tresse plus haut portent meilleure rentabilité s sur le marché boursier chinois A-share, le pouvoir explicatif de DRF existe dans le top extrê me (plus haut DR) et le bas (plus bas DR) groupes de portefeuille. Le pouvoir explicatif des trois facteurs de FF n'a pas de changement significatif avec ou sans DRF est pré senté dans le modè le, nous pouvons donc conclure que les facteurs FF ne peuvent pas repré senter DRF, le DRF explique plutôt les rentabilité s chronologiques moyennes en combinaison avec des facteurs FF sur le marché boursier chinois A-share. Toutefois, le pouvoir explicatif supplé mentaire de DRF est limité . 'objectif principal de cette thè se est d'explorer les facteurs de risque et les modè les des facteurs sur le marché boursier chinois A-share sur le contexte du modè le facteur de Fama-French.Les ré sultats principaux de cette thè se sont pré senté s comme suit: Tout d'abord, l'applicabilité du Modè le FF3F est ré -examiné pendant la pé riode de juillet 2004 à mai 2015, en tenant compte de plusieurs caracté ristiques spé cials du marché boursier chinois. Les ré sultats empiriques montrent que le Modè le FF3F peut expliquer la majorité des variations de sé ries chronologiques des rentabilité s des actions chinoises A-Le pouvoir explicatif du facteur RMW n'existe que dans les six portefeuilles Taille-OP. Le facteur CMA n'explique les rentabilité s moyennes des portefeuilles que dans les groupes OP ou Inv extrê mes, par exemple le groupe OP faible, le groupe OP robuste, les groupes Inv conservatifs et agressifs. Tandis que les coefficients significatives sur CMA pour les portefeuilles Taille-B/P sont relativement dispersives. xxxv D'après la comparaison des performances des modè les FF3F et FF5F en pré sence de facteurs de rentabilité et d'investissement, le Modè le FF5F ne peut pas capturer plus de variations des rentabilité s des actions attendus que le Modè le FF3F, à l'exception des six portefeuilles pondé ré es en valeurs qui formé s à partir de la taille et de la rentabilité opé rationnelle (mê me si l'amé lioration est limité e).Dans le chapitre 2, nous examinons si les facteurs FF SMB et HML, sont les proxys d'innovations de variables d'é tat sé lectionné es (rendement de dividende agré gé e, taux de Tbonds en un mois, l'écart de terme et l'écart de défaut) qui dé crivent, pendant la pé riode recherche, les opportunité s futures d'investissement sur le marché boursier chinois A-share. Les ré gressions chronologiques et les ré gressions transversales sont ré alisé es sur cinq modè les comparatifs. Les ré sultats empiriques indiquent que les facteurs FF ne perdent pas des rentabilité s transversale des actions. Et l'existence de prime de taille et le manque de de prime de valeur sur le marché boursier chinois A-share sont indé pendantes de la pé riode de recherche. Basé sur les ré sultats du Modè le FF3F sur le marché boursier chinois, tels que les gestionnaires d'actifs, ils peuvent cré er des portefeuilles qui inclinent vers le facteur de taille SMB plutôt que le facteur de valeur HML afin de gagner la taille de prime. De plus, les gestionnaires d'actifs ou les investisseurs individuels sont capable d'é valuer la performance potentielle d'un portefeuille par rapport au Modè le FF3F comme l'indice de ré fé rence.Ensuite, selon les ré sultats de l'examen du Modè le FF5F sur le marché boursier chinois Ashare, nous concluons que les facteurs de rentabilité et d'investissement ont un pouvoir explicatif supplé mentaire limité et en comparaison avec le modè le original à trois facteurs, Enfin, dans chapitre 3, il est dé montré que les facteurs FF ne sont pas les proxys du facteur du risque de dé tresse sur le marché boursier chinois, le facteur de risque de dé tresse, combiné avec les trois facteurs FF, explique plutôt la rentabilité moyenne excé dentaire des sé ries chronologiques. Le modè le augmenté à quatre facteurs explique la variation chronologique des rentabilité s moyennes des action meilleur que celui du Modè le FF3F. Dans ce cas, par exemple, si les portefeuilles sont construisent, en plus des facteurs FF, incline vers le facteur de risque de dé tresse imitant, on peut s'attendre à plus de rentabilité moyennes que les portefeuilles qui sont construisent uniquement basé sur des facteurs FF les investisseurs pour é valuer la valeur inhé rente des actions et pour prendre leurs dé cisions. Dans l'ensemble, afin de suivre le rythme des ré formes de la Chine et de la mondialisation de son é conomie, le marché boursier chinois a connu un dé veloppement rapide et des ré formes institutionnelles globales. Compte tenu des caracté ristiques spé cials, les rentabilité s des actifs et ses dé terminants pourraient ê tre diffé rents entre le marché boursier chinois et ceux des marché s boursiers dé veloppé s (tels que le marché amé ricain et le marché europé en). Nos recherches actuelles ne peut pas de trouver l'explication é conomique du succè s des facteurs FF sur le marché boursier chinois A-share, nous proposons donc d'examiner les facteurs de risque qui pré sentent les caracté ristiques particuliè res du marché boursier chinois ou d'autres variables é conomiques relatif aux rentabilité s des actions dans les recherches futures.

Dans ce chapitre, les données de recherche proviennent d'une pé riode de juillet 2005 à mai 2015 (119 mois). Dans la recherche des deux mé thodes, les entreprises financiè res, dont la structure capitale se distingue de celle des ordinaires, est exclu. Les entreprises ayant un ratio B/P né gatif sont é galement retiré de l'é chantillon. Puisque cet recherche se concentre sur les entreprises saines, les entreprises qui ont qualifié 'Traitement spé cial' et 'Transfert particulier' en Chine sont é galement hors de notre considé ration.

Pour procé der la recherche et pour effectuer la comparaison, tout d'abord,la probabilité par dé faut est calculé e en appliquant la formule de O-score d'Ohlson (mesure basé e sur la comptabilité ) et une procé dure ité rative complexe est utilisé pour ré soudre le modè le de 'option-pricing' afin de calculer le DLI (mesure basé e sur le marché ). Ces probabilité s par dé faut sont ensuite utilisé es comme un critè re principal pour la distinction du risque de dé tresse des entreprises.

Les proxys du risque de dé tresse que nous utilisons sont les DP calculé s par O-score et DLI. À la fin de chaque mois de juin de l'anné e t, nous classons les actions selon leur O-score (ou DLI) de fin d'anné e t-1 en trois groupes, dé signé s comme O1, O2 et O3 (ou DLI1, DLI2, DLI3) de bas à haut des probabilité s dé fauts. Les points des reptures sont 30% et 70% des percentiles du O-score (ou DLI) d'é chantillonnage. Les portefeuilles restent immuables de juillet de l'anné e t à juin de l'anné e t+1, et il sont ré formé s à la fin de juin de l'anné e t+1. Les donné es sont traité comme ç a pour toute la pé riode de recherche. Le portefeuille imitant DRF est le facteur de risque de dé tresse, qui mesure la diffé rence de rentabilité entre le portefeuille DP haut (O3 ou DLI3) et le portefeuille DP bas (O1 ou DLI1).

Les comparaisons sont effectué es entre les ré sultats obtenus à partir des deux modè les diffé rents (le modè le basé sur la comptabilité et le modè le basé sur le marché ). Ensuite, de la mê me maniè re que les chapitres pré cé dents, l'approche à deux é tapes de Fama-MacBeth et la mé thode ajusté e EIV de Shanken sont appliqué pour ré aliser les ré gressions.

xxxiii

Ré sultats et conclusions

Par ailleurs, en comparant les ré sultats de ré gression selon en utilisant O-score et DLI comme les proxys du risque de dé tresse, la performance du facteur de risque de dé tresse basé sur le DLI semble lé gè rement meilleure que celui basé sur le O-score.

Nous fournissons des preuves à partir des ré gressions transversales que les coefficients sur DRF ne sont jamais un dé terminant important des rentabilité s moyennes, peu importe le DRF est ré gressé avec le marché bê ta ou des trois facteurs de FF. D'autre part, peu importe le DRF est construit en utilisant O-score ou DLI comme le proxy, il existe une prime de taille robuste (prime de marché robuste lorsque DR est estimé en utilisant O-score). Ni le facteur de valeur HML ni le facteur de risque de dé tresse DRF est capable de capturer les variations transversale sur les rentabilité s moyennes des actions.

Les é tudes empiriques montrent que les facteurs FF ne perdent pas leur pouvoir explicatif en pré sence de DRF. Nous pourrions conclure que, bien que DRF est un facteur é valué pour dé terminer les rentabilité s chronologiques moyennes, il n'est pas le cas pour dé terminer les rentabilité s transversales moyennes. Les facteurs FF ne peuvent pas repré senter DRF dans la section transversale du marché boursier chinois A-share.

Ré sumé de la thè se en franç ais xxxiv

Conclusions gé né rales

Lshare, en utilisant la valeur marchande né gociable pour pondé rer les portefeuilles et la capitalisation boursiè re totale pour dé cider le point de rupture de taille, et le ratio B/P au lieu du ratio de B/M. Les ré sultats des ré gressions transversales sont conformes aux la plupart des é tudes anté rieures sur le marché boursier chinois, le marché bê ta et le SMB sont des dé terminants importants pour expliquer la variation transversale des rentabilité s moyennes des actions. Au cours de la pé riode d'é chantillonnage, il existe une prime de marché né gative et une prime de taille positive sur le marché boursier chinois A-share, mais aucune prime de valeur est trouvé . Ces ré sultats sont robustes avec l'ajustement EIV, et indé pendants de l'intervalle de recherche.

L'applicabilité du dernier Modè le FF5F sur le marché boursier chinois A-part est aussi é tudié au cours de la pé riode de juillet 2010 à mai 2015. Afin de ré aliser cette é tude, trois sé ries de portefeuilles, six portefeuilles Taille-B/P pondé ré s en valeur, six portefeuilles Taille-OP pondé ré s en valeur et six portefeuilles Taille-Inv pondé ré s en valeur, sont construisons. Pour tous les trois sé ries de portefeuilles, les trois facteurs originauxle facteur de marché , le facteur de taille et le facteur de valeurpossè dent toujours un pouvoir explicatif des sé ries chronologiques pour les rentabilité s excé dentaires attendus, en pré sence de facteurs de rentabilité et d'investissement. Il existe toujours un effet de taille dans tous les trois sé ries des portefeuilles et les rentabilité s excé dentaires sont né gativement lié s à la taille de l'entreprise; il existe l'effet de valeur dans les portefeuilles Taille-B/P, l'effet de rentabilité dans les portefeuilles Taille-OP et l'effet d'investissement dans les portefeuilles Taille-Inv. leur pouvoir explicatif, avec ou sans la pré sence des innovations des quatre variables d'état sé lectionné s, à la fois dans les examens de sé ries chronologiques et les examens transversaux. Les ré sultats des ré gressions transversales ré vè lent é galement qu'il existe les primes significatives de risque de marché et de taille.. Ils montrent que l'information contenue dans l'innovation du rendements en dividende (IDIV) est totalement capturé e par la combinaison du marché bê ta et du facteur de taille Les facteurs FF ont pu jouer un rôle limité dans la captation d'opportunité s d'investissement alternatives repré senté es par les innovations des quatre variables d'é tat sé lectionné es.

Basé sur les dé couvertes, dans le chapitre 3, nous é tudions si les facteurs FF sont des proxys de facteurs de risque de dé tresse et si diffé rentes mé thodes de construction des facteurs entraî nent des ré sultats diffé rents. Les ré sultats empiriques suggè rent qu'il n'y a pas de preuve significative que les facteurs FF repré sentent un risque de dé tresse sur le marché boursier chinois. La pré sence de DRF a peu d'effet sur le pouvoir explicatif de la sé rie chronologique des trois facteurs FF, alors que le DRF, combiné avec les trois facteurs FF, peut partiellement expliquer de la rentabilité excé dentaires moyenne des sé ries chronologiques. En comparant les ré sultats des ré gressions des sé ries chronologiques à partir de deux mé thodes diffé rentes, la performance du facteur de risque de dé tresse basé sur le DLI semble lé gè rement meilleure que celui basé sur le O-score. Cependant, le facteur de risque de dé tresse n'est pas un dé terminant important des rentabilité s transversales moyennes, et les facteurs FF ne peuvent pas repré senter le facteur de risque de dé tresse dans la section transversale du marché boursier chinois A-share.

De plus, les é tudes sur les facteurs de risque en Chine pré senté s dans cette thè se ont é galement fourni de nouvelles implications en pratique sur le marché boursier chinois: Tout d'abord, en tenant compte de plusieurs caracté ristiques spé cials du marché boursier chinois, les ré sultats indiquent que le facteur de marché et le facteur de taille SMB sont des Ré sumé de la thè se en franç ais xxxvi dé terminants importants le Modè le FF5F n'a pas d'amé lioration significative à expliquer la rentabilité excé dentaire moyenne. Nos ré sultats est incompatible avec ceux sur le marché boursier amé ricain. Similairement, si les investisseurs veulent investir sur le marché boursier chinois, il est pré fé rable de sé lectionner les portefeuilles construits en fonction de Modè le FF3F au lieu du Modè le FF5F. Cependant, si les investisseurs investissent sur le marché boursier amé ricain, il est judicieux de choisir les portefeuilles construits selon le Modè le FF5F, puisque le Modè le FF5F est meilleur que le Modè le FF3F sur le marché boursier amé ricain.

En plus, pendant l'étude d'explication é conomique des facteurs FF sur le marché boursier chinois, nous trouvons que les facteurs FF ne perdent pas le pouvoir explicatif en pré sence des innovations de variables d'é tat sé lectionné es dans les ré gressions chronologiques et les ré gressions transversales sur le marché boursier chinois A-share. Comparer avec le modè le original FF3F, la pré sence d'innovations des variables d'é tat ne capture pas plus de variation de rentabilité moyenne. Les ré sultats indiquent que sur le marché boursier chinois, la construction de portefeuilles incline vers les innovations des quatre variables é conomiques ne peut pas gé né rer une prime de risque supplé mentaire. Le Modè le FF3F semble ê tre le meilleur choix en pratique à ce jour sur le marché boursier chinois. initiaux. Cependant, le bé né fice supplé mentaire provient du facteur de risque de dé tresse est limité . Par ailleurs, les ré sultats peuvent é galement ê tre ré alisé s par les entreprises pour xxxvii estimer le coût de l'é quité ; par

1 Fama-French Five-Factor Model vs. Fama- French Three-Factor Model in China 1

  .1 Reviews of the main asset pricing theories and models ........................................ 1.2 Retrospective of empirical work of Fama-French factor models .......................... 1.3 Introduction of Chinese stock market .................................................................... 1.4 Empirical Analysis and Results of FF3F Model .................................................... 1.5 Construction of profitability and investment factors and empirical results of Fama-French Five-Factor Model ................................................................................................ 1.6 Conclusions ............................................................................................................

	This chapter re-examines the applicability of Fama-French Three-
	Factor Model by constructing Fama-French factors on Chinese A-
	share stock market, considering several special features of Chinese
	stock market. In addition, this chapter also investigates the latest
	FF5F Model using data of Chinese stock market by apply Fama-
	MacBeth two-stage approach. Empirical results answer the
	questions of whether Fama-French Three-Factor Model explain
	time-series and cross-sectional variation of average excess stock
	returns over the sample period; whether the profitability and
	investment factors have extra explanatory power and whether
	Fama-French Five-Factor Model performs better than Fama-
	French Three-Factor Model on Chinese A-share stock market.
	Furthermore, the comparisons of the empirical results between
	Chinese stock market and U.S stock market are conducted as well.

Table 1 .1 Summary of Chinese stock market 1990-2014 15

 1

  The symbol '-' indicate the data that we fail to obtain. market and B-share stock market, respectively) and the percent of B-share market capitalization in total market capitalization from 1992 to 2014. Figure1.3, Figure1.4 are created to visualized Table1.1. Figure

	Year	Total listed firms	SSE SZSE	Stocks of A	Total market cap	Total market cap of A	Total market cap of B	B value in total (%)
	1990	10	8	2	-	-	-	-	-
	1991	14	8	6	-	-	-	-	-
	1992	53	29	24	53	1048	978	70	6.68%
	1993	183		77	177	3531	3319	212	6.00%
	1994	291		120	287	3691	3516	175	4.74%
	1995	323		135	311	3474	3311	164	4.72%
	1996	530		237	514	9842	9449	394	4.00%
	1997	745		362	720	17529	17154	375	2.14%
	1998	851		413	825	19506	19299	206	1.06%
	1999	949		465	922	26471	26168	304	1.15%
	2000	1088		516	1060	48091	47456	635	1.32%
	2001	1160		514	1140	43522	42246	1277	2.93%
	2002	1224		509	1213	38329	37527	803	2.10%
	2003	1287		507	1277	42458	41520	937	2.21%
	2004	1377		540	1363	37056	36309	746	2.01%
	2005	1381		547	1358	32430	31811	620	1.91%
	2006	1434		592	1411	89404	88114	1290	1.44%
	2007	1550		690	1527	327141	324588	2553	0.78%
	2008	1625		761	1602	121366	120567	800	0.66%
	2009	1718		848	1696	243939	242127	1812	0.74%
	2010	2063		1169	2041	265423	263221	2202	0.83%
	2011	2342		1411	2320	214758	213310	1448	0.67%
	2012	2494		1540	2472	230358	228775	1582	0.69%
	2013	2489		1536	2468	239077	237403	1674	0.70%
	2014	2613		1618	2592	372547	370823	1724	0.46%

stock

  The Chinese government started the share-structure reform in April 2005 to legally convert non-tradable shares to tradable shares. Almost all Chinese listed companies completed the reform by the end of 2006. Using only tradable shares or all shares to value weight stock returns is necessary to investigate.

	1.3 Introduction of Chinese stock market
	Total market capitalization				Total market capitalization of A-share
	Total market capitalization of B-share
	400000
	300000
	200000
	100000
	0
	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014

Table 1 .3 Descriptive statistic of Fama-French six value

 1

				Book-to-Price (B/P) ratio
		L	M	H	L	M	H
		Panel A: Average of annual firm size	Panel B: Average of annual B/P ratio
	S	2171	2216	2351	0.2105	0.3680	0.5695
	B	11955	14265	16373	0.2294	0.3820	0.6358
		Panel C: Average of annual percent of	Panel D: Average of annual number
		market value in portfolio		of firms in portfolio
	S	4.39%	4.54%	4.78%	190	316	227
	B	24.74%	30.73%	30.83%	249	271	212
		Panel E: Average excess returns
	S	0.0236	0.0251	0.0244
	B	0.0161	0.0142	0.0123

-weighted Size-B/P portfolios (period: July 2004-May 2015)

This table reports the statistic description of six Size-B/P portfolios (SL, SM, SH, BL, BM and BH), their annually average of firm size and B/P ratio are presented in Panel A and Panel B separately, Panel C is annual average percentage of market value in portfolios, Panel D is the annual average of firm numbers and Panel E is the average excess return of the six portfolios. Across the columns are the two size groups (Small and Big) and across the rows are three B/P groups (Low, Medium and High). The unit of market value is 100 million 'yuan'.

Table 1 .4 Summary statistics of Fama-French three factors and correlation coefficients among variables (July 2004-May 2015)

 1

Panel A is the summary statistics of FF three factors: the excess market return, Rm-Rf; the size factor SMB and the value factor HML. Panel B is the correlation coefficients among FF three factors, and Panel C is the correlation coefficients between excess returns of six Size-B/P portfolios and FF three factors.

Panel A:

Summary statistics of Fama-French three factors

		M ,t RR 	f	SMB	HML
	Mean	-0.0006	0.0102	-0.0015
	Standard Error	0.0077	0.0035	0.0028
	Median	0.0051	0.0124	-0.0046
	S.D.	0.0884	0.0403	0.0316
	Sample Variance	0.0078	0.0016	0.0010
	Kurtosis	1.1271	2.2564	4.5290
	Skewness	-0.6384	-0.6685	0.4895
	Panel B:

Correlation coefficients among Fama-French three factors

  with size factor SMB (0.5342, 0.4989 and 0.4674), while the correlation coefficients between big size portfolios and SMB are low (0.1646, 0.1270 and -0.0137), all the six portfolios are positively related with size factor except the BH portfolio. Furthermore, the correlation coefficients between six portfolios and value factor HML are relatively low also except for the BH portfolio (0.4570).

	1.4 Empirical Analysis and Results of FF3F Model
	relatively highly correlated
	Rm-Rf	1
	SMB	0.0014	1
	HML	0.1857	-0.3224	1
	Panel C: Correlation coefficients between dependent variables and independent variables
	SL-Rf	0.8037	0.5342	-0.0460
	SM-Rf	0.8233	0.4989	-0.0024
	SH-Rf	0.8274	0.4674	0.1130
	BL-Rf	0.8990	0.1646	-0.0951
	BM-Rf	0.9320	0.1270	0.1372
	BH-Rf	0.9084	-0.0137	0.4570
				43

Table 1 .5 Descriptive statistic of Fama-French 25 Size-B/P portfolios (July 2004-May 2015)

 1 This table displays the descriptive statistic of FF 25 SBP portfolios for the period of July 2004 to May 2015 (131 months, 11 years). Across the columns of each panel are the five size portfolios which from Small to Big, and across the rows are the five B/P portfolios which from Low to High. Panel A is the value-weighted average excess returns of FF 25 Size-B/P portfolios, Panel B, C, and D are the annual average size, B/P ratio and firm numbers. The unit of size is 100 million 'yuan'.Similar as Table1.3, Table1.5 represents the descriptive statistics of FF 25 Size-B/P portfolios on CNAS market for the period July 2004 to May 2015. Panel A shows the average excess returns of 25 portfolios, annual average size, B/P ratio and firm numbers of the 25 portfolios are shown in Panel B, C, and D respectively.

			Book-to-price (B/P) ratio
		Low	2	3	4	High
			Panel A: Average excess returns
	Small	0.0123	0.0185	0.0173	0.0175	0.0172
	2	0.0091	0.0128	0.0109	0.0111	0.0106
	3	0.0055	0.0077	0.0090	0.0091	0.0089
	4	0.0072	0.0052	0.0071	0.0067	0.0036
	Big	0.0048	0.0029	0.0017	0.0025	0.0006
			Panel B: Annual average size
	Small	1100	1189	1187	1207	1204
	2	1880	1879	1881	1880	1893
	3	2810	2808	2781	2807	2788
	4	4731	4693	4693	4580	4658
	Big	18937	22764	25721	25807	28974
			Panel C: Annual average B/P ratio
	Small	-0.0066	0.2935	0.3881	0.5018	0.7094
	2	0.0895	0.2937	0.3859	0.5020	0.7540
	3	0.1474	0.2916	0.3879	0.5018	0.7385
	4	0.1704	0.2866	0.3869	0.4992	0.7714
	Big	0.1653	0.2874	0.3862	0.4995	0.7869
			Panel D: Average number of firms
	Small	67	51	62	69	45
	2	44	59	64	62	63
	3	48	61	60	62	67
	4	60	65	61	56	61
	Big	78	63	52	49	62

Table 1 .6 Time-series regression of six value-weighted Size-B/P portfolios on Chinese A-share stock market (July 2004-May 2015, 131 months)

 1 The time-series regression results of six value-weighted Size-B/P portfolios on FF3F Model are displayed in this table. Across the columns are the two size groups (Small and Big) and across the rows are the three B/P ratio groups (Low, Medium and High). The left part of the table reports the coefficients obtained from the time-series regressions and adjusted R-square. Correspondingly, the right part of the table is t-statistics corrected for heteroscedasticity and autocorrelation using the Newey-West estimator, and the standard error of the estimation. Numbers in bold are the t-statistics which are significant at 5% confidence level.

Regression: i ,t

Table 1 . 7

 17

Table 1 .

 1 8 shows the CSRs results on the estimated coefficients which obtained from the TSRs of FF 6 SBP value-weighted portfolios (Table1.6) and 25 Size-B/P value-weighted portfolios (Table1.7) separately. Panel A presents the CSR results of six value-weighted Size-B/P portfolios, and Panel B shows the CSR results of 25 value-weighted Size-B/P portfolios.

	 ,	 and		are the coefficients of the CSRs and their corresponding
	M	SMB	HML
	Fama-MacBeth (FM) and Shanken (SH) corrected t-stats are presented in the parentheses
	below the gammas.
	The CSR results of FM show that neither of

M

 are significant at 5% confidence level (- 0.0116 for the six portfolios with t-stats -0.6678, and -0.0251 for the 25 portfolios with tstats -1.5912), which is consistent with most of researches on Chinese stock market that market beta is not able to explain the cross-sectional stock returns. Both

SMB



of the two CSRs are

Table 1 .8 Cross-sectional regressions of six value-weighted Size-B/P portfolios and 25 value- weighted Size-B/P portfolios, Chinese A-share stock market (July 2004-May 2015)

 1

  French Five-Factor Model vs. Fama-French Three-Factor Model in China 52 significant (0.0102 for the six portfolios with t-stat 2.8861 and 0.0085 for 25 portfolios with t-stats 2.2805), which proves the significant positive size premium of cross-sectional stock returns. After corrected by the Shanken correction, the SH t-stats is significant (-3.0383) for the market beta; while the important size premium is robust to the EIV adjustment. However, neither the FM or the SH t-stats indicate that there exists significant value premium. FF3F Model can explain more cross-sectional variation of six portfolios (with average adjusted R-squares 68.40%) than 25 portfolios (with average adjusted R-squares 49.01%) on Chinese stock market.

	Chapter1 Fama-
	Panel A: Cross-sectional regressions of six Size-B/P portfolios
	gamma (coef.)	0.0224	-0.0116	0.0102	-0.0024	68.40
	FM t-stats	(1.6619)	(-0.6678)	(2.8861)	(-0.8454)
	SH t-stats		(-1.4218)	(2.8861)	(-0.8404)
	Panel B: Cross-sectional regressions of 25 Size-B/P portfolios
	gamma (coef.)	0.0252	-0.0251	0.0085	-0.0004	49.01
	FM t-stats	(1.7655)	(-1.5912)	(2.2805)	(-0.1200)
	SH t-stats		(-3.0383)	(2.2882)	(-0.1188)

Table B .

 B 1 and TableB.2 reports the TSR results of FF3F Model on U.S. market during the period July 2004 to May 2015 (to be consistent with the time interval that we implement empirical analysis on Chinese stock market), respectively by regressing FF six valueweighted Size-B/M portfolios and 25 value-weighted Size-B/M portfolios on FF three factors, excess market return, SMB and HML. Empirical Analysis and Results of FF3F Model 53 market beta and five out of six loadings on SMB are statistically significant at 5% confidence level; while in TableB.2, still, all the loadings on market beta and 24 out of 25 loadings on SMB are significant. Take TableB.2 for example, more significant loadings (18 out of 25 on U.S. market, while 12 out of 25 on Chinese market) on HML of U.S. market indicates that the value factor has more explanatory power for the time-series variation of U.S. stocks than that of CNAS stocks.There exist size and value effect on both CNAS stock market and U.S. stock market. Within each B/M group, the loading on SMB decreases as portfolio size increases, on U.S. market, there are even negative loadings of the portfolios that have big size; and within each size group, we find a positive relationship between the loading on HML and B/M ratio. Comparing the adjusted R-squares of TableB.2 and Table1.7, which are higher on U.S.

We compare Table

B

.1 with Table 1.6, while Table B.2 with Table 1.7. It is observed that the time-series results on both countries are quite close. In Table

B

.1, all the loadings on 1.4 market (averaged adjusted R-squares is 0.9396) than on Chinese market (averaged adjusted R-squares is 0.8995). The results reveal that the time-series variation of stock returns captured by FF3F Model in U.S. is more than that captured by FF3F Model in China, that is to say, FF3F Model performs better on U.S. stock market than on CNAS stock market during the sample period.

We also perform the CSRs on FF3F Model using U.S. data, and the results are reported in Table

B

.3 (Appendix B). It is interesting that none of the regression coefficients on loadings of market beta, SMB and HML is significant; the results are robust to the EIV problem except the market beta for the six portfolios. For the 25 value-weighted Size-B/M portfolios, FF3F Model does not have any explanatory power of the cross-sectional variation of stock returns on U.S. market over the period July 2004 to May 2015. FF3F Model performs better in capturing cross-sectional variation of average excess stock returns on CNAS stock market (with averaged adjusted R-square 68.40% of the six portfolios and 49.01% of the 25 portfolios) than on U.S. stock market (with adjusted R-square 58.14% and 40.76% for the six and 25 Size-B/P portfolios separately) over the research period.

1.

5 Construction of profitability and investment factors and empirical results of FF5F Model 1.5.1 Construction problems

  Fama-French Five-Factor Model vs. Fama-French Three-Factor Model in China 54 available than that of Inv, and before 2009, there are few firms (less than 30) that have available OP.

Table 1.9 shows the annual available number of firms which have available OP and Inv data from 2004 to 2014. The number of firms that has available data of OP are always less Chapter1

Table 1 .9 Annual firm numbers that have available data of OP and Inv (2004-2014)

 1

	This table presents the annual number of firms that have available OP and Inv data from 2004 to
	2014.
	Year	2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
	OP	12	17	24	26	27	131	294	392	777	1043 2417
	Inv	1154 1237 1346 1402 1624 1981 2241 2355 2361 2525 2525

Table 1 .

 1 10 shows the annual number of stocks in 25 Size-OP portfolios and 25 Size-Inv portfolios, in which, S indicates the size group, P is the profitability groups and I is the investment groups. For instance, S1P1 portfolio indicates the intersection of firms in the 1.5 Construction of profitability and investment factors and empirical results of FF5F Model 55 bottom 20% size quintile and firms in the bottom 20% OP quintile. It is obvious that there are more stocks of Size-Inv portfolios than that of Size-OP portfolios. Furthermore, there are no firms in several Size-OP portfolios (portfolio S1P2 of the year 2010, portfolio S2P5 of the year 2010 and 2012), and all the portfolios except one (portfolio S2P1 of the year 2011) of the year 2010 and 2011 have no more than 5 firms. In this case, we use the frame of six portfolios to test FF5F model on CNAS stock market instead of the 25 portfolios.

Table 1 .10 Annual number of stocks in 25 Size-OP portfolios and 25 Size-Inv portfolios (2010- 2014)

 1 This table presents the annual firm numbers in each 25 Size-OP portfolios (left-hand part) and 25 Size-Inv portfolios (right-hand part) from 2010 to 2014, in which, S indicates the size group, P is the profitability groups and I is the Investment groups. For instance, S1P1 portfolio indicates the intersection of firms in the bottom 20% size quintile and firms in the bottom 20% OP quintile.

	Year

2 Empirical results of Fama-French Five-Factor Model on Chinese A-share stock market 1.5.2.1 Summary information of factors and portfolios

  Then we sort portfolios into six value-weighted Size-OP portfolios and six value-weighted Size-Inv portfolios, the annual number of firms in the two sets of portfolios are displayed in Table1.11. The small size groups of Size-OP portfolios relatively have fewer stocks than that of big size groups and the SR portfolio has no stocks in the year 2009 and only one stock in SN portfolio. Therefore, because of the lack of data on firm numbers of CNAS stock market, the interval of our research to processing FF5F model is from July 2010 to May 2015 (59 months).

Table 1 .11 Annual number of stocks in six Size-OP portfolios and six Size-Inv portfolios

 1

	Year	2009	2010	2011	2012	2013	2014
			Panel A Size-OP portfolios
	SW	5	11	22	92	154	488
	SN	1	7	7	52	107	483
	SR	0	5	9	7	13	146
	BW	34	76	95	140	157	233
	BN	51	104	147	210	255	468
	BR	28	57	93	87	121	403
			Panel B Size-Inv portfolios
	SC	328	374	392	404	457	465
	SN	262	288	310	380	412	444
	SA	105	167	289	314	258	244
	BC	187	203	244	277	274	268
	BN	301	373	468	492	496	479
	BA	206	251	276	330	358	409

This table presents the annual firm numbers of six

Size-OP portfolios (Panel A) and six Size-Inv portfolios (Panel B) from 2009 to 2014. In the first column of Panel A presents the six Size-OP portfolios (SW, SN, SR, BW, BN and BR), and in the first column of Panel B shows the six Size-Inv portfolios (SC, SN, SA, BC, BN and BA).

Table 1 .12 Summary statistics of Fama-French five factors (July 2010-May 2015)

 1

	Panel A report the summary statistics of FF five factors, it summarizes the mean, standard error (Sd
	error), standard deviation (S.D), variance, kurtosis and skewness. Panel B reports the correlation
	coefficients among the five factors.
		Panel A: Summary statistics of FF five Factors
		M ,t RR 	f	SMB	HML	RMW	CMA
	Mean	-0.0014	0.0106	-0.0059	-0.0061	0.0008
	Sd error	0.0084	0.0038	0.0046	0.0036	0.0025
	Median	-0.0024	0.0117	-0.0075	-0.0128	0.0001
	S.D	0.0646	0.0294	0.0355	0.0273	0.0196
	Variance	0.0042	0.0009	0.0013	0.0007	0.0004
	Kurtosis	0.2068	6.4386	5.9071	-0.4204	-0.2635
	Skewness	0.1439	-1.2015	0.5658	0.3288	0.2217
		Panel B: Correlation coefficients among FF five factors
	RM-RF	1
	SMB	0.1165	1
	HML	-0.0013	-0.6970	1
	RMW	0.0418	-0.2227	-0.0217	1
	CMA	0.1190	-0.2199	0.4621	-0.3121	1

Table

Table 1 .13 Average monthly excess returns for portfolios formed on Size-B/M, Size-OP and Size-Inv (July 2010-May 2015, 59 months)

 1 The average excess returns of six Size-B/M portfolios, Size-OP portfolios, and Size-Inv portfolios are presented in panel A, B and C respectively. Across the columns are the two size groups (Small and Big) and across the rows are the three B/M groups (Low, Medium and High), three OP groups (Weak, Neutral and Robust) and three Inv groups (Conservative, Neutral and Aggressive), respectively.

		Panel A: Excess returns of size-B/M portfolios
		L	M	H
	S	0.0236	0.0231	0.0207
	B	0.0151	0.0092	0.0061
		Panel B: Excess returns of Size-OP portfolios
		W	N	R
	S	0.0172	0.0170	0.0081
	B	0.0046	0.0082	0.0016
		Panel C: Excess returns of Size-Inv portfolios
		C	N	A
	S	0.0136	0.0158	0.0121
	B	0.0033	0.0050	0.0031

Table 1 .14 Time-series regressions of six value-weighted Size-B/P portfolios, Size-OP portfolios and Size-Inv portfolios on FF5F Model, Chinese A-share stock market (July 2010 to May 2015, 59 months)

 1 1.5 Construction of profitability and investment factors and empirical results of FF5F Model 59

Time-series regressions of six Size-B/P portfolios

				Table1.14 Continued
			Panel B:
				Book-to-Price (B/P) ratio
		L	M	H	L	M	H
			a			t ( a )
	S	0.0102	0.0105	0.0108	7.4308	4.4938	5.6696
	B	0.0124	0.0091	0.0118	6.8522	3.8634	6.4458
			b			t (	b )
	S	0.9637	0.9964	0.9703	41.1513	36.2183	35.8284
	B	0.8361	1.0214	0.8295	27.6969	28.5669	20.8687
			s			t ( s )
	S	1.0039	0.9383	0.8557	15.9153	16.3385	11.3131
	B	-0.1946	-0.2434	-0.0465	-2.8370	-2.4971	-0.5165
			h			t (h)
	S	-0.5849	-0.5197	-0.2689	-6.2171	-6.9004	-3.9751
	B	-0.9928	-0.6007	0.6912	-12.4860	-7.2244	5.1532
			r			t (r)
	S	-0.0695	-0.1448	-0.0617	-1.1264	-1.9122	-0.7331
	B	0.0188	-0.0456	0.0110	0.2597	-0.6538	0.1965
			c			t (c)
	S	0.2515	0.1051	0.3064	2.6156	1.0264	2.3582
	B	0.1114	0.2802	0.0565	1.2338	3.4851	0.5584
			Adj. R-square		Residual standard error
	S	0.9782	0.9714	0.9606	0.0120	0.0137	0.0148
	B	0.9625	0.9609	0.9513	0.0122	0.0136	0.0134

Time-series regressions of six Size-OP portfolios

				Operating Profitability
		W	N	R	W	N	R
			a			t ( a )
	S	0.0012	0.0020	-0.0018	0.5498	0.4592	-1.0778
	B	-0.0009	0.0028	0.0021	-0.5008	1.4503	0.6190
			b			t (	b )
	S	1.0075	1.0408	1.0492	35.8879	20.1490	31.7018
	B	1.1300	1.0253	1.0883	26.7879	34.3991	25.3012
			s			t ( s )
	S	1.1712	0.9800	1.5637	13.2828	5.5382	18.1679
	B	0.2480	0.2628	-0.1445	2.3517	3.3480	-1.1030
			h			t (	h )
	S	-0.4482	-0.7244	-0.2020	-4.5108	-3.9157	-1.9726
	B	-0.4560	-0.5496	-0.7022	-4.4978	-5.9760	-6.6825
			r			t (	r )
	S	-0.3429	-0.2601	1.1319	-4.6763	-2.5519	15.7233
	B	-0.2265	-0.1198	0.2987	-3.5011	-1.3591	3.4009
			c			t ( c )
	S	0.2644	0.1610	0.5398	2.4244	0.7310	4.2483
	B	0.4613	0.0414	0.1860	5.8956	0.3561	1.3955
			Adj. R-square		Residual standard error
	S	0.9720	0.9301	0.9653	0.0143	0.0238	0.0172
	B	0.9643	0.9640	0.9486	0.0150	0.0139	0.0172

Panel C: Time-series regressions of six Size-Inv portfolios

	1.5 Construction of profitability and investment factors and empirical results of FF5F Model
				Table1.14 Continued
			Panel C:
				Investment
		C	N	A	C	N	A
			a			t ( a )
	S	-0.0016	0.0018	-0.0017	-0.9026	0.8186	-1.0068
	B	-0.0030	0.0003	-0.0029	-1.5819	0.1566	-1.5573
			b			t (	b )
	S	1.0708	1.0548	1.0274	31.3516	33.9728	35.4151
	B	1.0683	1.0704	1.1116	27.9726	32.5243	27.7982
			s			t ( s )
	S	1.2837	1.1137	1.1998	18.0777	14.7519	14.5888
	B	0.4139	0.3165	0.4978	4.0713	4.7070	5.5174
								61

Time-series regressions of six Size-Inv portfolios

				Investment
		C	N	A	C	N	A
			h			t (h)
	S	-0.2393	-0.5369	-0.5135	-2.2282	-6.2005	-4.8437
	B	-0.6269	-0.4482	-0.3527	-5.9485	-5.6888	-3.2055
			r			t (r)
	S	-0.1329	-0.0789	-0.0871	-1.3784	-0.8737	-0.9804
	B	0.0481	-0.0330	0.0023	0.5404	-0.5768	0.0249
			c			t (c)
	S	-0.7507	-0.0210	0.5330	-4.8137	-0.2007	3.2129
	B	-0.2540	0.0445	0.4623	-1.9740	0.4260	3.7475
			Adj. R-square		Residual standard error
	S	0.9722	0.9713	0.9739	0.0148	0.0149	0.0141
	B	0.9607	0.9680	0.9595	0.0157	0.0135	0.0160

2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market 2

  .1 Economic explanation of Fama-French factors in the context of ICAPM ............ 2.2 Innovations in predictive variables and Vector Autoregressive approach ............ 2.3 Time-series evidence on Chinese A-share stock market ....................................... 2.4 Cross-sectional validation of five comparative models .......................................

	Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock
	Market
	2.1
	This chapter examines whether the innovations of the four
	predictive variables (aggregate dividend yield, one-month T-bill
	rate, term spread and default spread) are able capturing excess
	stock returns in both time-series and cross-section, further whether
	Fama-French factors SMB and HML proxy for the innovations of
	selected state variables that describe future investment
	opportunities on Chinese A-share stock market. To derive the
	innovation terms, we apply the vector autoregressive (VAR) method.
	Following, Fama-MacBeth two-stage approach method is
	implemented to perform the regressions for five models, and
	Shanken correction is also performed to adjust for the Errors-in-
	Variables problem in the cross-sectional regressions. Then the
	comparisons are made among the five models.
	70

2.5 Conclusions ..........................................................................................................

Economic explanation of Fama-French factors in the context of ICAPM

  , Stock and Watson Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market

Table 2 .1 List of papers that document time variation of excess asset return and the state variables they use

 2

	State Variables	Paper/ author
	Dividend yield	Campbell and Shiller (1988a),

  Treasury bill rate (RF) is generally the one-month Treasury bill rate or called risk-free rate which is a typically proxy for the return on a one-month Treasury bill. In China, we use one-month fixed deposit rate as the proxy for the risk-free interest rate. Monthly value-weighted excess market returns (CNAS stock market, including both Shanghai A-share stock Market and Shenzhen A-share Stock Market), one-month deposit rate, aggregate dividend yields, and yields of government bonds and corporate bonds are obtained from Bloomberg from November 2006 to May 2015. Starting from November 2006 rather than 2004 (which is the starting year in Chapter 1), because the available data of 'Term Spread' from Bloomberg begins from November 2006. FF factors SMB and HML are constructed the same way using the six Size-B/P portfolios in Chapter 1.

Table 2 .2 Summary statistics of FF factors, state variables and their innovations (December 2006-May 2015, 102 months

 2 variables nor the innovations of FF factors are significant. Meanwhile, all the four state variables have high t-value. The significant t-stats indicate the high possibility to be priced in equity returns.

	m ,t R is the excess

)

This table presents the summary statistics of original FF three factors, the four state variables and their innovations. Sd error is the standard error, and S.D. is the standard deviation.

Table 2 .3 Correlation coefficients among risk factors This

 2 Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market 88 is 0.92 between SMB and ISMB, 0.90 between HML and IHML) in U.S., thus she suggests that "the returns on the HML and SMB portfolios are good proxies for the innovations associated with these variables". ITERM and IRF are also significantly correlated with the correlation coefficient -0.4842. The high correlation coefficients indicate the factors probably share common information in explaining equity returns.

	m ,t R 1 0.0065 0.1926 -0.3495 SMB 1 0.0000 -0.2593 ITERM 0.0000 0.1557 -0.3077 HML m ,t SMB HML 1 IDIV 0.0360 IDEF 0.0000 0.0184 0.0424 -0.1224 -0.2755 IDIV ITERM IDEF 1 0.0337 1 1 IRF 0.0000 -0.2288 0.2380 0.0686 -0.4842 0.1131 ISMB 0.0000 0.9943 -0.3533 -0.2608 0.1566 0.0185 -0.2301 IRF 1 R IHML 0.0000 -0.3614 0.9720 0.0370 -0.3166 0.0436 0.2449 -0.3635 ISMB IHML 1 1

table presents the correlation coefficients among risk factors (FF three factors, innovations of state variables, and innovations of SMB and HML). FF three factors are all demeaned. The underlined numbers show the most highly correlated coefficients.

Table 2

 2

	Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock
	Market

.5. Consistent with what we observe from the last regressions, IDIV and SMB, ITERM and HML are negatively and significantly correlated. However, the new

Table 2 .5 Time-series regressions of Contemporaneous innovations of state variables on FF factors

 2 This table presents time-series regressions' results of innovations of four state variables on FF three factors. The adjusted R-squared is represented in the last column and in percentage value. Three FF factors and four state variables are all demeaned, and the t-statistics presented below the coefficients are corrected for heteroscedasticity and autocorrelation using the Newey-West estimator with five lags. The sample period is from December 2006 to May 2015.

		Regression: t    i i M ,t f i i a b ( R R ) s SMB h HML    	i ,t
		a	b	s	h		Adj. R	2
	IDIV	0.0000 (0.0878)	0.0001 (0.0631)	-0.0057 (-2.1284)	-0.0015 (-0.4699)	4.24
	ITERM	-0.0000 (-0.0135)	0.0014 (0.6146)	0.0028 (0.4466)	-0.0192 (-2.9789)	7.30
	IDEF	0.0000 (-0.0122)	-0.0002 (-0.1216)	0.0013 (0.3391)	0.0021 (0.4608)	2.73
	IRF	0.0000 (0.0499)	-0.0008 (-0.3148)	-0.0082 (-2.2742)	0.0108 (2.4572)	5.39

  December 2006 to May 2015) data of CNAS stock market. We compare five different factor models, in each model, excess portfolios returns are regressed on different risk factors. The innovations are obtained from a VAR (1) process.

. In the first step, the TSRs are performed on each of 25 value-weighted Size-B/P portfolios. In this chapter, the TSRs are performed according to each model (five models) with 102 months (

  Model 1 represents TSRs of the 25 value-weighted Size-B/P portfolios on excess market return, innovations of state variables and innovations of FF factors SMB and HML (ISMB and IHML). Similarly, Model 2 represents TSRs on excess market return, innovations of state variables and the original FF factors SMB and HML. The independent variables in Model 3 are excess market return and four innovations of state variables. In Model 4, the independent variables are excess market return and innovations of SMB and HML, Model 5 is nothing but the original FF3F Model.We perform the TSRs of each model during the period December 2006 to May 2015 (102 months), and the regression results are reported separately in Table2.6, Table2.7, Table2.8, Table2.9 and Table2.10. The left-half part of each table shows the TSR loadings, the corresponding t-statistics are reported on the right-half part and are corrected for autocorrelation and heteroscedasticity using the Newey-West estimator with five lags. At the end of each table, the adjusted R-square and the residual standard error are also reported. The numbers in bold indicate the statistical significance at the 5% confidence level.

Table 2 . 6

 26

Table 2

 2 .7, which reports the regression results of Model 2, we replace ISMB and IHML by the original FF factors SMB and HML, the other risk factors remain the same. The results are much like those of Model 1. It is not difficult to understand the similar results

	
	t

  2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market 108 Considering our research, for each month, we regress the excess returns of 25 Size-B/P portfolios on the estimated betas that are obtained from the TSRs in the previous section. Since we have 102 months over our sample period (December 2006 to May 2015), 102

	's adjusted
	t-stats (SH t-stats) in the CSRs.

Chapter

  Size-B/P portfolios as in the TSRs, and for each model, the estimated betas are obtained from the TSRs of the corresponding model (for example the estimated betas in Model 1# are the TSR coefficients of Model 1). Model 1# is the CSR on the loadings of excess market return, four innovations of state variables and innovations of FF factors. Model 2# represents the CSR on the loadings of excess market return, four innovations of state variables and FF factors. Model 3# represents the CSR on the loadings of excess market return and four innovations of state variables. Model 4# is the CSR of market factor and innovations of SMB and HML, while Model 5# is nothing but the CSR of FF3F Model. 2.4 Cross-sectional validation of five comparing models 109The CSRs results of the five models are reported in Table2.11. Across the rows we report the regressions coefficients and the corresponding t-statistics below each coefficient. The adjusted R-squares are reported in the last column. The numbers in bold indicate statistical significance at the 5% confidence level. We analyze the results by comparing the models: Model 2#) are statistically significant in both models no matter regress with exposure to FF factor or their innovations. However, under the EIV correction, the significance of t-stats only exists for market factor. ISMB in Model 1# and SMB in Model 2# are both significantly priced, robust to the EIV adjustment; while the exposures to IHML or HML are not significant variables in the cross section. None of the exposures to innovations of state variables is significantly priced in explaining the cross-sectional excess portfolios' returns adjusted to EIV problem.

	19)  (with FM t-stats -2.9752 in Model 1# and -3.0838 in Model 2#) and exposure to the RR  innovation of one-month T-bill rate IRF  (with FM t-stats 2.2365 in Model 1# and are the same 25 -Comparing Model 1# and Model 2#, the loadings on exposure to market factor m 2.3197 in
	i	,t	f

Table 2 .11 Cross-sectional regressions of five comparative models

 2

	Fama-MacBeth
	the
	reports
	table
	This

  Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market

	2.4 Cross-sectional validation of five comparing models
		Adj. 2 R	(%)		52.01			51.99	56.22			56.05			46.66
	Table 2.11 Continued	m  IDIV  ITERM  IDEF  IRF  ISMB  IHML  SMB  HML 	-0.0330 0.0118 0.0022	(-2.1064) (2.8090) (0.5808)	(-3.2828) (2.8039) (0.5827)	m  IDIV  ITERM  IDEF  IRF  ISMB  IHML  SMB  HML  -0.0334 0.0117 -0.0002	0002 0.0012 0.0090 0.0048 (-2.1285) (2.7876) (-0.0654) (-3.3191) (-2.9752) (1.8283) (-0.1314) (0.6759) (2.2365) (2.1616) (1.2536) (2.7877) (-0.0643)	(-4.9132) (1.2735) (-0.0885) (0.4741) (1.6731) (2.0987) (1.1875)	-0.0534 0.0003 -0.0000 0.0002 0.0012 0.0088 0.0010	(-3.0838) (1.8186) (-0.0297) (0.6181) (2.3197) (2.1219) (0.2678)	(-5.0751) (1.2436) (-0.0196) (0.4279) (1.7166) (2.0600) (0.2481)	-0.0229 -0.0007 -0.0004 0.0005 -0.0008	(-1.2504) (-2.9932) (-0.5596) (1.3557) (-1.2350)	(-2.1532) (-2.0752) (-0.3679) (1.0195) (-1.0283)
		 Model 0	0.0313 Model 4#	(2.3868) FM t-stats	SH t-stats	0.0318 Model 5#	(2.4221) FM t-stats	FM t-stats (3.5969) SH t-stats	SH t-stats	Model 2# 0.0560	FM t-stats (3.7506)	SH t-stats	Model 3# 0.0196	FM t-stats (1.1463)	SH t-stats
															111

  Chapter 2 Fama-French Factors and Innovations in State Variables on Chinese A-Share Stock Market

Table 3 .1 Classification of financial distress prediction models

 3

	Classification	Author	Method/Model
		Beaver (1966)	Univariate Discriminant Analysis
	Accounting-based models	Altman (1968)	Multiple Discriminant Analysis
		Ohlson (1980)	Logit model
		Zmijewski (1984)	Probit model
	Market-based models	Merton (1974)	Option-pricing model
	(Option-pricing theory)	Crosbie and Bohn (2003)	KMV model
	Market-based model (dynamic reduced-form model)	Shumway (2001)	Hazard model

  Chapter 3 Distress Risk Factor and Stock Returns on Chinese A-Share Stock Market 122 Altman's Z-score improves accounting-based techniques of the identification of financial distress risk, and it has advantages over Beaver's univariate model by considers a set of weighted combined accounting ratios. Altman proves that his model has an extremely accurate in predicting bankruptcy.

  Chapter 3 Distress Risk Factor and Stock Returns on Chinese A-Share Stock Market 128

  The concept of Shumway's hazard model comes from the survival model that estimates firm's hazard rate according to the sample's survival condition. In other words, "a typical discrete-time hazard at time t can be interpreted as a conditional probability of default at time t, given that the default did not happen prior to time t Outecheva (2007)". There are two main functions to understand the hazard model: the survivor function To estimate hazard function, many of which are difficult to estimate because of their nonlinear likelihood functions and time-varying covariates. Shumway shows that the discrete-time hazard model has the same likelihood function as logit model: or equal to zero if otherwise. So it is possible to estimate a hazard model with a logit program by "adjusting the sample size assumed by the logit program to account for the lack of independence between firmyear observations" 37 .

	3.2 Measurement of financial distress risk
	  t,x;			  f t,x; S t,x;  	 					(3.15)
	where,  f	 t,x; is the probability function of default, and θ is the vector of parameters of f,
	x is a vector of explanatory variables for predicting default. The survivor function (3.14)
	gives the probability of surviving up to time t, and the hazard function (3.15) gives the
	probability of failure at t conditional on surviving to t
	n
	i1   L=			t	i	i ,x	; 	  i y S	t	i	i ,x	; 		(3.16)
	 S t,x;    jt 1 f j,x;   		(3.14)
	and the hazard function
															133

i y is a dummy variable which equals one if firm i default at i t

  Chapter 3 Distress Risk Factor and Stock Returns on Chinese A-Share Stock Market

	renegotiation results in a hump-shaped relationship between expected returns and default
	probability".
	138

  Our research period is from 2005 to 2014, mainly because the number of firms that have data of O-score is rare before 2005. The annual available number of firms for which Oscore and DLI could be calculated are displayed in Table3.2, it is obvious that there are few firms which have available data of O-score before 2005 (0 for the year 2002 and 2003, 7 for the year 2004).

Table 3 .2 Annual available number of firms whose O-score and DLI can be calculated

 3 This table presents the annual number of firms which have available O-score and DLI from the year 2002 to the year 2014, "-" indicates the data which is not available.

	Year	O-score	DLI	Year	O-score	DLI
	2002	0	-	2009	1178	1370
	2003	0	-	2010	1205	1389
	2004	7	822	2011	1226	1676
	2005	938	1109	2012	1252	1997
	2006	1013	1146	2013	1285	2193
	2007	1128	1160	2014	1356	2259
	2008	1151	1255

Table 3 . 3

 33

Table 3 .4 Size effect controlled by distress risk (DLI as proxy), 2005-2014

 3 This table presents the results of size effect controlled by distress risk proxy by DLI onChinese Ashare stock market during 2005 to 2014. Stocks are first sorted into five DLI quintiles and then within each DLI quintile, stocks are sorted into five size quintiles based on their market capitalization, thus we have got 25 DLI/Size portfolios. The average returns, size, B/P ratio and DLI of 25 portfolios are listed in Panel A, B, C, and D respectively. Across the rows of each panel are the five size quintiles, and across the columns of each panel are five DLI quintiles. The values of DLI are percentage values, and the unit of size is 100 million 'yuan'.

	DR

Table 3 .5 Value effect controlled by distress risk (O-score as proxy)

 3 This table presents the results of value effect controlled by distress risk proxy by O-score onChinese A-share stock market during 2005 to 2014. Stocks are first sorted into five O-score quintiles and then within each O-score quintile, stocks are sorted into five B/P quintiles based on their book-to-price ratio, thus we have got 25 O-score/B/P portfolios. The average returns, B/P ratio size, and O-score of 25 portfolios are listed in Panel A, B, C, and D respectively. Across the rows of each panel are the five B/P ratio quintiles, and across the columns of each panel are five O-score quintiles. The unit of the size is 100 million yuan.

	DR			B/P ratio
		Low-B/P	2	3	4	High-B/P	High-Low
			Panel A: average return
	Low-O	0.0230	0.0206	0.0237	0.0243	0.0217	-0.0013 (-0.2722)
	2	0.0177	0.0246	0.0245	0.0228	0.0229	0.0052 (1.4291)
	3	0.0200	0.0253	0.0234	0.0215	0.0226	0.0026 (0.7053)
	4	0.0201	0.0205	0.0232	0.0238	0.0227	0.0026 (0.5363)
	High-O	0.0216	0.0253	0.0249	0.0278	0.0253	0.0037 (0.8270)
	Whole sample	0.0220	0.0248	0.0245	0.0253	0.0237	0.0017 (0.4963)
				Panel B: B/P ratio
	Low-O	0.1723	0.2929	0.3923	0.5109	0.7808
	2	0.1921	0.3159	0.4150	0.5390	0.8007
	3	0.1879	0.3252	0.4322	0.5632	0.8399
	4	0.1901	0.3221	0.4245	0.5551	0.8649
	High-O	0.0809	0.2076	0.3203	0.4471	0.7178
				Panel C: size
	Low-O	14998	8727	6297	10278	11381
	2	8873	12183	9712	15495	14865
	3	8497	5994	7845	6364	7379
	4	6116	5952	5638	5787	7842
	High-O	2565	3507	3981	4125	5225
				Panel D: O-score
	Low-O	-2.3082	-2.0629	-2.0357	-1.9592	-1.9006
	2	-0.5188	-0.5231	-0.5225	-0.5127	-0.5454
	3	0.3479	0.3297	0.3343	0.3387	0.3445
	4	1.1593	1.1657	1.1459	1.1256	1.1352
	High-O	3.1856	2.4067	2.2171	2.1017	2.0868

Table 3 .6 Value effect controlled by distress risk (DLI as proxy)

 3 This table presents the results of size effect controlled by distress risk proxy by DLI onChinese Ashare stock market during 2005 to 2014. Stocks are first sorted into five DLI quintiles and then within each DLI quintile, stocks are sorted into five size quintiles based on their market capitalization, thus we have got 25 DLI/Size portfolios. The average returns, size, B/P ratio and DLI of 25 portfolios are listed in Panel A, B, C, and D respectively. Across the rows of each panel are the five size quintiles, and across the columns of each panel are five DLI quintiles. The value of DLI is percentage value and the unit of the size is 100 million yuan.

	B/P ratio

Table 3 .7 Summary statistics of four factors: market factor, SMB, HML and distress risk factor (July 2005 to May 2015)

 3 This table presents summary statistics of four factors, market factor, size factor, value factor and distress risk factor ( Statistic description of these factors are shown in Panel A and the correlation matrix among these factors is presented in Panel B.

			O score DRF 	or
			Mf RR 	SMB	HML	O score DRF 	DLI DRF
			Panel A Statistic description of four factors
	Mean		0.0024	0.0119	-0.0020	0.0010	-0.0026
	Standard Error		0.0083	0.0038	0.0030	0.0019	0.0030
	t-statistic		0.2892	3.1316	-0.6667	0.5263	-0.8667
	Median		0.0064	0.0137	-0.0057	0.0011	-0.0014
	S.D.			0.0905	0.0414	0.0329	0.0206	0.0326
	Sample Variance		0.0082	0.0017	0.0011	0.0004	0.0011
	Kurtosis		1.1923	2.3341	4.0778	-0.2535	2.0064
	Skewness	-0.7299	-0.7784	0.5098	0.2176	0.1691
			Panel B Correlation matrix of four factors
	RM-RF		1
	SMB	-0.0175	1
	HML		0.1985	-0.3246	1
	O score DRF 		0.2362	0.2806	0.3672	1
	DLI DRF		0.4040	-0.2983	0.7139	0.6665	1
	and	DLI DRF (-0.0026) are negative. The only significant t-stats is from SMB, and the size
	factor is most likely to be priced in equity returns.
	The correlation matrix of the four factors in Panel B indicate that the two DRF factors are
	highly correlated (with correlation coefficient 0.6665), which means that	O score DRF 	and

DLI DRF ). DLI DRF may contain most of the same information. It is worth noting that DLI DRF and

Table 3 .8 Summary statistics of 18 (2x3x3) Size-B/P-O-score sorted portfolios (July 2005-May 2015)

 3 The 18 portfolios are constructed from the intersection of three independent sorts of all stocks into two size, three B/P and three DR portfolios. DR is estimated by O-score. The table has two parts: small size and big size, and in each part, average excess returns, firm numbers, size, B/P ratio and O-score of 18 portfolios are presented. Across the rows are the three B/P portfolios (L, M and H), and across the columns are the three O-score portfolios (O1, O2 and O3).

	The unit of size is 100

Table 3 .9 Time-Series Regressions of 18 Size-B/P-O-score sorted portfolios on augmented four-factor model (July 2005-May 2015)

 3

Table 3 .9 Continued Big size

 3

	O-score				B/P ratio
		L	M	H	L	M	H
			a			t ( a )
	O1	-0.0022	-0.0034	-0.0047	-0.9766	-1.2719	-1.8308
	O2	-0.0038	-0.0004	-0.0045	-1.2982	-0.1281	-1.7928
	O3	-0.0054	-0.0060	-0.0001	-1.7151	-2.0373	-0.0473
			b			t (b)
	O1	0.9715	1.0489	1.0288	18.0644	19.9291	18.9004
	O2	1.0192	1.0881	1.0399	18.1832	20.2544	17.9173
	O3	1.0165	1.1039	1.0602	16.4040	17.4080	24.4310
			s			t (s)
	O1	0.6021	0.8563	0.8358	5.3909	6.8872	8.3814
	O2	0.8453	0.6659	0.7390	7.1385	5.1131	6.2367
	O3	0.7488	0.7823	0.6491	5.7002	6.0745	5.8866
			h			t (h)
	O1	-0.4976	0.0938	0.5270	-3.4900	0.6492	4.2189
	O2	-0.2723	0.0177	0.5810	-1.7387	0.1078	3.7957
	O3	-0.4012	0.0356	0.6480	-2.5041	0.2226	4.9922
			d			t (d)
	O1	-0.4896	-0.4684	-0.0989	-3.9778	-3.5396	-0.8279
	O2	-0.2171	0.0833	0.2654	-1.4397	0.5639	2.2562
	O3	0.4937	0.3375	0.5305	3.0586	1.9698	3.1082
			Adj R-square		Residual standard error
	O1	0.8744	0.8848	0.9061	0.0336	0.0354	0.0324
	O2	0.8752	0.8928	0.9090	0.0364	0.0354	0.0329
	O3	0.8592	0.8796	0.9166	0.0402	0.0395	0.0326

Table 3 .10 Summary statistics of 18 (2x3x3) Size-B/P-DLI sorted portfolios

 3 The 18 portfolios are constructed from the intersection of three independent sorts of all stocks into two size, three B/P and three DR (proxy by DLI) portfolios. DR in this table is proxy by DLI. The table has two parts: small size and big size, and in each part, average excess returns, firm numbers, size, B/P ratio and DLI of 18 portfolios are presented. Across the rows are the three B/P portfolios (L, M and H), and across the columns are the three DLI portfolios (D1, D2 and D3). The DLI is percentage value, and the unit of size is 100 million 'yuan'.

	DLI			B/P ratio
		L	M	H	L	M	H
			Small size
			Average excess returns			Firm numbers
	D1	0.0176	0.0201	0.0176	70	104	52
	D2	0.0135	0.0173	0.0188	80	136	94
	D3	0.0206	0.0189	0.0160	37	73	82
			Size			B/P ratio
	D1	1797	1735	1712	0.2016	0.3924	0.6429
	D2	1748	1815	1838	0.1992	0.3934	0.6573
	D3	1767	1871	1956	0.1955	0.3944	0.7034
			DLI (%)
	D1	0.0432	0.0510	0.0612
	D2	0.5721	0.6073	0.6332
	D3	4.4861	3.8763	4.5588
			Big size
			Average excess returns			Firm numbers
	D1	0.0110	0.0096	0.0072	118	74	32
	D2	0.0075	0.0102	0.0090	98	118	74
	D3	0.0087	0.0064	0.0065	45	91	120
			Size			B/P ratio
	D1	12069	15431	33975	0.1951	0.3856	0.6680
	D2	10399	13418	14494	0.2113	0.3930	0.6913
	D3	11296	11844	11611	0.2185	0.4021	0.7384
			DLI (%)
	D1	0.0419	0.0454	0.0615
	D2	0.5209	0.6115	0.6679
	D3	4.5184	4.9209	5.7250

Table 3 .11 Time-Series Regressions of 18 Size-B/P-DLI sorted portfolios on augmented four factor model (July 2005-May 2015)

 3

Table 3 .11 Continued

 3

	Big size

Table 3 .12 Cross-sectional regressions of 18 Size-B/P-DR sorted portfolios on augmented four- factor model, on FF3F Model, and on market factor and DRF (July 2005-May 2015, 119 months)

 3 The cross-sectional regression results of 18 Size-B/P-DR sorted portfolios on the augmented fourfactor model (R1), on FF3F Model (R2), and on market factor and DRF (R3) are reported in this table. In Panel A the DRF is constructed by O-score sorted portfolios and in Panel B the DRF is constructed by DLI sorted portfolios. Each panel contains three parts (R1, R2, and R3), the first row of each part reports the cross-sectional regressions' intercepts and coefficients (gammas), the second and third rows report the corresponding Fama-MacBeth t-statistics (FM t-stats) and Shanken corrected t-statistics (SH t-stats). The numbers in bold are the t-statistics that are significant at 5% confidence level. The averaged adjusted R-squared are reported in the last column in percentage form.

	Regressions1 (R1):	i ,t		R	f	    i	  ˆˆR   M i SMB i HML i b s h	 	DRF i d	 	i ,t
	Regressions2 (R2):				R		   	ˆR b s h    	 
			i	,t			f	i	M	i	SMB	i	HML	i	i	,t
	Regressions3 (R3):				R		   	ˆR b d    
			i	,t			f	i	M	i	DRF	i	i	,t
		Const.(α)			
	R1	0.0230			-0.0214		0.0101	-0.0002	0.0009	48.92
	FM t-stats	(1.8014)			(-1.4530)	(2.4481)	(-0.0717)	(0.4641)
	SH t-stats							(-2.4014)	(2.5008)	-0.0711	0.4622
	R2	0.0255			-0.0236		0.0098	-0.0003	44.05
	FM t-stats	(1.9885)			(-1.6110)	(2.3688)	(-0.1059)
	SH t-stats							(-2.6479)	(2.4250)	(-0.1042)
	R3	0.0627			-0.0545				0.0032	35.62
	FM t-stats	(2.6825)			(-2.4364)			(1.4291)
	SH t-stats							(-5.6066)			(1.2769)
		Panel B:

M  SMB  HML  DRF Adj. 2 R (%) Panel A: Cross-sectional regressions on FF3F Model and on DRF (O-score)

Cross-sectional regressions on FF3F Model and on DRF (DLI)

	3.6 Augmented four-factor model and empirical evidence
	R1	0.0058	-0.0065	0.0127	-0.0025	-0.0026
	FM t-stats	(0.4761)	(-0.4702)	(3.0848)	(-0.7622)	(-0.8765)	57.24
	SH t-stats		-0.7325	(3.1387)	-0.7578	-0.8735
	R2	0.0038	-0.0046	0.0127	-0.0023
	FM t-stats	(0.2963)	(-0.3298)	(3.0897)	(-0.7190)		50.39
	SH t-stats		(-0.5220)	(3.1698)	(-0.7087)
	R3	0.0409	-0.0278			-0.0049
	FM t-stats	(2.4606)	(-1.7412)			(-1.5825)	23.07
	SH t-stats		(-2.9414)			(-1.5804)
							167

Table B .4 Time-series regressions of six value-weighted Size-B/M portfolios, Size-OP portfolios and Size-Inv portfolios on FF5F Model on U.S. stock market (July 2010 to May 2015, 59 months)

 B

			H	0.0700 15.9565 -1.1176 14.8860 1.1510 7.6054 -0.4470 6.8010 0.3999 7.8523		23.2255 0.0115 32.5759 0.0127 25.8979 0.0178 22.3479 0.0163 13.9923 0.0222		15.0989	13.6579	10.1764	3.6529	0.2377
	Table B.2 Continued	B/P ratio	4 H L 2 3 4	.3958 -2.2758 -0.1898 0.4896 0.0694 -0.1141 -0.1646 2.0533 2.4736 0.5674 0.4500 0.2086 0.1795 0.2361 0.1989 -0.0792 1.9938 0.2368 -0.4563 0.0876 0.1585 0.5757 0.7294 -1.9032 0.8687 -3.5719 0.6287 -8.7449 0.6970 -7.4663 0.8925 -9.0766 -0.0012 2.3832 2.0916 1.7311 1.0221 -1.1539 1.7058 1.8226 1.2430 -2.1494 (b) t t (h) 1.5451 4.3873 6.2762 -0.9898 7.2889 11.6221 -0.8861 2.3422 3.7369 -1.7359 1.0111 3.6067 Residual 0.8738 0.9491 21.3603 0.955 0.9170 1.0880 30.6065 0.9589 1.0175 0.9960 24.4732 0.9283 1.0606 1.0737 23.9754 0.9102 1.1195 1.0956 32.9666 0.9155 0.9655 0.9653 0.9114 0.9231 0.8728 0.0194 0.0138 0.0130 0.0116 0.0078 26.4149 40.2759 18.7566 34.4155 35.9649 38.7462 38.8964 28.8771 31.6152 25.6645 15.7197 18.5949 51.0610 26.0271 12.5321 (s) t 0.0147 0.0113 0.0121 0.0125 0.0094 standard 0.0113 0.0105 0.0124 0.0158 0.0116 -0.3747 2.4142 7.2239 error 0.0119 0.0112 0.0143 0.0157 0.0157	0.9804 0.9628 15.0696 19.5260 18.0505 24.1812	0.8377 0.8737 14.0170 30.4977 20.2644 24.1121	0.5290 0.6720 12.6354 13.1719 13.3856 8.0100	0.2586 0.2551 10.0698 5.9816 4.1488 3.6079	-0.3180 0.0284 -4.6713 -5.0276 -3.5593 -3.8461
			2 3	h	0.1969 0.2419 0.0783 -0.0499 0.2748 0.2386 -0.0488 0.1115 -0.2138 -0.1128 0.1418 0.1174 0.0392 0.2095 0.2415 0.0939 -0.0435 0.1710	b	0.9998 0.9807 0.9398 0.9970 0.9603 0.9602 1.0611 1.0178 0.9500 1.0948 1.1823 0.9397 0.9204 0.9536 0.9429 Adj R-square 0.9606 0.9655 0.9457 0.9196 0.9248	s	1.1139 0.9662	1.0148 0.9695	0.6803 0.6301	0.3314 0.3331	-0.1845 -0.1960
		Size	L		2 -0.0157 S -0.1231 2 -0.2822 3 -0.0001 3 -0.3366 4 0.2159 4 -0.3117 B 0.0118 B -0.3729		S 1.1111 S 2 1.0783 2 3 1.1181 3 4 1.0636 4 B 0.9766 B 0.9122 0.9454 0.9452 0.9460 0.9595		S 1.2024	2 1.0246	3 0.7051	4 0.4484	B -0.1985

Table B .4 Continued Panel B: Time-series regressions on Size-OP portfolios

 B

									Operating Profitability
		W			N					R						W		N	R
					a													t ( a )
	S	-0.0188			0.0898				-0.0396					-0.3438		1.1708	-0.4349
	B	-0.0842			0.0989				-0.0640					-0.7461		2.2880	-1.9871
					b													t (b)
	S	0.9812			0.9853				1.0646					81.0285		51.1117	32.7726
	B	1.1136			0.9412				1.0298					27.2225		50.5000	97.2971
					s													t (s)
	S	0.8675			0.9675				0.9317					33.4687		20.9395	14.3934
	B	-0.0693	R		R    a -0.0541	b	(	R	R -0.1339 ) 		s	SMB		h -1.0857 HML 	r	RMW -1.2950 c CMA 		e	-4.5316
			i	,t	f	i	i		M	,t	f		i			i	i	i	i	,t
	S	-0.1143	h Panel A: Time-series regressions on six Size-B/M portfolios t (h) 0.2669 0.2011 -4.5007 6.3486	3.9980
	B	0.2443			0.0392	Book-to-Market (B/M) ratio -0.0708 4.5818		1.0984	-2.7060
		L			M r					H						L		M t (r)	H
	S	-0.6348			a 0.2597				0.4475					-18.4610		t ( a ) 5.1374	9.5450
	S B	-0.2123 -0.5864			-0.0328 -0.1016				0.2391 0.3304					-1.2440 -8.4796		-0.3040 -2.7847	1.4394 12.2607
	B	0.0339			-0.0369 c				0.0197					0.2766		-0.2794 t (c)	0.1673
	S	0.0768			b -0.0627				-0.1247					1.6662		t (b) -1.0611	-1.5351
	S B	0.9867 -0.2849			1.0036 0.1389				0.8091 -0.0839					18.0426 -3.0221		37.3893 2.6995	18.0305 -2.0856
	B	1.0715	1.1142 Adj. R-square			1.0577					30.4708 Residual standard error 21.6453 42.6438
	S	0.9945			s 0.9851				0.9826					0.0040		t (s) 0.0058	0.0063
	S B	0.7036 0.9775			0.7975 0.9863				0.4312 0.9903					13.4733 0.0069		17.5148 0.0041	5.5548 0.0033
	B	0.2231			0.1980				0.1550					4.6577		3.4748	2.2473
					h													t (h)
	S	-0.2137			0.2549				0.3912					-2.0573		4.1878	3.8325
	B	-0.2152			0.0582				0.6456					-4.9748		0.9063	9.2306
					r													t (r)
	S	-0.7327			-0.1351				-0.3846					-5.4871		-2.2599	-3.0270
	B	-0.1506			-0.0322				0.0110					-2.7377		-0.3318	0.1531
					c													t (c)
	S	-0.3047			-0.2155				-0.0974					-2.7655		-2.3334	-0.7657
	B	-0.2294			-0.0887				-0.1666					-2.3567		-1.1923	-1.4554
			Adj. R-square									Residual standard error
	S	0.9517			0.9733				0.9084					0.0115		0.0080	0.0125
	B	0.9670			0.9591				0.9580					0.0077		0.0088	0.0089

Panel C: Time-series regressions on Size-Inv portfolios

	Appendix B
				Investment
		A	N	C	A	N	C
			a			t ( a )
	S	0.0071	0.1144	-0.0540	0.1573	2.3620	-0.8730
	B	0.0259	-0.0428	0.0831	0.4733	-0.7299	1.1236
			b			t (b)
	S	0.9681	0.9710	1.0880	47.1125	35.9423	81.6853
	B	1.0521	0.9912	0.9326	77.8118	48.6599	32.4959
			s			t (s)
	S	0.9702	0.8942	0.8760	30.5318	26.8312	19.7427
	B	-0.1786	-0.0167	-0.0835	-5.7904	-0.9118	-2.1632
							201

Table B .4 Continued Panel C: Time-series regressions on Size-Inv portfolios

 B

				Investment
		A	N	C	A	N	C
			h			t (h)
	S	0.0238	0.1754	-0.0163	0.7234	5.4018	-0.3663
	B	-0.0658	0.0615	-0.0260	-1.4661	1.3401	-0.4450
			r			t (r)
	S	-0.2181	0.1339	-0.2339	-4.7274	3.5684	-5.6108
	B	-0.0174	0.0573	-0.0001	-0.3659	1.1884	-0.0013
			c			t (c)
	S	-0.4264	0.1159	0.3567	-7.7210	2.0770	5.2777
	B	-0.5734	0.1819	0.6429	-8.1165	3.4479	7.3145
			Adj. R-square		Residual standard error
	S	0.9907	0.9879	0.9908	0.0048	0.0051	0.0051
	B	0.9799	0.9872	0.9764	0.0052	0.0041	0.0054

Table C .1 Time-series regression of three sets of portfolios on FF3F Model, Chinese A-share stock market (July 2010-May 2015, 59 months)

 C This table presents the time-series regressions results of six Size-B/P portfolios, six Size-OP portfolios and six Size-Inv portfolios on FF3F Model on Chinese stock market in Panel A, Panel B, and Panel C respectively. In each panel, the regression coefficients and adjusted R-square are presented in the left part of the table, the corresponding t-statistics corrected for heteroscedasticity and autocorrelation using the Newey-West estimator and residual standard error are presented in the right part. Across the columns of each panel are the two size groups (S and B); across the rows of Panel A are the three B/M groups (L, M and H)., across the rows of Panel B are the three OP groups (W, N and R), across the rows of Panel C are the three Investment groups (A, N and C). Numbers in bold are the t-stats which are significant at 5% confidence level.

	Regression: i ,t R		R	f	i a b ( R i M ,t  		f R ) s SMB h HML e i i i ,t   
	Panel A:

Time-series regression of six value-weighted Size-B/P portfolios

	Size			Book-to-Price (B/P) ratio
		L	M	H	L	M	H
			a			t ( a )
	S	0.0113	0.0113	0.0112	7.4842	4.5837	6.1412
	B	0.0123	0.0092	0.0123	6.2322	3.3146	6.4849
			b			t (b)
	S	0.8979	0.9231	0.9059	32.6701	27.0157	32.2014
	B	0.8504	1.0340	0.8424	27.3918	22.4104	22.1472
			s			t (s)
	S	0.9057	0.8874	0.8548	27.9738	15.5660	19.8422
	B	-0.1441	-0.1149	-0.0931	-3.4693	-1.3686	-2.7201
			h			t (h)
	S	-0.4025	-0.3497	-0.0262	-5.0751	-4.3756	-0.4383
	B	-0.9630	-0.4761	0.6607	-15.1937	-5.5671	7.1594
			Adj. R-square		Residual standard error
	S	0.9803	0.9782	0.9746	0.0114	0.0120	0.0119
	B	0.9623	0.9545	0.9542	0.0122	0.0147	0.0130

Table C .1 Continued Panel B: Time-series regression of six value-weighted Size-OP portfolios

 C

				Profitability
		W	N	R	W	N	R
			a			t ( a )
	S	0.0038	0.0042	-0.0022	1.3466	0.7791	-0.5303
	B	0.0000	0.0027	0.0010	-0.0179	1.5449	0.3059
			b			t ( b )
	S	0.9236	0.9733	1.0657	24.3001	17.2826	17.4507
	B	1.0967	0.9896	1.1164	19.0453	34.3179	20.3752
			s			t ( s )
	S	1.0674	0.8611	0.7540	7.9772	5.1362	5.5995
	B	0.4230	0.3508	-0.1688	3.8493	7.9956	-1.5525
			h			t ( h )
	S	-0.2302	-0.5825	-0.4059	-1.8362	-3.4193	-2.2086
	B	-0.1523	-0.4188	-0.7060	-1.3302	-4.9840	-6.5449
		Adj. R-square		Residual standard error
	S	0.9456	0.9158	0.8514	0.0200	0.0261	0.0356
	B	0.9520	0.9698	0.9388	0.0174	0.0127	0.0188
		Panel C:

Time-series regressions of six value-weighted Size-Inv portfolios

				Investment
		A	N	C	A	N	C
			a			t ( a )
	S	-0.0015	0.0024	-0.0002	-0.7269	1.1784	-0.1061
	B	-0.0038	0.0000	-0.0025	-2.4503	0.0310	-1.3087
			b			t ( b )
	S	0.9667	0.9745	0.9521	50.2415	37.7947	34.0437
	B	1.0323	1.0393	1.0796	31.6716	37.0603	26.3027
			s			t ( s )
	S	1.0170	0.9787	1.1180	16.8657	22.2040	19.8524
	B	0.3535	0.3491	0.5370	5.0630	7.1627	8.8230
			h			t ( h )
	S	-0.3873	-0.4312	-0.2089	-3.2013	-5.7192	-2.3319
	B	-0.6595	-0.3505	-0.1090	-7.1360	-4.6239	-0.9868
			Adj. R-square		Residual standard error
	S	0.9508	0.9778	0.9701	0.0197	0.0131	0.0151
	B	0.9621	0.9742	0.9595	0.0155	0.0121	0.0160
							205

   , µ is the drift rate which is the expected return on the firm's asset, and ε is the random component of the firm's return which is normally distributed assumed by BS model.Then the probability of default above can be rewritten as follows:According to the normal distribution of ε, the probability of default

	Appendix D
					H	0.3179	0.2458	-0.0510	-0.6578	-1.6547	0.4097	0.4492	0.5193	1.2321	0.5102			-1.1219	-1.3050	-2.5375 -1.4693 -0.4960 -3.0771 0.6946 -3.6844	-4.5735	-2.4231
					4	0.3304	0.7630	0.4922	0.4080	-0.2406	0.6228	0.6908	0.3260	-0.0533	-0.3124			-1.2874	-2.0012	-2.7667 -1.6033 -0.9592 -3.3345 0.0756 -3.8017	-3.2671	-2.1580
	Table D.1 Continued V where ln	B/P ratio  3 4 H L 2 3 Panel B: Regressions on market factor and ITERM ITERM    ITERM t  2.8511 1.3541 1.2907 0.4802 0.7913 0.7025 4.1306 2.5430 0.8026 1.2628 0.9301 1.0870 2.6859 1.3648 -0.1431 0.9611 1.3439 0.8586 2.4330 0.9741 -1.4101 1.3249 1.4546 1.0761 0.1241 -0.3270 -4.0864 1.4070 1.6004 0.0775 Panel  C: Regressions on market factor and   IDEF IDEF t  IDEF ln V T T 2            T     tT W t T W t =    , tT   N 0,1	2.8085 0.2210 0.4635 3.6790 2.4471 0.5640	1.4571 0.0427 0.2412 3.7144 2.0826 0.1970	1.4575 0.2649 0.2756 1.5554 2.0615 0.6695	0.8468 -0.0270 0.2104 -0.2386 3.9225 -0.0184	1.9757 -0.0392 0.7604 -0.8604 2.0447 0.8670	Panel IRF D: on market factor and Regressions	IRF    IRF t 	-6.3742 -1.5769 -2.0364 -3.4335 -1.9355 -4.2995	-6.7521 -1.3826 -2.3392 -3.2150 -2.6154 -5.6511	-21.6904 -20.6291 -20.2875 -2.4626 -2.9855 -3.3198 -5.8271 -4.1635 -21.2079 -24.0719 -22.1941 -3.5465 -2.5009 -3.1129 0.1862 -17.4444 -20.3365 -20.8928 -2.8355 -3.7192 -3.1053 -2.2262 -2.0668 0.1158 -2.1871 -2.6614 -1.2005 -3.0693 -2.0189 -0.8936 -2.6779 1.3394 -2.1198 -3.8025 -2.2150 0.1231	-16.4696 -17.8200 -20.6227 -2.6344 -2.8928 -3.3502	-12.3718 -8.8154 -13.2603 -1.7570 -1.8305 -3.1659
	t P	 	Prob Prob	L 2   A,t ln V   2.1979 3.1786 4.3519 3.1261 3.9247 4.4774 3.9734 4.1571 3.2004 2.5767 3.7428 1.5203 1.1381 0.2448 4.1031 1.5287 -0.0922 -0.1408   2 A A t T t T T ln X 2              2 A,t A t tT A V ln T X2 T                     	3.6214 -0.1257			-6.1567 -5.3639	-7.6940 -4.5895	-23.4954 -6.5573 -5.9295 -6.3293 -24.2059 -18.1294 -6.0462 -4.3878 -19.6072 -25.9214 -2.0402	-16.2248 -17.2302	-9.5801 -7.8102
				Size	S	2	3	4	B	S	2	3	4	B			S	2	3	2 4 B 3	4	B
	206

t P can be defined in terms of the cumulative normal distribution:

Table F .1 Time-series regressions of 18 Size-B/P-O-score sorted portfolios on FF3F Model, Chinese stock market (July 2005 to May 2015)

 F This table reports the time-series regression results for 18 Size-B/P ratio-O-score on FF3F Model. The stocks are divided into two size groups, three B/P groups, and three groups based on their Oscore, seperately. The intersection of these groups forms 18 portfolios. The left part of the table is the coefficients of time-series regressions and adjusted R-square, the right part is the corresponding t-stats corrected for heteroscedasticity and autocorrelation using Newey-West estimator and residual standard error, and the numbers in bold are significant at 5% confidence level.

			Table F.1 Continued
				Big size
	O-score				B/P ratio
		L	M	H			L	M	H
			a					t ( a )
	O1	-0.0017	-0.0029	-0.0046		-0.7289	-1.0484	-1.7760
	O2	-0.0036	-0.0005	-0.0048		-1.2359	-0.1598	-1.8854
	O3	-0.0060	-0.0063	-0.0007		-1.8987	-2.1111	-0.2422
			b					t (b)
	O1	0.9549	1.0330	1.0255		18.6257	20.9052	18.9205
	O2 O3	Regression: i ,t R 1.0119 1.0910 R a b ( R f i i M ,t    1.0489 1.0332 1.1153 1.0781		f R ) s SMB h HML e i i i ,t   18.3348 19.0292  15.0781 16.2983	16.7194 22.2291
			s	Small size		t (s)
	O-score O1	0.4950	0.7539	0.8142	B/P ratio	5.1068	6.2125	8.9078
	O2	L 0.7978	M 0.6842	H 0.7971			L 7.4561	M 6.0882	H 7.4711
	O3	0.8567	a 0.8561	0.7651			7.0660	t ( a ) 6.7420	7.2620
	O1	0.0003	-0.0015 h	-0.0042			0.0950	-0.6211 t (h)	-1.4931
	O2 O1	-0.0072 -0.6448	-0.0019 -0.0470	-0.0019 0.4973		-2.0880 -5.0173	-0.8494 -0.3281	-0.6544 4.4956
	O3 O2	-0.0056 -0.3376	-0.0011 0.0427	0.0000 0.6607		-1.8313 -2.3818	-0.3788 0.3042	-0.0104 4.6627
	O3	-0.2528	b 0.1370	0.8074		-1.6469	t (b) 0.9250	6.4202
	O1	0.9738	0.9995 Adj R-square	0.9741		18.6385 Residual standard error 19.9970 21.0746
	O2 O3 O1 O2	1.0262 0.9945 0.8678 0.8750	0.9931 0.9981 0.8800 0.8936	1.0063 0.9964 0.9066 0.9081		18.9585 18.7994 0.0345 0.0364	23.7498 18.4143 0.0361 0.0353	17.0678 0.0323 16.3521 0.0331
	O3	0.8542	s 0.8781	0.9109			0.0409	t (s) 0.0398	0.0337
	O1	1.3451	1.3748	1.5414		11.4333	12.7305	14.9231
	O2	1.4930	1.3699	1.3850		13.5019	15.0567	11.7254
	O3	1.5798	1.4035	1.3333		15.4323	12.6156	11.2084
			h					t (h)
	O1	-0.1961	0.1113	0.5427		-1.3753	0.8522	3.9638
	O2	0.0477	0.1810	0.4657			0.3208	1.4722	3.4695
	O3	0.1713	0.3048	0.4942			1.2575	2.3177	3.4456
			Adj R-square				Residual standard error
	O1	0.8677	0.9121	0.9038			0.0404	0.0329	0.0355
	O2	0.9000	0.9179	0.9031			0.0368	0.0315	0.0353
	O3	0.9072	0.9058	0.8986			0.0352	0.0344	0.0356

Table F .2 Time-series regressions of 18 Size-B/P-DLI sorted portfolios on FF3F Model, Chinese stock market (July 2005 to May 2015)

 F This table reports the time-series regression results of 18 Size-B/P-DLI sorted portfolios on FF3F Model. The stocks are divided into two size groups based on the breakpoint of median market capitalization, and the breakpoints for the three B/P groups are the top 30%, median 40% and bottom 30% of B/P ratio, similarly as B/P groups, the stocks are divided into three groups based on their O-score (O1, O2 and O3, represent the low, medium and high O-score separately). The intersection of two size groups, three B/P groups and O-score groups form 18 portfolios. The left part of the table is the coefficients of time-series regressions and adjusted R-square, the right part is the corresponding t-stats corrected for heteroscedasticity and autocorrelation using Newey-West estimator and residual standard error, and the numbers in bold are significant at 5% confidence level.

			Table F.2 Continued
				Big size
	DLI				B/P ratio
		L	M	H			L	M	H
			a					t ( a )
	D1	Regression: i ,t R -0.0001 -0.0032 R a b ( R f i i M ,t    -0.0051		f R ) s SMB h HML e i i i ,t    -0.0287 -1.2382	-1.6917
	D2 D3	-0.0054 -0.0027	-0.0022 -0.0051	-0.0022 Small size -0.0039	-1.9525 -0.8710	-0.8175 -1.6936	-0.8457 -1.6293
	DLI		b		B/P ratio	t (b)
	D1	L 0.9290	M 1.0053	H 0.9359			L 20.0667	M 27.0452	H 17.9607
	D2	1.0405	a 1.0926	1.0638			15.5261	t ( a ) 20.9450	20.9343
	D1 D3	-0.0025 1.0942	0.0002 1.1301	-0.0031 1.0846			-0.9101 22.2336	0.0587 17.9663	-0.9167 18.8849
	D2	-0.0081	-0.0019 s	-0.0005			-2.8124	-0.8704 t (s)	-0.2072
	D3 D1	0.0014 0.6290	0.0004 0.8346	-0.0013 0.9219			0.3786 5.9958	0.1655 7.5760	-0.5089 8.1997
	D2	0.7953	b 0.7991	0.7913			6.3616	t (b) 7.6778	8.4618
	D1 D3	0.9817 0.6881	0.9758 0.7427	0.9545 0.7786			19.5959 6.7352	21.2488 5.4622	23.9619 7.5786
	D2	1.0116	1.0041 h	1.0103			20.3742	22.2973 t (h)	20.1025
	D3 D1	1.0067 -0.6961	1.0209 -0.2435	1.0050 0.4531			19.4264 -5.5203	25.5842 -1.6542	16.4963 3.5546
	D2	-0.4687	s -0.1322	0.4000			-3.2566	t (s) -0.8330	3.3928
	D1 D3	1.4510 -0.2559	1.4549 0.0840	1.6158 0.7448			17.1267 -1.7169	12.7620 0.6183	13.5801 5.6516
	D2	1.6063	1.4122 Adj R-square	1.4775			14.7615 Residual standard error 16.0700 12.1172
	D3 D1	1.4346 0.8559	1.3751 0.8798	1.3206 0.8687			14.0215 0.0362	14.3170 0.0356	12.4977 0.0366
	D2	0.8724	h 0.8993	0.9105			0.0379	t (h) 0.0346	0.0323
	D1 D3	-0.2634 0.8781	-0.1172 0.8830	0.4312 0.9203			-1.9823 0.0380	-0.8851 0.0387	2.8019 0.0317
	D2	-0.0145	0.0316	0.3284			-0.1077	0.2800	2.3027
	D3	0.1395	0.2050	0.4360			1.0807	1.7397	3.3278
			Adj R-square				Residual standard error
	D1	0.9173	0.9073	0.8990			0.0321	0.0339	0.0364
	D2	0.9211	0.9286	0.9087			0.0328	0.0297	0.0347
	D3	0.8847	0.9205	0.9090			0.0389	0.0317	0.0336

The dividend discount model and the free cash flow to equity model are also two well-known models that are supposed to estimate inherent value of common equities.

SFG Consulting report of the Fama-French model.

Recently, Novy-Marx (2013) identifies a proxy today that predicts expected earnings tomorrowthe profitability factor, which is strongly related to average stock return, and the investment factor was documented by[START_REF] Aharoni | Stock returns and the Miller Modigliani valuation formula: Revisiting the Fama French analysis[END_REF], see also[START_REF] Titman | Capital investments and stock returns[END_REF], although it has a high correlation with the value and profitability factors, the investment effect is perhaps half as strong, but it is still reliable and significant.1.1 Reviews of the main asset pricing theories and models

Portfolio SW contains firms with small size and weak profitability, SN contains firms with small size and neutral profitability, SR contains firms with small size and robust profitability, similarly to BW, BN and BR, which contains firms with big size and weak profitability, neutral profitability and robust profitability separately.

Portfolio SC contain firms with small size and conservative investment, SN contains firms with small size and neutral investment, SA contains firms with small size and aggressive investment, similarly to BC, BN and BA portfolios.

1.2 Retrospective of empirical work of Fama-French factor models

[START_REF] Eun | Asset pricing in China's domestic stock markets: Is there a logic?[END_REF],[START_REF] Wang | The cross section of expected stock returns in the Chinese A-share market[END_REF],[START_REF] Burmeister | Cross-sectional stock return predictability in China[END_REF] and[START_REF] Gan | An empirical cross-section analysis of stock returns on the Chinese A-share stock market[END_REF].1.2 Retrospective of empirical work of Fama-French factor models

Source: Bloomberg Finance L.P.

Source: http://www.stats.gov.cn/

See Sun and Tong (2000),[START_REF] Chen | Foreign ownership restrictions and market segmentation in China's stock markets[END_REF],[START_REF] Fung | SEGMENTATION OF THE A-AND B-SHARE CHINESE EQUITY MARKETS[END_REF] and[START_REF] Fernald | Puzzles in the Chinese stock market[END_REF].

[START_REF] Ahlgren | Panel cointegration of Chinese A and B shares[END_REF]

The financial firms are excluded because their high leverage which is normal for these firms maybe does not have the same meaning for non-financial firms, where high leverage more likely presents high distress risk.1.4 Empirical Analysis and Results of FF3F Model

Chapter1Fama-French Five-Factor Model vs. Fama-French Three-Factor Model in China

For example,[START_REF] Jagannathan | The conditional CAPM and the cross-section of expected returns[END_REF] include a labor income growth factor which performs well in explaining the cross-section of average returns,Li, Vassalou, and Xing (2006) introduce Sector Investment Growth Rates,[START_REF] Liew | Can book-to-market, size and momentum be risk factors that predict economic growth?[END_REF] document that the size and B/M factors predict future economic growth in some countries,[START_REF] Vassalou | News related to future GDP growth as a risk factor in equity returns[END_REF] find that much of information contained in the size and B/M factors is related to future GDP growth.

[START_REF] Campbell | Intertemporal Asset Pricing without Consumption Data[END_REF] extends[START_REF] Merton | An intertemporal capital asset pricing model[END_REF]'s model to a discrete-time ICAPM and derives a simple non-consumption based model with two risk factors: the unexpected current period return on the market portfolio, and news about future expected returns on the market portfolio.

See also researches on inflation:[START_REF] Shi | Augmenting the Intertemporal CAPM with Inflation: Some Further Evidence in Alternative Models[END_REF],[START_REF] Adams | The effects of inflation news on high frequency stock returns[END_REF],[START_REF] Bottazzi | Analysing the risk premium in the Italian stock market: ARCH-M models versus non-parametric models[END_REF] on Italy market.

There are other approaches to estimate the innovations of state variables:[START_REF] Brennan | Estimation and test of a simple model of intertemporal capital asset pricing[END_REF] assumed the Ornstein-Uhlenbeck process whereas[START_REF] Hahn | Yield spreads as alternative risk factors for size and book-tomarket[END_REF] use the simple changes of state variables.

We examine the cross-sectional validation of FF3F Model on Chinese A-share stock market during July 2004 to May 2015, and we find that there exists market premium and size premium over this sample period.

[START_REF] Lev | The Boundaries of Financial Reporting and How to Extend Them (Digest Summary)[END_REF],[START_REF] Mensah | An examination of the stationarity of multivariate bankruptcy prediction models: A methodological study[END_REF],[START_REF] Hillegeist | Assessing the probability of bankruptcy[END_REF],[START_REF] Wu | A comparison of alternative bankruptcy prediction models[END_REF],[START_REF] Begley | Bankruptcy classification errors in the 1980s: An empirical analysis of Altman's and Ohlson's models[END_REF].

For a rigorous discussion of Ito's Lemma, see[START_REF] Mckean | Stochastic integrals[END_REF] and for references to its application in portfolio theory, see[START_REF] Merton | Theory of rational option pricing[END_REF]

Their database includes over 250,000 company-years of data and over 4,700 incidents of default or bankruptcy.

In the static logit model, the number of firm-years is used in calculating the Wald statistics. However, this is not correct for the dynamic logit model because in the dynamic logit model, unlike the static logit model, firm-year observations are not independent of each other. For the dynamic logit model, it is the number of firms rather than the number of firm-years that should be used.

Acknowledgement

The journey of my research in IGR-IAE (Université de Rennes 1, France) will come to the end soon. I am so lucky that I could study for my Ph.D. degree in France and in Rennes with the help of so many excellent professors and colleagues. First of all, I would like to thank my supervisor Mr. Jean-Jacques LILTI, I appreciate that you accept me as your student, thanks for your patient guidance, encouragement, and advice that you have provided throughout my research.

List of Tables

In applying standard OLS method to a CSR, we assume that the right-hand variables β are fixed. However, when implementing Fama-MacBeth two-stage approach, the β in the CSR are not fixed, of course, but are estimated in the TSR. Therefore, the explanatory variable in the CSR is measured with error. Hence, it is very important to determine whether the relation between average stock returns and the risk factors is the result of the misspecification of the asset pricing model or is simply a consequence of the EIV problem. [START_REF] Shanken | On the estimation of beta-pricing models[END_REF] modifies the traditional two-pass procedure and derives an asymptotic distribution of the CSR estimator within a multifactor framework in which asset returns are generated by portfolio returns and prespecified factors. Shanken also provides an adjustment for the standard errors of the CSR estimators with a multifactor interpretation [START_REF] Cochrane | Asset Pricing[END_REF] derives the correct asymptotic standard errors due to [START_REF] Shanken | On the estimation of beta-pricing models[END_REF],.

With the simplifying assumption that the errors ε are i.i.d. over time and independent of the factors, the result is

where λ is the factor risk premia, β is the TSR coefficients matrix,  is the variance- covariance matrix of residuals, f  is the variance-covariance matrix of the factors.

Appendix B

Performance of FF3F Model and FF5F Model on U.S. stock market This table presents the results of cross-section regressions on FF3F Model of FF six value-weighted Size-B/M portfolios (Panel A) and 25 value-weighted Size-B/M portfolios (Panel B). In each panel, the first row is the cross-sectional regressions' coefficients (coef.); the second row is the corresponding Fama-MacBeth t-statistics (FM t-stats) at 5% confidence level, and the third row is the Shanken corrected t-statistics (SH t-stats). The numbers in bold are the t-stats which are significant at 5% level. The adjusted R-squares are percentage values. The default probability is the probability that the firm's assets value is less than the book value of the firm's liabilities, which is:

where t P is the probability of default at time t, A,t V and t X are the market value of the firm's assets and the book value of the firm's liabilities at time t, and A,t T V  is the market value of the firm's assets due at time T.

Since the value of firm's assets follows GBM of

(equation 3.5), the value of assets at time t is given by: