Ma contribution la plus importante est de montrer qu'après les opportunités sont grandes, les rendements ultérieurs des actions difficiles à évaluer sont plus importantes. Par exemple, les actions avec petite capitalisation ont des rendements avec 1,32% par mois plus grands quand les opportunités précédentes avaient été grandes, par rapport aux moments quand les opportunités précédentes avaient été petites. Pour les actions volatiles, la différence est 1,83% par mois. Pour les actions pas suivie, la différence est 1,05% par mois. Les résultats sont robustes aux différentes constructions de la mesure des opportunités. Elles sont robustes aussi à l'exclusion du mois janvier de l'échantillon. xii

Chapitre 3 : Quand et comment les fonds d'investissements changent-ils leur style ? J'étudie comment les fonds d'investissements changent-ils leur style. Sans être exhaustive, un fond peut changer son style d'investissement dans les situations suivantes : (Hypothèse 1) le gérant réagit aux circonstances ; (Hypothèse 2) après une performance mauvaise ; (Hypothèse 3) le gérant veut être plus proche du style des autre gérants ; (Hypothèse 4) il y a un nouveau gérant pour le fond ; (Hypothèse 5) les fonds changent leur style simultanément à travers plusieurs dimensions (plutôt que de le faire pour chaque dimension séparément). Je trouve que (1) les gérants ne prennent pas plus des risques quand ça serait plus profitable de la faire ; (2) après le gérant avait connu une mauvaise performance, il ne prend pas des risques en dehors du son style ; (3) les fonds avec mauvaise performance se rapprochent du style des fonds avec bonne performance ; (4) nouveau gérants se différencient des ancien gérants des fonds ; (5) quand un fond prend des risques dans une dimension du style, il ne considère pas simultanément son risque dans les autre dimensions du style (à l'exception du momentum). Ces résultats suggèrent que les styles des fonds sont stables, ce qui est en ligne avec la littérature (Wermers (2012)). Le style et le risque sont entrelacés. Je me réfère aux changements de style comme style drift (glissement du style), comme dans Wermers (2012), notamment parce que ces changements ne sont pas très importants. Je classe les styles en tenant compte des quatre dimensions : capitalisation, valeur comptable -valeur de marché, performance passé, et liquidité. Je définis le style d'un fond d'investissement comme exposition aux facteurs de risque connus. Pour les investisseurs, connaître la position du fond, d'après son exposition aux risques, leurs permet d'évaluer si un fond correspond à leurs préférences pour risque. En plus, ils peuvent surveiller si et quand un fond s'éloigne de son style. Si un fond améliore soudainement sa performance, il pourrait être que le fond investit dans des actions avec plus du risque, et non pas parce qu'il est devenu meilleur à sélectionner les actions. En utilisant les quatre dimensions du risque, xiii on peut regarder comment le style d'un fond glisse : un fond peut passer à investir plus dans des actions plus illiquides, sans changer son exposition au risque de capitalisation (size risk) ; un investisseur qui surveille seulement l'exposition au risque de capitalisation pourrait rester ignorant vis-à-vis son exposition au risque de liquidité devenue plus élevée. xiv

Résumé en français: Trois essais sur la gestion des actifs Il y a une vaste littérature scientifique qui étudie la performance des fonds d'investissements, et particulièrement les questions suivantes: Est-ce que les fonds d'investissements actifs ont-ils une meilleure performance que les fonds qui suivent des indices ? Est-ce qu'il y a des opportunités des prix dans les marchés, et si c'est le cas, est-ce que les fond d'investissements sont-ils suffisamment compétents pour les exploiter ? Si quelques fonds sont compétents, est-ce que leurs investisseurs peuvent en bénéficier, ou c'est bien les gérants des fonds qui profitent ? S'il y a des profits pour les investisseurs, est-ce qu'ils ne sont pas que des compensations pour des risques augmentés ? Ma thèse contribue à cette littérature dans les directions suivantes : premièrement, je trouve que les fonds qui investissent dans des actions plus illiquides sont compètent, et que leurs investisseurs peuvent en bénéficier. Deuxièmement, j'identifie une mesure des opportunités d'investissements, et je montre que si les opportunités sont grandes, la performance suivante pour les actions difficiles à évaluer est plus grande aussi. Cependant, cette performance supérieure provient d'un risque plus élève de sélection défavorable. Troisièmement, j'étudie si les gérants des fonds changent leur style d'investissement en fonction des conditions du marché, et je trouve que les styles sont très stables (ce qui est en ligne avec la littérature existante). Néanmoins, je trouve quelques exemples intéressants concernant les styles des gérants. En-dessous, il y a une description des trois chapitres de la thèse. Dans ce chapitre je trouve que les fonds qui investissent dans des actions illiquides ("fonds illiquides") surpassent les fonds qui investissent dans des actions liquides (1,38% par an avant les frais, 1,18% per an après les frais, ajustés pour risque en utilisant le model de Carhart).

Je trouve que cette surperformance arrive parce que les fonds illiquides ont une meilleure capacité de sélectionner les bonnes actions. Sélectionner les bonnes actions signifie investir dans des actions qui auront un meilleur rendement.

Une explication possible pour mes résultats est que les fonds qui ne sont pas compétents ne survivent pas s'ils investissent dans des actions illiquides, parce que les actions illiquides ont des coûts de transaction plus grands. Par exemple, considérons des fonds compétents et des fonds non qualifié, qui peuvent investir soit dans des actions liquides, soit dans des actions illiquides.

Je définis compétence comme la capacité de trouver et exploiter les opportunités de prix. Si les fonds compétents et les fonds non qualifié sont appariés au hasard avec des actions liquides ou illiquides, on aura quatre paires : fonds compétents investis dans des actions liquides ; fonds compétents investis dans des actions illiquides ; fonds non qualifié investis dans des actions liquides ; fonds non qualifié investis dans des actions illiquides. Les coûts de transaction sont plus grands dans les actions illiquides, et par conséquent, ce n'est que les fonds compétents qui survivent s'ils investissent dans des actions illiquides. Autrement dit, seulement les fonds illiquides peuvent identifier des opportunités de prix si grandes qu'ils produisent un grand alpha même après la soustraction des coûts de transaction. Pour donner cet exemple, j'ai fait l'hypothèse que les quatre paires ont la même probabilité d'apparition, et que la paire "fond non qualifié -actions illiquides" disparaît vite parce que, sans compétence et avec des coûts de transaction grands, le fond aura des mauvais rendements. Les investisseurs retirent leur argent au point où le fond doit fermer. Comme une paire avec corrélation négative entre compétence et illiquidité (fond non qualifié, donc bas compétence -actions illiquides, donc haut illiquidité) disparaît vite, on aura une corrélation positive entre compétence et illiquidité parmi les fonds restants. Cette explication requiert peu de structure : les fonds n'ont pas besoin de savoir s'ils sont compétents ou non ; ils n'ont pas besoin de choisir s'ils investissent dans des actions liquides ou illiquides. La relation entre compétence et illiquidité provient v automatiquement de la survie des fonds. Les fonds illiquides qui survivent sont compétents.

Pour mesurer l'illiquidité de chaque action, j'utilise la mesure introduit par [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series effects[END_REF].

La mesure se calcule comme le changement absolu du rendement qui correspond à la quantité transactioneé, en dollars. L'avantage de cette mesure c'est sa simplicité, parce qu'il n'y a pas besoin de data de la microstructure du marché. Je divise les actions dans des déciles d'illiquidité et j'attribue à chaque action le nombre du décile où elle se trouve. Ensuite, je calcule le score d'illiquidité pour chaque fond et pour chaque date, en fonction des actions qui sont dans son portefeuille.

Mon échantillon contient des fonds qui investissent dans des actions. Les données proviennent de la base de données CRSP Mutual Funds et couvrent la période 1983-2014. Pour les actions détenues, j'utilise la base de données Thomson Reuters. Je trouve que les fonds illiquides surpassent les fonds liquides avec 1,38% par an (t-stat 2,93). Les rendements sont ajustés pour risque en utilisant le model de Carhart (1997). Les résultats sont robustes si on divise d'abord les fonds en fonction de capitalisation, âge, rotation des actions détenues ou frais.

Les résultats tiennent aussi par sous-échantillons (1983-1998 et 1999-2014), mais ils sont plus forts pour la deuxième période. Pour les deux sous-échantillons, la différence des rendements entre les fonds illiquides et les fonds liquides est 1,20% par an (t-stat 1,85) pour la période 1983-1998, et 1,56% per an (t-stat 2,28) pour la période 1999-2014.

Si les rendements sont ajustés pour risque en utilisant le model de Pástor et Stambaugh (2003), la différence entre les fonds illiquides et les fonds liquides devient 0,64% par an (t-stat 1,25). Le model de Pástor et Stambaugh inclut un facteur en plus, la liquidité. La différence entre les fonds illiquides et les fonds liquides devient plus petite, et le t-stat est plus petit aussi, ce qui suggère que une partie de cette différence est en effet une compensation pour le risque d'illiquidité. Les détenteurs des actions illiquides doivent être compensés pour l'illiquidité, parce que l'illiquidité implique des périodes plus longues pour vendre ses actions, un impact sur les prix plus important, etc.

Pour tester s'il y a des fonds compétents qui arrivent à bien sélectionner les actions, j'utilise les dates concernant les actions détenues par les fonds. Je compare chaque action avec un portefeuille des actions avec les mêmes caractéristiques, comme dans l'article de Daniel, Grinblatt, vi Titman et [START_REF] Daniel | Measuring Mutual Fund Performance with Characteristic-Based Benchmarks[END_REF] (désormais DGTW). Les caractéristiques utilisées par DGTW sont capitalisation, valeur comptable -valeur de marché, et momentum (la tendance qu'ont les actions à persister dans leur performance). Je rajoute une quatrième caractéristique, la liquidité. Ensuite, je calcule les rendements ajustés pour les caractéristiques : la différence entre les rendements basés sur les actions détenues en réalité par les fonds, et les rendements théoriques, comme si les fonds avaient investi dans les portefeuilles avec les mêmes caractéristiques, correspondent à chaque action. Je trouve que les fonds illiquides surpassent les fonds liquides avec 2,57% per an (t-stat 3,98) quand les rendements sont ajustés pour les caractéristiques comme en-dessus. Cela démontre que les fonds illiquides peuvent sélectionner les meilleures actions.

Je teste si les fonds liquides déclarent dans leurs brochures des indices opportuns, même si ces indices ne sont pas les plus proches en termes de portefeuilles. Si les fonds liquides sont en effet moins compétents que les fonds illiquides, alors les fonds liquides seront motivés pour cacher leur (mauvais) performance. Une possibilité serait de déclarer dans la brochure un indice qui n'est pas le plus proches en termes de portefeuille. Par exemple, si un fond déclare comme indice le S&P500, mais il est investi dans des actions petites (d'après capitalisation), alors les rendements du fond par rapport au S&P500 seront mieux que ses rendements par rapport au Russell 2000 (actions avec petite capitalisation) à cause de l'effet de capitalisation (size effect). Toutefois, l'indice correct pour ce fond serait Russell 2000. Je calcule des rendements ajustés pour l'indice, avec l'indice qui est déclaré dans la brochure. Je trouve que les fonds illiquides surpassent les fonds liquides avec 1,59% par an (t-stat 1,21). La différence devient 5,63% par an (t-stat 1,32) si j'utilise plutôt l'indice le plus proche en termes de portefeuille (au lieu de l'indice déclaré dans la brochure), comme dans [START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF]. Les fonds illiquides ont des rendements ajustés pour l'indice de 1,12% par an en moyenne, et les fonds liquides ont des rendements ajustés pour l'indice de -0,47% par an en moyenne. Si on utilise les indices les plus proches en termes de portefeuilles, les fonds illiquides ont des rendements ajustés pour l'indice de 1,63% par an en moyenne, et les fonds liquides ont des rendements ajustés pour l'indice de -4% par an en moyenne. Cela indique la possibilité que quelques fonds choisissent de déclarer leurs indices stratégiquement [START_REF] Sensoy | Performance evaluation and self-designated benchmark indexes in the mutual fund industry[END_REF]. Sensoy Je teste si les investisseurs bénéficient de la compétence des fonds. Je calcule la différence entre les rendements ajustés pour le risque, après les frais, pour les fonds illiquides et les fonds liquides. La performance est mesurée comme dans le model de Carhart. Les fonds illiquides surpassent les fonds liquides avec 1,18% par an après les frais, (t-stat 2,53), pour une période de détention de 1 mois. Cette différence devient 1,21% par an, après les frais, pour une période de détention de 3 mois, 1,18% par an après les frais pour une période de détention de 6 mois, et 1,09% par an après les frais pour une période de détention de 12 mois.

Même après les frais, les fonds illiquides surpassent les fonds liquides.

Le Taux de Fausses Découvertes (TFD ; FDR en anglais), développé par Storey (2002) et utilisé par [START_REF] Barras | False discoveries in mutual fund performance: Measuring luck in estimated alphas[END_REF] pour les fonds d'investissement permet de calculer quel pourcentage de fonds ont un vrai alpha positif. J'applique cette procédure séparément pour le groupe de fonds illiquides et le groupe de fonds liquides. Je trouve que 77,45% des fonds liquides ont l'alpha zéro (après les frais), par rapport au 84,76% parmi les fonds illiquides. Le pourcentage de fonds avec alpha positif est 2,78% parmi les fonds illiquides, par rapport au 0,80% parmi les fonds liquides. Il y a 21,75% fonds avec alpha négatif parmi les fonds liquides, et 12,46% fonds avec alpha négatif parmi les fonds illiquides.

Globalement, cela indique qu'il y a plus de compétence parmi les fonds illiquides.

La différence de compétence n'est pas bien saisie par Morningstar Ratings, bien que cela viii puisse être parce que les scores Morningstar sont calculés en arrière.

Si les fonds illiquides sont plus compétents et produisent alpha, alors la théorie prédit que cette compétence attirait des entrées de capitaux jusqu'au point ou le rendement attendu pour les investisseurs serait zéro. Je teste comment c'est possible que les fonds illiquides aient alpha positif, sans qu'il soit annulé par les entrées de capitaux. Une explication possible serait que les investisseurs dans des fonds illiquides ont une élasticité des flux de capitaux à la performance de fonds moins grande. Je trouve le résultat surprenant comme qu'il y a une corrélation positive entre l'élasticité des flux de capitaux à la performance et illiquidité de 13%. Cela signifie que plus un fond est illiquide, plus l'élasticité des flux de capitaux à la performance est grande.

Un autre test pour la compétence des fonds illiquides est d'analyser la performance des actions détenues par les fonds illiquides contre la performance des actions détenues par les fonds liquides. Je réalise ça séparément pour les actions illiquides et pour les actions liquides. Les testes pour les actions illiquides manquent de la puissance statistique parce que les fonds liquides détiennent très peu des actions illiquides, moins de 1% de leur portefeuille.

Pour les actions liquides, les actions liquides détenues par les fond illiquides surpassent les actions liquides détenues par les fonds liquides avec 1,81% par an (t-stat 1,71), pour les trois mois suivants, ajustés pour risque en utilisant le model de Pástor-Stambaugh, qui contient un facteur pour la liquidité. Une explication alternative serait que les rendements des fonds illiquides sont générés mécaniquement, et non pas en fonction de la compétence des fonds.

Si, par exemple, plusieurs fonds illiquides achètent une action illiquide au même temps, le prix d'action monte, et ça apparaît comme rendement positif pour les fonds. J'analyse si les transactions des fonds se superposent, séparément pour les fonds illiquides et pour les fonds liquides. Je ne trouve pas une différence entre les deux groups. Il n'y a toujours pas une différence, même si j'analyse séparément les achats et les ventes. En plus, le pourcentage moyen des actions existantes dans le marché qui est transactioné d'un trimestre à l'autre, par les fonds illiquides, est assez petit (moins de 2%) pour produire un impact sur le prix. ix Chapitre 2 : Opportunités de prix et rendements attendus Grossmann et Stiglitz (1980) démontre qu'il y a toujours des opportunités de prix (actions qui n'ont pas le prix correct) dans les marchés financiers. L'information privée est difficile à obtenir, donc s'il n'y a pas des opportunités de prix qui donnent des profits, il n'aura pas des traders informés. Mais dans l'absence des traders informés, il aura sûrement des opportunités de prix, parce que ce ne que l'action des traders informés qui réduit les opportunités de prix.

Pour résoudre ce paradoxe, Grossmann et [START_REF] Grossman | On the Impossibility of Informationally Efficient Markets[END_REF] introduisent des noise traders, des traders sans information. Les traders informés peuvent donc profiter des opportunités de prix créés par les noise traders.

En ligne avec Grossmann et [START_REF] Grossman | On the Impossibility of Informationally Efficient Markets[END_REF], je définis les opportunités simplement comme l'existence des actions qui n'ont pas le prix correct. Si on suppose que les opportunités sont le résultat des chocs aléatoires de prix, on peut s'attendre que les opportunités varient dans le temps.

Dans ce chapitre, j'utilise des opportunités qui varient dans le temps pour identifier les moments où les avantages d'avoir de l'information privée sont grands ou pas. Ensuite, ça permet d'identifier la variation de sélection défavorable, qui à son tour permet de prédire une partie des primes de risque.

Considérons le cas d'un trader informé, qui doit payer pour acquérir l'information. Il peut payer le prix pour apprendre après qu'il n'y a pas beaucoup des opportunités de prix dans le marché à un moment donné. Idéalement, il payerait le prix pour acquérir l'information au moment où il y a beaucoup des opportunités de prix dans le marché. Autrement dit, il payerait le prix pour acquérir l'information au moment où le bénéfice de l'information est grand.

Comment un trader pourrait-il savoir quand il y a plus des opportunités de prix dans le marché ? Considérons d'abord le rôle de l'information. C'est raisonnable que les actions pour lesquelles il y a plus d'information aient des prix plus corrects. Pensons aux actions suivies par les analystes et aux actions qui ne sont pas suivies. C'est raisonnable de penser que les actions suivies aient des prix plus corrects parce que les analystes cherchent l'information

x concernant les actions et ils font des recommandations. Les actions qui ne sont pas suivie contiennent moins d'information publique, simplement parce qu'il y a moins d'information publique concernant les actions pas suivie. Les actions qui ne sont pas suivi pourraient contenir de l'information privée, mais ça serait difficile d'évaluer. Donc, sans connaître quel type d'information, et combien d'information, est contenue dans les actions pas suivie, la première pensée de quelqu'un serait que les actions pas suivie se déplacent vers le haut et vers le bas avec le marché. Une possibilité alternative serait que les actions pas suivie sont toujours plus risquées que les actions suivies, mais dans ce cas on pourrait observer une prime de risque, ce qui n'est pas le cas. Si on construit un portefeuille où on achète les actions pas suivies et on vend les actions suivies, ce portefeuille a un rendement de -0,64% par an en moyenne.

Ce portefeuille a une déviation standard de 3,53%, ce qui suggère que les actions pas suivies réagissent au même temps que les autres actions pas suivies, et que les actions suivies réagissent au même temps que les autres actions suivies. Cette réaction est importante, parce qu'il signifie que les actions pas suivie pourraient réagir au même facteur de risque.

Quand un trader informé voit que les actions pas suivies se déplacent avec les actions suivies, il tire la conclusion qu'il n'y a pas beaucoup des opportunités de prix dans le marché. Il ne serait pas rentable de payer le prix pour acquérir de l'information, parce que le bénéfice de l'information ne serait pas important. Toutefois, quand le trader observe que les rendements des actions pas suivies sont différents de ceux des actions suivies, le trader serait plus disposé à acquérir l'information privée : il y a potentiellement plus des opportunités de prix.

En plus, ces opportunités seront probablement concentrées parmi les actions pas suivies. Je vais me référer au moment où les rendements des actions pas suivies s'éloignent des rendements des actions suivies comme des opportunités de prix étant importantes dans le marché.

Un investisseur, en observant que les rendements des actions pas suivies s'éloignent des opportunités des actions suivies, sait qu'il y a potentiellement plus des opportunités de prix parmi les actions pas suivies. Il sait que les traders informés vont payer le prix pour acquérir l'information (supplémentaire) et qu'ils vont réaliser des transactions en fonction de cette information. Ainsi, les investisseurs craindront la sélection défavorable et demanderont un rendement attendu plus élevé pour détenir des actions pour lesquelles il y a potentiellement xi des opportunités de prix.

Introduction

There is a large literature that focuses on the performance of mutual funds, and in particular on the following important questions: Do active mutual funds perform better than index mutual funds? Are there mispricing opportunities in the market, and if so, are mutual fund managers skilled enough to exploit them? If some active mutual funds are skilled, do investors gain anything, or is it the managers who extract the surplus? If there are indeed gains for the investors, do they translate into actual alpha, or are these gains simply compensation for more risk exposure (in which case the true alpha is zero)?

My thesis contributes to this literature in the following three directions: First, I find evidence that mutual fund managers who invest in illiquid stocks are skilled, and investors benefit from this skill. Second, I identify a measure of investment opportunity (not limited to mutual fund managers) and I show that a high investment opportunity predicts superior performance of a particular type of stocks that are difficult to value. This superior performance, however, can be attributed to an increase in adverse selection risk. Third, I study whether mutual fund managers change their investment style with market conditions, and I find (consistent with the existing literature) that manager styles are very stable. Nevertheless, I find some interesting patterns regarding the managers style choices. Below there is a brief overview of the chapters corresponding to the three research directions mentioned above.

Liquidity, performance and skill in mutual funds

In the first chapter I explore whether managers who invest in illiquid stocks perform better than managers that invest into liquid stocks, even after accounting for the illiquidity premium.

I find that this is indeed the case. Intuitively, when investing predominantly in illiquid stocks managers potentially find more mispricings, but their transaction costs are expected to also be higher. Hence, only managers skilled enough to identify the most mispriced stocks "survive" while investing their fund in illiquid stocks. Consistent with this intuition, I find that the 4-factor alphas of mutual funds that hold illiquid stocks ("illiquid funds") are higher than xv for funds that hold liquid stocks ("liquid funds") by 1.38% per year if one ignores fees, or by 1.18% if fees are taken into account.

I further provide evidence that this outperformance arises from the stock selection skills of illiquid fund managers. Illiquid funds outperform liquid funds in subsamples, and by various tranches of size, age, turnover and fees. Illiquid funds are smaller, younger and have slightly higher fees. The stocks held by illiquid funds outperform portfolios matched by characteristics. At the same time, I find that liquid funds choose to declare benchmarks that make their benchmark-adjusted returns appear larger. All funds are very close to their benchmarks in terms of illiquidity of their holdings. A portfolio of stocks held by illiquid funds subsequently outperforms a portfolio of stocks held by liquid funds, in simple returns and risk-adjusted returns that account for differences in liquidity.

Opportunities and expected returns

The second chapter studies the effects that information opportunities have on stock average returns. Normally, one expects neglected stocks (i.e., stocks not covered by analysts) to have a higher cost of producing information than covered stocks. But the benefit of information production in neglected stocks is also potentially higher. Therefore, in the cross-section of stocks, one cannot say with certainty that neglected stocks should have a higher risk premium than covered stocks. Indeed, the literature does not find any such pattern in the data, and neither do I.

Nevertheless, in the time-series one can find periods called "high opportunities" in which by definition neglected and covered stocks strongly diverge, possibly because of random order flow shocks. When these high opportunities occur, the benefit of information production in neglected stocks, or in general in difficult-to-value stocks, is expected to rise. As a result, there is more adverse selection in difficult-to-value stocks during high opportunities, and thus higher risk premia for the hard-to-understand stocks. Note that this is not true unconditionally, and this is why the previous literature does not find significant unconditional risk premium differences between neglected and covered stocks.

xvi Thus, I document a predictability pattern in returns: after a period of high opportunities, the subsequent risk premia of difficult-to-value stocks (small stocks, neglected stocks, illiquid stocks, young stocks, etc.) are higher. This pattern is consistent with a theoretical model in which following a period of high opportunities investors expect a higher probability of informed trading in difficult-to-value stocks and therefore demand a higher premium to hold these stocks. Empirically, I find that the average returns of small stocks are higher by 1.32% per month when previous opportunities are high as compared to times when previous opportunities are low. For stock with high volatility the difference is 1.83% per month, and for neglected stocks the difference is 1.05% per month.

When and How Do Mutual Funds Change Their Style?

The third chapter describes instances when a mutual fund manager changes her investment style. In general, mutual fund style is defined by its exposure to various risk factors (size, value, liquidity, momentum). My results are that mutual funds do not take more risk when it is actually more profitable to do so. After performing badly, mutual funds move closer to the style of good performing peer funds. Young funds' styles diverge from the style of old peer funds. Recently hired managers diverge in style from veteran managers of peer funds.

When the average fund takes more risk alongside a style dimension, it does not simultaneously consider other style dimensions. Funds do not take riskier bets outside their style when they lag behind their peers.

xvii

Contents

Hypothesis 1:

The manager takes more risk in response to incentives .

Hypothesis 2:

The manager takes more risk after bad times, or takes bets outside his style when he lags behind his peers . . . . . . . . . . .

Hypothesis 3:

The manager wants to be close to the style of his peers . superior skill (if they perform better than a passive investment) and whether investors benefit from it. This is of particular interest to the investors as well, given that active funds have higher fees than index funds. Performance seems the natural candidate to assess skill. The evidence is that roughly half of the funds have positive, and half negative, risk-adjusted performance before fees, while the median performance is negative after fees [START_REF] Pástor | Mutual fund performance and seemingly unrelated assets[END_REF]). The average fund does not appear to have skill. What about the best performing funds? The difficulty is one cannot easily distinguish between skill and luck in the realisation of performance.

Hypothesis

The literature has converged to identify groups of funds, by some characteristics, that outperform a benchmark. For example, [START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF] show that more active funds outperform less active funds. [START_REF] Kacperczyk | Fund manager use of public information: New evidence on managerial skills[END_REF] find that reliance on public information contains information about manager skill. [START_REF] Pástor | Do Funds Make More When They Trade More[END_REF] find that active mutual funds perform better after trading more.

My paper contributes to this literature. I find that active mutual funds holding illiquid stocks outperform those holding liquid stocks (1.38% per year before fees, 1.18% per year after fees, risk-adjusted using the 4-factor risk model of Carhart). I find evidence this outperformance arises at least partly from stock selection skills, so it is not entirely an illiquidity premium.

Stock selection implies picking individual stocks that the fund expects to outperform other

1 Source: Investment Company Institute, 2015.

stocks. Also, fees of funds invested into illiquid stocks are slightly higher (with 0.03% per year higher). In the paper I use the term funds to refer to fund managers -the fund is only as good as its manager. For ease of exposition, I henceforth refer to funds invested into illiquid stocks as illiquid funds, and to funds invested into liquid stocks as liquid funds.

One possible intuition behind my findings is that unskilled funds do not survive the high trading costs in illiquid stocks. Consider skilled and unskilled funds that can invest into either liquid or illiquid stocks. I define skill as the ability of a fund to identify and exploit mispricings in the stock market. If skilled or unskilled funds are matched randomly to liquid or illiquid stocks, there will be four pairings: skilled funds holding liquid stocks; skilled funds holding illiquid stocks; unskilled funds holding liquid stocks; and unskilled funds holding illiquid stocks. Because trading costs are greater in illiquid stocks, only the skilled funds survive in illiquid stocks. In other words, only skilled funds can identify mispricings so great that there is still a high alpha even after subtracting the high trading costs. For this example, I assume that the four pairings are equally likely, and I assume that the negative correlation "low skill-high illiquidity" pairing disappears fast because in the absence of skill and with high trading costs, the funds will have poor performance. Investors then move money away from the funds to the point where the funds close. Because a negative correlation pairing disappears ("low skill-high illiquidity"), then a positive correlation between skill and illiquidity is induced among the surviving funds. This intuition requires very little structure: the funds need not know their type, and need not separate into investing in liquid or illiquid stocks.

The relationship between skill and illiquidity arises mechanically from the survival of mutual funds. The remaining illiquid funds have skill. This is different from saying that skilled funds choose to invest into illiquid stocks. There may be skilled funds in liquid stocks as well, but there are no unskilled funds in illiquid stocks. The purpose of the paper is only to identify a group of skilled funds.

To measure the illiquidity of each stock, I use [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series effects[END_REF]. The measure is computed as the absolute change in return associated to the dollar traded value. The advantage of the measure is that it is straightforward and does not require any microstructure data. I divide stocks into illiquidity deciles based on the illiquidity measure and assign to each stock the corresponding decile number. Then, based on the holdings of the mutual funds, I compute the illiquidity score of each fund at each holdings disclosure date.

The tests I conduct provide a conservative measure of skill. As a researcher, I can only observe alpha after trading costs. However, if alpha after trading costs is higher for illiquid funds than for liquid funds, and assuming that trading costs are higher in illiquid stocks, then alpha before trading costs (the unobserved measure of skill) is even higher for illiquid funds than for liquid funds. samples (1983-1998 and 1999-2014), but they are stronger for the second period. For the two subsamples, the difference in performance between illiquid and liquid funds is 1.20% per year (t-stat 1.85) for 1983-1998 and 1.56% per year (t-stat 2.28) for 1999-2014.

If, instead, performance is risk-adjusted as in [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF], the difference between illiquid and liquid funds becomes 0.64% per year (t-stat 1.25). The model of Pástor and Stambaugh includes and additional factor, liquidity. The difference between illiquid and liquid funds becomes smaller, and the t-stat is smaller, suggesting that part of the initial outperformance is due to an illiquidity premium. Holders of illiquid stocks need to be compensated for illiquidity, as this means longer time to sell the stocks, higher price impact, etc.

To test if there is skill in the way illiquid funds pick stocks I exploit the holdings-based nature of the data. I match each stock held by a mutual fund with a portfolio of stocks with the same characteristics, as in [START_REF] Daniel | Measuring Mutual Fund Performance with Characteristic-Based Benchmarks[END_REF] (henceforth DGTW).

The characteristics they use are size, book-to-market and momentum. I augment with a fourth characteristic, illiquidity. Then I compute characteristics-adjusted performance: the difference between returns of actual holdings of the fund, and returns of the characteristics matched portfolios. I find that illiquid funds outperform liquid funds with 2.57% per year (t-stat 3.98) when performance is characteristics-adjusted as above. This is evidence that illiquid funds can select stocks better than liquid funds.

I test if liquid funds declare in prospectuses benchmarks that make them look better, without it being the closest benchmark in terms of holdings. If it is true that liquid funds are less skilled than illiquid funds, then liquid funds will have an incentive to hide their (poor) performance.

One way of doing so is to declare a benchmark that is not the closest in terms of holdings.

For example, if a fund declares the S&P500 as benchmark, but it invests in very small stocks then the fund will appear to do better with respect to the S&P500 benchmark than it would do with respect to the Russell 2000 index (small-stocks) because it will capture the size effect.

However, Russell 2000 index would be the correct index, or the "minimum-distance" index (the index that resembles the most in terms of holdings). I compute benchmark-adjusted returns, where benchmarks are those declared in the prospectuses. I find that illiquid funds outperform liquid funds by 1.59% per year (t-stat 1.21). The difference is 5.63% per year (t-stat 1.32) when I use instead the minimum-distance benchmark. The minimum-distance benchmark is the benchmark to which the fund is the closest in terms of holdings (as in [START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF]). The illiquid funds have average benchmark-adjusted returns of 1.12% per year, and the liquid funds have average benchmark-adjusted returns of -0.47% per year. If we use the minimum-distance benchmark instead, illiquid funds have average minimum-distance benchmark adjusted return of 1.63% per year, while the liquid funds have average minimumdistance benchmark adjusted returns -4% per year. This is evidence of strategic benchmark choosing as in [START_REF] Sensoy | Performance evaluation and self-designated benchmark indexes in the mutual fund industry[END_REF]. [START_REF] Sensoy | Performance evaluation and self-designated benchmark indexes in the mutual fund industry[END_REF] finds that 31% of funds report questionable benchmark in there prospectuses. Liquid funds may be choosing to declare benchmarks that make them look better because they are less skilled than illiquid funds.

Illiquid funds may hold stocks that are much more illiquid than the stocks in their benchmark. Then, in the benchmark-adjusted returns of illiquid funds there will also be a liquidity premium that may make them appear as being more skilled. If this is true, then some benchmarks that account for illiquidity would be needed. To test for this, I compute the illiquidity scores of the benchmarks. I find that there is not an economically significant difference in the illiquidity score of funds and their benchmarks (or their minimum-distance benchmarks).

This indicates the the currently existing benchmarks are sufficient to account for differences in liquidity between the holdings of mutual funds.

I test if investors benefit from the skill of the illiquid funds. I compute the difference in risk-adjusted performance after fees between illiquid funds and liquid funds. Performance is risk-adjusted as in Carhart's model. Illiquid funds outperform liquid funds by 1.18% per year after fees (t-stat 2.53) if there is a a 1-month holding period. This difference becomes 1.21% per year after fees if there is a 3-month holding period, 1.18% per year after fees if there is a 6-month holding period and 1.09% per year after fees if there is a 12-month holding period.

Even after fees the illiquid funds outperform liquid funds.

The False Discovery Rate (FDR), developed by Storey (2002) and used by [START_REF] Barras | False discoveries in mutual fund performance: Measuring luck in estimated alphas[END_REF] for mutual funds, allows to calculate what percentage of funds have a true positive alpha. I apply this procedure separately for the group of illiquid funds and for the group of liquid funds. I find that 77.45% of the liquid funds have 0-alpha (after fees), compared to 84.76% among the illiquid funds. The percentage of positive-alpha funds is 2.78%

among the illiquid funds, as compared to 0.80% among the liquid funds. There are 21.75%

negative-alpha funds among the liquid funds, and 12.46% negative-alpha funds among the illiquid funds. Overall, this indicates the presence of more skill among the illiquid funds.

The difference in skill between the illiquid and liquid funds in not captured by the Morningstar Ratings, although this may be because the ratings are backward looking.

If illiquid funds are more skilled and have alpha, then the theory predicts this should attract flows to the point where the expected return to investors becomes zero. I investigate why illiquid funds have positive alpha, without this being driven away by inflows. One possible explanation would be that investors into illiquid mutual funds have a lower sensitivity of flows to performance. I find the puzzling result that there is a positive correlation between sensitivity of flows to performance and illiquidity of 13%. This means that the more illiquid a fund is, the higher its sensitivity to performance.

One additional test for the skill of illiquid mutual funds is to evaluate the performance of stocks held by the illiquid funds versus the performance of stocks held by the liquid funds.

I do this test separately, for illiquid stocks and for liquid stocks. The test for illiquid stocks is weak, because liquid funds hold less than 1% of their portfolio in illiquid stocks. For the liquid stocks, liquid stocks held by illiquid funds overperform liquid stocks held by liquid funds by an average 1.81% (annualized, t-stat 1.71) over the following three months, risk-adjusted using the Pástor-Stambaugh model that includes a liquidity factor.

Another concern might be that the observed pattern of the returns of illiquid funds is mechanical, and not a result of skill. For example, if many illiquid funds buy an illiquid stock at the same time, its price will go up and this will appear as positive return for the mutual funds.

I investigate if the overlap in trades differs between the group of illiquid funds and the group of liquid funds, and I find that the answer is no. There is no difference in overlap between illiquid and liquid funds even if I consider separately buys and sells. Also, the average across stocks of the percentage of shares outstanding that is traded (quarter-to-quarter) by illiquid or liquid stock is small enough (below 2%) to produce a significant price impact.

To my knowledge, this is the first paper that uses the holdings-based data to study the difference in performance between illiquid and liquid funds. It is also the only one to motivate theoretically why illiquid funds should outperform liquid funds, ex-ante. This paper contributes to the large literature that studies performance of mutual funds. The seminal paper of [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF] predicts that expected returns (net of fees) for investors are zero, because flows act as a regulatory mechanism and there are decreasing returns to scale. More recently, [START_REF] Stambaugh | Presidential address: Investment noise and trends[END_REF] builds a model in which the switch from individual investors to institutional investors reduces the noise trading and the mispricings, so that there is less scope for active management. [START_REF] Carhart | On Persistance in Mutual Fund Performance[END_REF] shows empirically that persistence in mutual funds is explained by common factors, and that the only significant persistence manifests in the worstperforming mutual funds. [START_REF] Fama | Luck versus Skill in the Cross-section of Mutual Fund Returns[END_REF] argue that almost all good performers just got lucky. As the average fund does not appear to be skilled (nor there appears to be theoretical support for the existence of skill, on average), the literature has focused on iden-tifying groups of funds, defined by certain characteristics, that appear to be skilled. Directly connected to liquidity, [START_REF] Dong | Time-varying arrival rates of informed and uninformed trades[END_REF] use liquidity-beta exposures and document an annual liquidity beta performance spread of 4% in the cross-section of mutual funds.

Chen, Jegadeesh, [START_REF] Chen | The Value of Active Mutual Fund Management: An Examination of the Stockholdings and Trades of Fund Managers[END_REF] note that the preference for liquidity of mutual funds may be hurting their performance. [START_REF] Cohen | Best Ideas[END_REF] find that active managers' "best ideas" are more effective in illiquid stocks. My paper falls into the strand of literature that looks if mutual funds add value and identifies skilled groups of mutual funds. Chen, Hong, [START_REF] Chen | Does fund size erode mutual fund performance? The role of liquidity and organization[END_REF] show that smaller funds outperform larger funds. [START_REF] Pástor | Do Funds Make More When They Trade More[END_REF] find that active mutual funds perform better after trading more. [START_REF] Cohen | Judging fund managers by the company they keep[END_REF] find that funds whose portfolio decisions are similar to those of other funds with strong track records perform better. [START_REF] Kacperczyk | Fund manager use of public information: New evidence on managerial skills[END_REF] show that reliance on public information contains information about manager skill. Chen, Jegadeesh, and [START_REF] Chen | The Value of Active Mutual Fund Management: An Examination of the Stockholdings and Trades of Fund Managers[END_REF] find that stocks recently bought by funds in aggregate outperform stocks recently sold, suggesting that funds have stock picking skill. Cremers and Petjisto (2009) find that fund managers with higher "active share" have higher risk-adjusted returns (before and after fees). [START_REF] Kacperczyk | Unobserved Actions of Mutual Funds[END_REF] find that a fund's actions between holdings disclosure dates (the "return gap") predicts fund performance.

The chapter proceeds as follows. Section 1.2 covers the theoretical predictions. Section 1.3 describes the data and variable construction. Section 1.4 interprets the results. Section 1.5 concludes.

The model

I build the intuition on the model of [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF], in which I interpret cost as being proportional to the illiquidity of stocks traded. I conjecture that mutual funds survival induces a positive correlation between skill and illiquidity. Consider skilled and unskilled funds that can invest into either liquid or illiquid stocks. I define skill as the ability of a fund to identify and exploit mispricings in the stock market. For this example, skilled and unskilled funds are randomly matched to holding liquid or illiquid stocks. Then there will be four pairings of skill and liquidity: skilled funds holding liquid stocks; skilled funds holding illiquid stocks;

unskilled funds holding liquid stocks; and unskilled funds holding illiquid stocks. Because trading costs are greater in illiquid stocks, only the skilled funds survive in illiquid stocks. I assume that the four pairings are equally likely, and I assume that the negative correlation "low skill-high illiquidity" pairing disappears fast because in the absence of skill and with high trading costs, the funds will have poor performance. Investors move money away from the funds to the point where the funds close. Because a negative correlation pairing disappears, then a positive correlation between skill and illiquidity is induced among the surviving funds.

This intuition requires very little structure: the funds need not know their type, and need not separate into investing in liquid or illiquid stocks. The relationship between skill and illiquidity arises mechanically from the survival of mutual funds.

In [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF], a fund survives if the condition Φ t ≥ 2 √ F λ is satisfied, where Φ t is the expected return of the fund, F is the opportunity cost of the fund manager, and λ is a parameter. Parameter λ appears in the trading cost of the fund which is defined as C(q t ) = λq 2 t , where q t measures assets under management. Parameter λ is unexplored in the paper of [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF]. In my paper, I interpret parameter λ to be a measure of illiquidity of the stocks held by the mutual fund. Thus λ differs from one fund to another.

We can express the trading cost of a fund as C(q t ) = λ × q t price impact ×q t , as in the model of [START_REF] Kyle | Continuous Auctions and Insider Trading[END_REF]. Price impact is the adverse movement in price incurred by a market participant when she trades. Price impact is higher when the stock is more illiquid and when she trades a higher quantity. If λ is a measure of illiquidity, and if the expected return Φ t is correlated with the skill of the fund, then from the survival condition, Φ t ≥ 2 √ F λ, I obtain that funds with low skill (low Φ t ) and invested into illiquid stocks (high λ) will not survive. Because funds with negative correlation between skill and illiquidity of their holdings do not survive, we will observe a mechanical positive correlation between skill and illiquidity.

I present below the optimization problem of the fund manager. I show that Φ t and λ are positively correlated whether funds charge a variable fee or a fixed fee. Under the assumption of decreasing returns to scale, the flows to funds act as a regulatory mechanism. Under a high perception of ability, investors pour money in the fund. Because of decreasing returns to scale, this continues up to the point where expected returns (in excess of benchmark and after costs and fees) are zero. This is also the participation constraint of investors, as they need to obtain (at least) zero expected return to participate into the fund. In the model, there is perfect competition among investors, while skill is the scarce resource. Therefore, in equilibrium, the funds are able to capture all the rents, while the investors get zero expected returns. Each period, managers optimize their total compensation, subject to the participation constraint of investors. The manager charges a percentage fee, so his total compensation is given by the fee multiplied by assets under management. There are two cases: constant fee, and variable fee.

Case 1: Variable fee

The manager maximizes total compensation (f t is the fee, q t is assets under management, r t+1 is the return over the benchmark that the investors get in period t):

max ft f t qt s.t. E(r t+1 ) ≥ 0 (participation constraint)
The total payout (TP) to investors, over what would be earned on the passive benchmark is:

T P t+1 = q t R t+1 -C(q t ) -q t f,
where R t is the return over the benchmark, before costs and fees, C denotes costs of actively manage the fund -they are increasing and convex in q. Let r t denote the return over the benchmark that investors in the fund receive in period t. Then:

r t+1 = T P t+1 q t+1 = R t+1 - C(q t+1 ) q t -f = R t+1 -cq t ,
where c(q t ) ≡ C(qt) qt + f.

Denote φ t ≡ E(R t+1 |R 1 , ..., R t ). The cost is C(q t ) = λq 2 t .
For the empirical tests, I approximate λ with the illiquidity of the mutual fund holdings. Taking expectations and setting them to 0, we have:

0 = φ t -c(q t ) φ t = c(q t ) = C(q t ) q t + f = λq 2 t q t + f f t q t = φ t q t -λq 2 t
Because f t is the choice variable of the manager, he can pick the f t which insures that f t q t intersects φ t q t -λq 2 t at the maximum of the latter. In other words, the manger first determines the quantity that maximizes the right hand side. As C(q t ) is increasing and convex in q t , this solution exists and we have φ t = 2λq * t , so:

q * t = φ t 2λ
The manager now sets the fee f t that insures the investors will invest q * t in the fund.

f * t = φ t -λq * t = φ t - φ t 2 = φ t 2
For the fund to survive, the manager needs to obtain at least as much as his opportunity cost.

We need:

f * t q * t ≥ F φt 2 φt 2λ ≥ F
Since φ t > 0, we have:

φ t ≥ 2 √ F λ (1)
As I assume that φ t , the expected return of the fund, is correlated with α, the skill of the manager, we see that there are four possible cases involving illiquidity (λ) and skill(α):

(1) high λ, high α; the fund survives, unless the manager has particularly bad luck;

(2) high λ, low α; the fund is not born or dies right away;

(3) low λ, low α; the fund survives, unless the manager has bad luck;

(4) low λ, high α; the fund survives, unless the manager has particularly bad luck.

Assuming that the four cases are equally likely, the fact that funds in case (2) die very fast means we will see a positive correlation between λ and α. This is what I find in the data.

To make this point, I also run a simulation. I pick 5,000 values of α ∼ N (φ 0 , 1 γ ). Based on [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF], I take φ 0 =6.5%, γ=277. I pick 5,000 values of λ from the uniform distribution [1,10]. ∼ N (0, 1 ω ). ω is 25. I compute φ t as Bayesian, then I compute f t = φt 2 , from the equilibrium solution. I take an average value for F = φ 2 0 4×5 , as 5 is the median liquidity on a 1-10 scale. I use each year the survival condition to decide if the fund lives or dies. I compute q t = φt 2λ . I follow the funds over a period of 20 years. I observe that, as predicted, there appears a positive correlation between α and λ among the surviving funds.

Case 2: Fixed fee

Let us now derive the maximization problem of the manager in the case where f is fixed. This is a more realistic case, as mutual funds do not change their fees as often. In this case, the manager is allowed to index the quantity in excess of the optimal quantity that is actively managed. As showed by [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF], this contract is equivalent to the contract where the manager chooses instead the fee. In this second contract, the choice variable of the manager is the quantity that he invests in the passive index. The manager still maximizes his total compensation (q a t is the quantity that is actively managed, and q i t is the quantity that is placed into an index):

max q i t f (q a t + q i t )
From the condition that expected returns are 0, and the manager captures all the rents, we have:

f (q a t + q i t ) = φ t q a t -λ(q a t ) 2

Figure 1.1: The optimization problem of the manager; on the X-axis we have the actively managed quantity, q a t In Figure 1.1, the line represents f (q a t +q i t ), and the parabola is φ t q a t -λ(q a t ) 2 . Now the manager can not choose f, which is fixed, so he can not always make sure that the line intersects the parabola at the maximum of the latter. I will further analyze the different subcases that appear.

Subcase 1: no solution

There is no solution when the slope of the line is greater than the slope of the parabola at 0. This translates into f ≥ φ t . So the manager wants to choose a fee f < φ t .

Subcase 2: there is an intersection point between the line and the parabola, other than the origin First we have f < φ t . Then, I rewrite the problem in the following way: Denote x = q a t ,

y = q i t , z = q t , a = φt f , b = λ f .
Since f is fixed, maximizing f z is the same as maximizing z:

max y z s.t. 0 ≤ x ≤ z = ax -bx 2 s.t. x + y = z
This gives:

ax -bx 2 = x =⇒ (a -1)x -bx 2 = 0 =⇒ x = a-1 b .
How does a-1 b compare to a 2b , the point where the parabola reaches its maximum?

Subcase 2.1. a < 2, that is f < φt 2
There is a maximum, on the increasing part of the parabola, equal to φt-f λ .

Subcase

2.2. a ≥ 2, that is f ≥ φt 2
There is a maximum, that coincides with the maximum of the parabola, which is equal to

φ 2 t 4λf .
To summarize the case with fixed fee f :

• f ≥ φ t .
There is no solution. The intuition is that the fee is too big and the manager can not attract funds;

• f ∈ ( φt 2 , φ t ). We have q a t = q t = φt-f λ , and q i t = 0. At this fee, q i t ≥ 0 becomes binding, meaning the optimal quantity the manager would like to actively manage is bigger than the total quantity he has under management, but the manager does not have enough funds, so he will actively manage all he has;

• f ≤ φt 2 . Then q a t = φt 2λ ; q t = φ 2 t 4λf ; q i t = φt(φt-2f ) 4λf
. Part of the quantity is actively managed and part is placed into an index.

As for the variable fee case, the relationship between the illiquidity of the fund and the skill of the manager comes from survival. We have:

f ((q a t ) * + q i t ) ≥ F
• f ≥ φ t , the fund dies;

• f ∈ ( φt 2 , φ t ), for the fund to survive it needs to satisfy:

f q t ≥ F f φt-f λ ≥ F φ t ≥ F λ + f 2 f (2)
• f ≤ φt 2 , for the fund to survive it needs to satisfy:

f q t ≥ F f φ 2 t 4λf ≥ F φ 2 t ≥ 4λF
Since φ t > 0, we have:

φ t ≥ 2 √ λF (3)
As φ t is correlated with α, the skill of the manager, we see that there are four possible cases in inequalities 2 -3, as in the variable fee case:

(1) high λ, high α; the fund survives, unless the manager has particularly bad luck;

(2) high λ, low α; the fund is not born or dies right away;

(3) low λ, low α; the fund survives, unless the manager has bad luck;

(4) low λ, high α; the fund survives, unless the manager has particularly bad luck.

Assuming that the four cases are equally likely, the fact that funds in case (2) die very fast means we will see a positive correlation between λ and α. This is what I find in the data. ). In selecting the sample, I follow [START_REF] Kacperczyk | Unobserved Actions of Mutual Funds[END_REF]. I focus on domestic equity mutual funds, so I take out balanced, bonds, money market, sector and international funds, as well as funds not invested primarily in securities. I select the funds that have the following codes in the CRSP objective code: EDCL, EDCM, EDCS, EDCI, EDYG, EDYH, EDYS, EDYI 2 . I also screen for some other words in the name of the fund 3 , and I exclude those funds from the sample. I take out observations for which the year for the observation is prior to the reported fund-started year (to remove the incubation bias, as in [START_REF] Elton | A First Look at the Accuracy of the CRSP Mutual Fund Database and a Comparison of the CRSP and Morningstar Mutual Fund Databases[END_REF] and [START_REF] Evans | Does alpha really matter? Evidence from mutual fund incubation, termination and manager change[END_REF]. To make sure they are invested mostly in equity, I exclude funds if the average invested in common stocks is lower than 80% or higher that 105%. As data on fees (expense ratios, management fees and 12B-1 fees) is reported annually, I divide the fee by 12 to obtain the monthly value, then I carry it forward for all the months in a given year. As fiscal years do not always coincide with calendar years, I am careful to assign the monthly values according to the fiscal year they apply to. The database contains fiscal yearend, the end of the fiscal year for which fees apply. When fiscal yearend is missing, I search during the whole life span of the fund the month in which the fiscal year usually ends, and I assume the fiscal year ends in the same month for all years. Fiscal yearend is missing for years before 1998, although I have data for fees. I assume the end of the fiscal year is December, 31 whenever fiscal yearend is missing for the whole lifespan of the fund.

Data and variable construction

For turnover, I report only the annual value 4 . When the 12B-1 fee is not reported, but the Global, International, Int'l, Japan, Regional, Transatlantic, World Trends, Air Transportation, Automotive, Basic Materials, Biotechnology, Broadcast, Chemicals, Commodities, Computer, Consumer Goods, Consumer Services, Defense, Electronics, Energy, Export, Food, Gold, Health, Industrial, Leisure, Medical, Oil & Gas, Paper, Pharmaceuticals, Precious Metals, Property, Real Estate, Retail, S&L, Sectors, Semiconductors, Software, Tech, Telecommunication, Television, Transportation, Utilities, ING Solution, Lifecycle, LifeCycle, LifePath, LIVESTRONG, Lifetime, RealRetirement, Retirement, RetirementReady, RetireSMART, Target, Balance, Dow, Futures, OTC, Sovereign, State Bond, Tax Aware, Tax-Efficient, Tax-Managed 4 From the Survivor-Bias-Free US Mutual Fund Guide published by CRSP: Turnover ratio = "minimum (of aggregated sales or aggregated purchases of securities), divided by the average 12-month Total Net Assets of the fund." Given this definition, it is not practical to determine the monthly turnover of mutual funds from maximum 12B-1 fee is reported, I fill in the 12B-1 fee with the value of the maximum 12B-1 fee. I drop negative values of fees, except for management fees. Management fees can be negative when there are waivers and reimbursements. I interpret this as managers waiving their fee when performance is bad, so it is informative to keep them in the sample. When expense ratio is missing I assume it is the same as for funds with similar TNA (as in [START_REF] Fama | Luck versus Skill in the Cross-section of Mutual Fund Returns[END_REF]. I winsorize fees, turnover ratios and returns at 1th and 99th percentiles to remove outliers. TNA is reported quarterly before 1990 and monthly after that. Before 1990 I carry forward the TNA for the months in between two consecutive quarters. I take out observations for a fund before it reaches at least $5 mil. TNA for the first time, also to mitigate the incubation bias. I take out observation where returns or TNA's are missing.

I then match the CRSP data with the Thomson Reuters database using MFLinks. When a fund has multiple share classes, I collapse the different share classes into one observation.

I exclude index funds and ETFs. For qualitative attributes (e.g. name, year it started), I retain the observation for the oldest fund. For the TNA, I sum the TNAs of the different share classes. For other quantitative attributes (e.g. returns, expense ratios, turnover ratios), I take the weighted average, where the weights are the TNAs of the individual share classes.

I have quarterly holdings for mutual funds. In the Thomson Reuters database I have RDATE which is the report date and FDATE which is the file date (actually a vintage date assigned by Thomson). As [START_REF] Frazzini | The Disposition Effect and Underreaction to News[END_REF] explains, neither of the two corresponds to the actual filing date at SEC, but RDATE identifies the date at which the portfolio snapshsot is taken. For FDATE, Thomson assigns the quarter-end of the filing. For RDATE, although reports can be made on any date, the last date of the quarter is usually used. Sometimes, RDATE can be as much as 6 months before FDATE, because of the managers' discretion. To avoid staleness of data, I keep only those observations where FDATE is the same as RDATE. When I merge the CRSP data with the holdings information in Thomson, what is CUSIP in Thomson is actually NCUSIP in CRSP, so I merge accordingly.

After applying all the filters above I retain a sample of 2,532 mutual funds over the period 1983-2014, and 204,793 fund-month observations. the annual ratio.

I focus on gross returns (net returns plus expense ratios), because I am interested in the ability of a fund to generate risk-adjusted return, and not in the value it brings to the clients after fees. However, I do provide a test with net returns to see if there can be an investable strategy.

For the months in between two reportings, I assume the fund maintained the most recent holdings (provided these are not older than 6 months). I have to decide whether to regard the holdings on December 31, year t as the holdings between September 30, year t-1 and December 31, year t, or as the holdings between December 31, year t and March 31, year t.

I follow the advice in [START_REF] Kacperczyk | Unobserved Actions of Mutual Funds[END_REF]. They compare the forward-looking hypothetical returns (based on future holdings) to the backward-looking hypothetical returns and observe that the former are 3% per year higher. They attribute this finding to momentum strategies and window-dressing, and conclude that the backward-looking return is a better proxy for the effective fund holdings than the forward-looking return.

Illiquidity -the Amihud measure

For illiquidity, I use the measure of [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series effects[END_REF], which is a measure of price impactabsolute daily return divided by daily dollar volume, but the interested reader can also see [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF], [START_REF] Acharya | Asset pricing with liquidity risk[END_REF]. The intuition of the Amihud measure is a stock is more or less liquid depending on how much the price is moved by a certain volume traded in a given day. I prefer to use the Amihud measure over the measure of [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF] for example, because the latter is computed as a regression coefficient. In their case, as they aggregate over all the stocks in a month, and assuming the errors for individual stocks are less than perfectly correlated, the estimate for illiquidity becomes less noisy with more stocks. In my case, I need to sort each month by the individual illiquidity of stocks. The advantage of the Amihud measure is that it is easy to compute, without the need for microstructure data. It is also longer (TAQ data begins only in 1993).

For each stock, I compute the Amihud measure, each month. I compute it as the average of daily values. The daily illiquidity of a stock is 1, 000, 000 * |return| |price| * volume . I then sort all stocks each month on their illiquidity and assign each stock to an illiquidity decile.

For robustness, I also tried a modified measure of liquidity. There are cases when the volume is low (or 0) and the return is 0 (before decimalization the price could only move in 1 8 before June, 24 1997 and 1 16 before April, 9 2001). A 0 return can thus mean a tiny price movement. With a 0 return and a low (or 0) volume, the stock may appear as very liquid when it is actually illiquid, or I am missing an observation when I have 0 0 . I change slightly the Amihud measure: I replace the 0 return with half of the tick-size at the time, divided by price; I replace the 0 volume with half of the typical lot (so 50 shares). These transformations are meant to gain more observations. In an alternative attempt, I compute the Amihud measure as average over the quarter (and not month), and I carry the value for the months in between. This also gains more observations. I compute the scores for the stocks using all these measures.

The scores series, using the alternative measures, have pairwise correlations over 91%, so the original measure is not too noisy.

Risk-adjusted returns

I measure performance with respect to several asset pricing models. Later in the paper, I will also consider a characteristics benchmark, and benchmark-adjusted returns.

The four asset pricing models I use from the existing literature are: Carhart, Pástor-Stambaugh, Fama-French five-factor model and Novy-Marx. I describe them below:

Carhart : r i,t = β 0 i + β M i M KT t + β S i SM B + β H i HM L t + β U i U M D t + i,t
Pástor-Stambaugh :

r i,t = β 0 i + β M i M KT t + β S i SM B + β H i HM L t + β L i L t + i,t
Fama-French five-factor :

r i,t = β 0 i + β M i M KT t + β S i SM B + β H i HM L t + β R i RM W t + β C i CM A t + i,t
Novy-Marx :

r i,t = β 0 i + β M i M KT t + β S i SM B + β H i HM L * t + β U i U M D * t + β P i P M U t + i,t
where r i,t is return in excess of the risk-free rate, M KT is return of the market in excess of the risk-free rate, SM B is small minus big, HM L is value minus growth, U M D is up minus down, or momentum, L is illiquid minus liquid, RM W is robust minus weak (profitability), CM A is conservative minus aggressive (investment), P M U is profitable minus unprofitable5 . I run regressions for each stock, provided there are at least 10 observations in the past 24 months. I compute alpha with respect to a certain model as the difference between excess returns and the predicted values from the model.

Characteristic benchmarks -stock picking

I also compute adjusted-returns with respect to a characteristics benchmark. I then look if illiquid funds have a higher benchmark-adjusted return than liquid funds. If they do, it means that illiquid funds are better at picking stocks. The methodology follows the DGTW paper.

The intuition is as follows: every end of June, every stock is matched to a benchmark based on characteristics (I use size, value, previous returns and illiquidity). Every beginning of a quarter, I compute a monthly hypothetical return for the mutual fund, based on the stock holdings (assuming the fund buys the stocks on the first day of the quarter, and keeps them until the last day). For the stock weights is each month, I use the most recent stock holdings (the previous quarter-end holdings). For example, in January, February and March 2000, I use the weights as given by the stock holdings in December 1999. I then look if this hypothetical return of the fund is higher than what the return would have been if the fund had been invested into the benchmark portfolio of each stock instead. I use 3 × 3 × 3 × 3 sorts, first by size, then by B/M, then by past returns, then by illiquidity (a similar methodology was recently used by [START_REF] Agarwal | Mandatory Portfolio Disclosure, Stock Liquidity, and Mutual Fund Performance[END_REF]). This gives a total of 81 portfolios.

Using sorts in this way (and not by 4 or by 5) ensures that I have a sufficient number of stocks in each portfolio. The portfolios are constructed at the end of June and held until next

June. The stocks are assigned to a benchmark every June as well. To construct the portfolios I use size at the end of June. Size is computed as price times number of shares outstanding.

I retain only the stocks that have the first digit of their Share Code 1 (= Ordinary common shares), and the second digit 0 (= Securities which have not been further defined) or 1 (= Securities which need not be further defined).

I use B/M at the end of the fiscal year that ended in the previous calendar year. This ensures that book-equity is publicly known. This is the method used in DGTW and in [START_REF] Davis | Characteristics, Covariances, and Average Returns: 1929 to 1997[END_REF]. [START_REF] Basu | The relationship between earnings' yield, market value and return for NYSE common stocks: Further evidence[END_REF] assumes that book-equity becomes known after 3 months instead of 6. 6 months is a more conservative number. To compute B/M, I use the CRSP/Compustat Merged. The database contains the stocks in Compustat, but it includes the variables permno and permco, which makes it easy to link to CRSP. To compute B/M, I use the method outlined on the website of Kenneth French6 : "Book equity (BE) is constructed from Compustat data. BE is the book value of stockholders' equity, plus balance sheet deferred taxes and investment tax credit (if available), minus the book value of preferred stock. Depending on availability, we use the redemption, liquidation, or par value (in that order) to estimate the book value of preferred stock. Stockholders' equity is the value reported by Compustat, if it is available. If not, we measure stockholders' equity as the book value of common equity plus the par value of preferred stock, or the book value of assets minus total liabilities (in that order)."

Past return is computed as the average monthly return for the months t-11 to t-1. The most recent month is excluded to account for reversals (as in Jegadeesh, ( 1990)).

Illiquidity is computed as the average over the previous year (that ends in June). To compute the size terciles (3-quantiles), I compute the breakpoints based on the NYSE stocks only.

This is done to ensure that there is the same number of NYSE stocks into each size tercile.

I take all stocks that are listed on NYSE. I include only the stocks that have the first digit of their Share Code 1 (= Ordinary common shares), and the second digit 0 (= Securities which have not been further defined) or 1 (= Securities which need not be further defined).

I sort the stocks on size and form terciles. Then I compare the size of all NYSE, Amex, Nasdaq stocks (with Share Codes 10 or 11) with the size breakpoints and assign them into terciles. In each size tercile, I subsequently sort by book-to-market and form terciles again.

In each size and book-to-market group, I sort by past returns and form terciles again. Lastly, in each size-book-to-market-past-returns group, I sort by illiquidity, and form terciles again.

In the end, I obtain 81 portfolios. The 81 portfolios contain between 21 and 167 stocks. At the end of each June, I assign each stock in CRSP a characteristics benchmark from the 81 portfolios. In the following months, I measure the return of the stock against the return of its benchmark. I rebalance the portfolio each month to keep the same weights in between two reporting dates. I compute the cumulative characteristic benchmark-adjusted returns between two successive report dates and divide by the number of months in the period to obtain a monthly DGTW-adjusted return. To obtain an average measure of skill of the fund, I replace characteristic-benchmark adjusted returns each month with the past 12 months average. To check that the methodology for computing the benchmarks is correct, I recreate the original DGTW portfolios (based on 5 × 5 × 5 sorts on size, book-to-market and past returns) and check that my program produces the same stock assignments and benchmark returns as on the website of Russ Wermers7 . The correlation between my assignment and the assignment on the website of Russ Wermers is 96% for size, 74% for book-to-market and 80% for past returns. The correlation for the overall assignment (I identify portfolio {1, 1, 1} by 1, portfolio {1, 1, 2} by 2 and so on until 125) between my assignment and the the assignment on the website of Russ Wermers is 95%. The correlation between the returns on my benchmarks and the benchmarks on the website of Russ Wermers is 82% (however, the book-to-market used on the website of Russ Wermers contains an additional adjustment for industry as in Wermers, ( 2004)).

1.3.4 Benchmark-adjusted returns I have used above various factors (Fama-French, Carhart, etc.) to adjust for style and risk profiles of mutual funds. These factors are widely used as they are freely available. However, these factors are are long-short portfolios whose returns cannot be costlessly replicated by mutual fund managers. Cremers, Petajisto, and Zitzewitz, (2013) argue that the Fama-French model produces biased assessments of fund performance, and they recommend using index-based benchmarks instead. I present differences in returns between the illiquid and liquid funds, where returns are benchmark-adjusted. I adjust the returns in two ways: first, with respect to the actual benchmark, declared by the mutual fund; second, with respect to the "minimum-distance" benchmark. The "minimum-distance" benchmark is from the website of Antti Petajisto Growth, in total 17 indexes9 . I was not able to obtain data for Wilshire 5000 and Wilshire 4500 indexes. For the funds benchmarked against Wilshire 5000, I replace the benchmark with Russell 3000 (both capture the whole market, Russell 3000 already covers over 98% of the market, and in June 30, 2015 Wilshire 5000 contained only 3,691 stocks). The funds benchmarked against Wilshire 4500 make up for less than 2% of the sample, so I ignore them.

All the returns of the indexes are computed using the prices available in the Compustat -North America database.

Liquidity of the benchmarks

I compute the liquidity scores of the benchmarks (both for declared benchmarks and for the "minimum-distance" benchmarks). The purpose is to see if the difference in liquidity score between the funds and their benchmarks differs for funds invested into liquid stocks and funds invested into illiquid stocks. If, for example, the benchmarks of illiquid funds are more liquid than the illiquid funds, it means there is a liquidity premium in the benchmark adjusted returns of illiquid funds. It means additional benchmarks would be needed that account for liquidity. I compute the liquidity score of the indexes quarterly for the S&P Indexes Indexes (as they are being reconstructed quarterly, on the 3rd Friday of March, June, September and December). I compute the liquidity score of the Russell Indexes yearly, as they are reconstructed yearly. I obtain the constituents of the S&P indexes from the Compustat -North America database. I obtain the constituents of the Russell Indexes from Russell Investments 10 . The Russell files identify the stocks by ticker and the company name. To merge with CRSP I use the ticker, and whenever this is not available I use a fuzzy string matching of the company name. Table 1.13 contains the statistics for the liquidity of the benchmarks. Not surprisingly, the small cap indexes have a higher illiquidity score.

Results

Table 1.1 presents the summary statistics for mutual funds. There is a total of 2,532 funds over the period 1983-2014. The average illiquidity of mutual funds (on a 1-10 scale, 1=most liquid) is 1.83, and the 90th percentile is 3.38. On average, mutual funds are invested into very liquid stocks. I will exploit the differences between the most illiquid and the most liquid funds. Illiquidity investing is persistent: 90.27% of funds who are in decile 10 of illiquidity are still in decile 10 after 3 months; 86.41% are still there after 6 months; 83.21% are still there after 9 months; and 80.63% are still there after 12 months. Funds do not seem to move 10 I thank Jennifer Mercier from Russell Investments for providing the data.

in and out of illiquidity so as to time illiquidity.

Cross-section vs. time series

One way to test if it is about skill of the manager or characteristics of the illiquid stocks is to look in the cross-section versus time series. If it is about characteristics of the illiquid stocks, then for a given fund we should observe that when it invests more in illiquid stocks it has a higher performance. On the contrary, if it is about the skill of the manager, we would see in cross-section that the funds who invest more in illiquid assets have higher performance (assuming that the skill of the manager is time-invariant). I use a simple test to distinguish between the two. Pástor, Stambaugh, Taylor, (2015) prove that the fixed effects estimator in a pooled regression is equivalent to running period-by-period (or fund-by-fund) regressions and doing a weighted average of the slopes. The weight is higher for the periods where there are more observations and when the variation of the independent variable is higher. I run a simple regression of risk-adjusted performance on the illiquidity score of the fund. In the first specification, I use month fixed-effects. In the second specification, I use fund fixed-effects.

In both specifications I report t-stats based on heteroskedasticity-robust errors that are clustered by month. If the relationship holds in time-series (so for a given fund we observe higher performance when it invests more in illiquid assets), we should observe a significant slope on illiquidity when I specify fund fixed effects. If the relationship holds in cross-section (so funds that are invested in illiquid assets have higher performance, consistent with managers of those funds being skilled), we should observe a significant slope on illiquidity when I specify month fixed effects. Table 1.2, Panel A, shows that the t-stat when I specify fund fixed effects is 1.85, while the t-stat when I specify month fixed effects is 2.55. The coefficient on the regression with time FE can be interpreted in the following way: as the between standard deviation of the illiquidity coefficient is 0.99, it means that a one standard deviation in the illiquidity score of the fund leads to 0.0003 × 0.99 × 1200 = 0.36% per year higher risk adjusted return. Also, the average illiquidity score for Decile 1 (most liquid) is 1.05. The average illiquidity score for Decile 10 (most illiquid is 3.84). It means that moving from Decile 1 to Decile 10 represents a 0.0003 × (3.84 -1.05) × 1200 = 1% increase in risk-adjusted return. In all Panels of the table, the time FE specification is significant, while the fund FE specification is not. Importantly, in Panel B, I regress Pástor-Stambaugh risk-adjusted return, before fee, on illiquidity score. We observe that the time FE is significant, while the fund FE is not. This is evidence of skill in the cross-section of funds, beyond an illiquidity premium. Overall, Table 1.2 shows that the relationship between risk-adjusted performance and illiquidity is stronger (at least in terms of t-stat) in cross-section than in time series.

Performance and illiquidity

In Table 1.3, I present evidence for the relationship between performance before fees and illiquidity. Each month, I sort funds into deciles according to the previous available score for illiquidity. I form the portfolios, and I compute an equally weighted excess return. I track back the same portfolio over the previous 24 months and I compute factor loadings (for the four risk models previously discussed). I then subtract the factor loadings times the factors for the current month and I obtain the risk adjusted returns. I take averages across each decile and report them in the table. Then each month, I take the difference in alphas (that is in risk-adjusted returns, before fees) between the most illiquid and the most liquid deciles.

I average and I report the difference in the table, as well as the t-stat. We observe that Decile 10-Decile 1 alpha with respect to Carhart (the one usually reported in the literature) is positive at 1.38% p.a. and significant with a t-stat 2.93. The Decile 10-Decile 1 alpha with respect to Pástor and Stambaugh is still positive but less significant, suggesting there might be an illiquidity premium. Alpha with respect to Fama-French five-factor model is not significant, which means that illiquidity might be correlated to another risk factor. The Fama-French five factor model includes two additional factors, profitability and investment.

However, the challenge remains to explain why illiquidity would be correlated to one, or both, of these factors. Overall, Table 1.3 suggests that mixed evidence warrants a more detailed analysis. This is what I later do in Table 1.11, when I study the holdings of mutual funds and compare each stock to a portfolio of matching characteristics, as in DGTW.

For robustness, I repeat the analysis in two subsamples : 1983-1998 more expensive in terms of expense ratios). Surprisingly, turnover of illiquid funds is greater than turnover of liquid funds, but by a small amount. This might indicate that part of the skill of the illiquid funds resides in obtaining better trading costs in illiquid stocks than the average fund would obtain.

Stock-picking skills

In order to do a more rigourous analysis of the stock-picking skills of mutual fund managers invested into illiquid stocks, I present the characteristic benchmark-adjusted returns of the funds. The characteristics benchmarks are constructed as described in the data construction section. I present both the DGTW-returns (with respect to the 5 × 5 × 5 benchmark matched by size, book-to-market and previous returns), and the newly computed DGTW with liquidity returns (with respect to the 3 × 3 × 3 × 3 benchmark matched by size, book-to-market, previous returns and illiquidity). I present two versions: the first is where the holdings of the fund are kept constant from one reporting to another meaning the same number of shares;

the second is where the holdings of the fund are kept constant from one reporting to another meaning the same weights -the portfolios are rebalanced every month. The characteristic benchmark-adjusted returns show the stock-picking skills of the manager. The method compares the return computed based on the actual holdings with the return had the fund been invested into the portfolio matched by characteristics of each stock. The results are in Table 1.11. The difference between Decile 10 and Decile 1 is 2.30% per year (t-stat 3.30). This is evidence that illiquid stocks can better select stocks than liquid funds.

1.4.5 Benchmark-adjusted returns and liquidity of the benchmarks I then study the benchmark-adjusted returns, where the benchmarks are those declared in the prospectuses of funds (like S&P 500 or Russell 1000), or the minimum-distance benchmarks (as described in the Data construction section). In both cases, illiquid funds outperform liquid funds by 1.59% per year (respectively, 5.63% per year), with t-stats 1.21 (respectively 1.32).

The big outperformance for the minimum-distance benchmark-adjusted returns comes from big negative performance of liquid funds. This is evidence that liquid funds might strategically declare benchmarks that make them look good. The results are presented in Table 1.12.

Table 1.13 summarizes the benchmarks used, as well as their average illiquidity score. As expected, most benchmarks are very liquid (in terms of their constituents). The most illiquid benchmarks are the small-cap benchmarks. The purpose of computing illiquidity scores for benchmarks is the following: I want to test if there is a significant difference in illiquidity between funds and their benchmarks. Benchmarks are chosen based on their style proximity to the funds (in terms or size and value). As illiquidity is not taken into account, it may happen that the illiquid funds are much more illiquid than their benchmarks. If this is the case, then again the benchmark-adjusted returns will contain an illiquidity premium that is not taken into account. I find that the difference in illiquidity scores of funds and their benchmarks is small (both for illiquid and liquid funds), as presented in Table 1.14.

1.4.6 Is it an investable strategy? After fee returns I test if investors could benefit from illiquid funds being more skilled. Table 1.15 presents the results on 1 to 12-month holding period risk-adjusted returns (Carhart's model, after fees).

In a long-short portfolio, the difference is 1.18% per year (t-test 2.53) if investors sort funds by illiquidity of holdings, based on latest available disclosure date. The difference becomes 1.09% per year in over a 12-month holding period (t-stat 6.18).

False Discovery Rate (FDR)

Barras, Scaillet and Wermers (2010), BSW, apply the FDR methodology to mutual funds.

The FDR method was developed by Storey (2002). The method permits to separate Type I errors (false discoveries), from significant t-stats of mutual funds. It allows the partition of the mutual funds universe into zero-alpha, positive-alpha and negative-alpha groups. BSW find that 75% of funds exhibit zero-alpha (after fees), and that there are virtually no positive alpha funds.

I provide a quick overview of the method (the method is described at length in BSW). The null hypothesis is that a fund has no abnormal performance, the alternative hypothesis is that the fund delivers either positive or negative performance. For a given significance threshold γ, a fund has a significant t-stat (of its alpha) if the p-value for the t-stat is less than equal than γ 2 . For a given γ, the proportion of zero-alpha funds who appear as positive-alpha funds (are "lucky") is γ 2 . If the proportion of truly zero-alpha funds among M existing funds is π 0 , then the expected proportion of false-positive funds is:

E(F + γ ) = π 0 × γ 2 . It follows that the proportion of truly positive-alpha funds is E(T + γ ) = E(S + γ ) -E(F + γ ) = E(S + γ ) -π 0 × γ 2
, where E(S γ ) is the proportion of significant positive-alpha funds. In other words, the significant positive-alpha funds minus the false positives gives the true positive-alpha funds. Picking different levels of γ allows to identify whether the truly skilled funds are concentrated or dispersed in the right tail. For example, if the proportion of truly positive-alpha funds does not change when γ decreases, it means that the funds are concentrated into the right tail. If the proportion changes when γ decreases, it means that the funds are dispersed in the right tail.

To estimate E(S + γ ), we observe the number of significant funds. To compute π 0 , I use the result 11 that truly positive and negative alpha funds have p-values clustered around 0, while truly zero-alpha funds have p-values uniformly distributed on interval [0,1]. To estimate π 0 (λ), we need to choose a sufficiently high value of λ, such that the histogram of p-values to the right of λ is flat. Then,

π 0 = W (λ) M ×(1-λ)
, where W (λ) is the number of funds for which p-value > λ and M is the total number of funds.

The calculations above depend on the estimation of p-values. I use a bootstrap method to account for non-normality in the regression residuals (as in Cuthbertson, Nitzsche, O'Sullivan (2011)). Consider a model of equilibrium returns of the form: r e i,t = αi + β i X t + êi,t , where i = 1, ..., M funds, T i is the number of observations for fund i, r e i,t is the excess return of fund i at time t, X t is the vector of risk factors (I use the 4-factor model of Carhart), êi,t is the vector of residuals, ti is the estimated t-statistic for alpha. I resample the residuals, under the null hypothesis of zero-alpha. In the first step, I estimate the Carhart model for each fund, and I save the vectors βi , êi,t . In the second step, for each fund, I draw a random 11 proof in BSW, page 187 sample, of length T i from the residuals e i,t and I use the resampled residuals to generate a simulated excess return ri,t under the null hypothesis α i = 0. In the third step, I estimate the 4-factor model of Carhart on the ri,t , and I compute a t-statistic for alpha, t i,b . I repeat this for 1000 times, and then I compute the the two-sided p-value for the t-statistic of α:

p i = 2 × min 1 1000 1000 b=1 I(t b i > ti ), 1 1000 1000 b=1 I(t b i < ti )
, where I(.), is an indicator function that takes value 1 if the argument is true, and 0 otherwise. The results in Table 1.16 show that 81.11% of funds have 0-alpha after fees. This is consistent with BSW (2010), who find that percentage to be 75%. I then split the sample if half, based on the average liquidity of the holdings of the funds. Between the liquid and illiquid funds, I find that 77.45% of the liquid funds have 0-alpha, compared to 84.76% among the illiquid funds. The percentage of positivealpha funds is 2.78% among the illiquid funds, as compared to 0.80% among the liquid funds.

There are 21.75% negative-alpha funds among the liquid funds, and 12.46% negative-alpha funds among the illiquid funds. Overall, this indicates the presence of more skill among the illiquid funds.

Morningstar Ratings

I look if the superior skill of illiquid funds is reflected into the Morningstar Ratings of funds.

That would offer an external validation to the claim that illiquid funds have higher skill and perform better. However, given the methodology of the ratings, it is not clear ex-ante if an illiquid fund should have a higher rating than a liquid fund. On the one hand, the Morningstar Rating takes into account the past performance of funds over the long run 12 . The test I presented so far show that subsequent returns are higher for a fund that invests today in liquid stocks, while the Morningstar Ratings evaluate relative past performance, going back to 10 years. On the other hand, illiquidity investing is persistent: 90.27% of funds that are in decile 10 of illiquidity this month are still in decile 10 in 3 months (86.41% in 6 months, 83.21% in 9 months and 80.63% in 12 months). That means that an illiquid fund today might have been illiquid in the past as well, so then Morningstar Ratings might be able to capture the overperformance of illiquid funds. I merge the Morningstar database with the CRSP database using the CUSIP and the Ticker. I am able to match 83% of the funds and 82% of the observations. The results presented in Table 1.17 show that the difference in rating between the Decile 10 (illiquid) and Decile 1 (liquid) is positive but statistically insignificant (t-stat 0.82) and very small -the average rating 13 for illiquid funds is 3.06 and the average rating for liquid funds is 3.09, for the period 01/2000-2014 in which I have at least 50 funds in a given month in each decile. The supposed difference in skill between illiquid and liquid funds is not well captured by the Morningstar Ratings, although this may be because the ratings are backward looking.

Sensitivity of flows to performance

According to [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF], if illiquid funds are more skilled and have higher performance, then they should attract flows from the investors. When this happens, the capacity of the fund to generate superior returns decreases to the point where the expected returns to investors are zero. I investigate why illiquid funds outperform, without this outperformance being driven away by inflows. One possibility is that flows are less sensitive to performance for illiquid funds. [START_REF] Huang | Participation costs and the sensitivity of fund flows to past performance[END_REF] and Gil-Bazo and Ruiz-Verdú (2009) document that different funds have different sensitivities of flows to performance. If it were true that illiquid funds have a lower sensitivity of flows to performance, then this could explain why they do not attract inflows even when they outperform. A first observation towards that point is that illiquid funds are indeed smaller than liquid funds: Decile 10 (illiquid) funds manage on average $865.85 million, while Decile 1 (liquid) funds manage on average $1,188.32 million.

I construct a sensitivity measure of flows to performance as in Gil-Bazo and Ruiz-Verdú

13 On a 1-5 scale, where the best performing funds receive 5 stars.

(2009). The measure is computed annually. For a fund i, I define flows as the relative growth of assets under management (TNA), adjusted for the net annual return R n it :

Flow it = TNA it -TNA it-1 (1 + R n it ) TNA it-1 .
In a first step, I regress flows on past performance:

Flow it = a 0t + b 0 Perf it-1 + b 1 Perf it-1 rel age it-1 + b 2 Perf it-1 rel Q/MAX it-1 + a M I M,it-1 + b M Perf it-1 I M,it-1 + a P C M I M,it-1 PC it-1 + b P C M Perf it-1 I M,it-1 PC it-1 + a H I H,it-1 + b H Perf it-1 I H,it-1 + a P C H I H,it-1 PC it-1 + b P C H Perf it-1 I H,it-1 PC it-1 + c w it-1 + φ it ,
Past performance, Perf it-1 , is the fund's Carhart alpha in year t-1, after fees, and in excess of the performance of all funds in that year. The variable rel age it-1 is the log of the fund's age, in years, in excess of the average age for all funds in year t-1. The variable rel Q/MAX it-1

is the ratio of the fund's TNA t-1 and the maximum TNA of that fund in the period up to t-1. I M,it-1 and I H,it-1 are dummy variables that equal 1 if the the fund is in the middle third, or top third respectively, by performance in year t-1. The variable PC is a proxy for participation costs. It is a dummy that equals 1 if there is another fund managed by the same management company that is in the top 5% by performance (a "star" fund). The controls summarized by w it-1 are: size, age, marketing fees, volatility of returns, log of TNA of all funds under the same management company.

In a second step, the measure of flow-to-performance sensitivity is computed as the first derivative of conditional expected flow with respect to performance:

S it = ∂E t-1 (Flow t-1 ) ∂Perf t-1 = b0 + b1 rel age it-1 + b2 rel Q/MAX it-1 + bM I M,it-1 + bPC M I M,it-1 P C it-1 + bH I H,it-1 + bPC H I H,it-1 P C it-1 .
There is a positive correlation between sensitivity of flows to performance and illiquidity of 13%. This means that the the more illiquid a fund is, the higher its sensitivity to performance.

As illiquid funds also have higher performance, then they should attract more flows and grow bigger. This is puzzling because, in the data we observe that the illiquid funds are smaller.

However, there is evidence that illiquid funds grow in size if their sensitivity to performance is higher. This is indirect evidence for skill of illiquid mutual funds: if illiquid funds with greater sensitivity to performance grow in size, it means they have performed well. I regress yearly log of size on the illiquidity of the fund, on the sensitivity of fund to performance and on an interaction term between illiquidity and sensitivity to performance. The regression has time fixed effects (it is a cross section regression), and errors are clustered by time. The interaction term is positive and significant (t-stat 10), meaning that among the illiquid funds, the ones with higher sensitivity of flows to performance have a bigger size.

1.4.10 Illiquid stocks bought by illiquid funds vs. illiquid stocks bought by liquid funds If illiquid funds are truly better at picking stocks than liquid funds, then illiquid stocks bought by illiquid funds should subsequently outperform illiquid stocks picked by liquid funds. This test would prove that there is not a characteristic of illiquid stocks that makes illiquid funds outperform liquid funds, but a higher stock picking ability of illiquid funds.

For these tests, I define as illiquid the stocks that have a liquidity score greater or equal to 5 (on a 1 to 10 scale). The rest would represent liquid stocks. I compare between illiquid funds (Decile 10) and illiquid funds (Decile 1). The first observation is that while illiquid stocks make up for 34% on average (standard deviation 6%) of the holdings of illiquid funds, illiquid stocks represent less than 1% of the holdings of liquid funds. That makes it difficult to compare the illiquid stocks held by illiquid funds to the illiquid stocks held by liquid funds.

I will present the results, but I will bring additional evidence by looking at the liquid stocks held by illiquid funds versus the liquid stocks held by liquid funds. At the end of each quarter, for each group of funds (illiquid and liquid), I form a portfolio of all the illiquid stocks (or all liquid stocks). I denote this formation quarter Q. I then compute the returns of this portfolio at the end of the previous quarter (Q-1), at the end of the current quarter (Q), at the end of the following quarter (Q1) and at the end of the the second following quarter (Q1 to Q2).

Then I repeat the analysis for liquid stocks. I compute both simple returns and risk-adjusted returns, using the Pástor-Stambaugh model that includes a liquidity factor. The results are in Table 1.18.

In the top left quadrant there are the simple returns of the illiquid stocks held by illiquid funds. Post formation, illiquid stocks held by illiquid funds have a positive and significant return (12.36% at the end of Q1 and 13.27% at the end of Q2). Returns are averages over the three months of the quarter and they are annualized. In the bottom left quadrant, postformation returns are positive and significant even after accounting for risk (2.56% at the end of Q1 and 4.27% at the end of Q2). In the bottom right quadrant, we see that illiquid funds are also better at picking liquid stocks than liquid funds. The difference at the end of Q1 is 1.81%, t-stat 1.71, between the risk-adjusted returns of the liquid stocks held by illiquid funds and those held by liquid funds. This is evidence that illiquid funds are better at selecting stocks that subsequently outperform.

The other result I was interested in is whether illiquid stocks picked by illiquid funds outperform (after adjusting for risk) liquid stocks also picked by illiquid funds. If this is the case, it provides evidence that, even with skilled managers, there are more opportunities in illiquid stocks than in liquid stocks. The results are not conclusive: in Q1, liquid stock outperform illiquid stocks (3.96% relative to 2.56%), but in Q2 illiquid stock outperform liquid stocks 4.27% relative to 3.35%).

Overlapping trades

An alternative explanation of higher returns of illiquid mutual funds may reside in overlapping of trades. If, for example, many illiquid mutual funds buy an illiquid stock at the same time, there will be a large price impact (especially as the stock is illiquid). The price of the stock will increase and this will appear as positive returns for the illiquid mutual funds.

I perform a simple test to see if trades of illiquid funds overlap. I perform this for all trades, and then separately for buys (trades>0) and for sells (trades<0). For each stock i held by illiquid or liquid funds and in each quarter q, I compute the fraction of holdings, as in [START_REF] Chen | The Value of Active Mutual Fund Management: An Examination of the Stockholdings and Trades of Fund Managers[END_REF]: Frac Holdings i,g,q = No. shares held by group of funds g i,q

Total shares outstanding i,q . Thus, for each stock, there will be two fractions of holdings, one corresponding to the group (g) of illiquid funds, and one corresponding to the group of liquid funds. At the end of each quarter, I compute trades as the changing in the Frac holdings: Trades i,g,q = Frac Holdings i,g,q -

Frac Holdings i,g,q-1 . Then, I compute the weighted average of trades, by each group of funds (illiquid and liquid). The results are in Table 1.19.

In the first column of the table, trades are in absolute value, and then I take the average over the liquid or illiquid funds groups. This is to understand how much the funds trade, irrespective of the direction. Of course, whether these are buys or sells makes a difference if there is a price impact, as buys tend to increase the price and the returns, and sells tend to decrease them. The average trades, as percentage of the shares outstanding is 1.36% for illiquid funds and 1.23% for liquid funds, and there is no significant difference between the two groups. The second column keeps the sign of the trade when averaging across each of the two groups of funds. Again, there is no significant difference between the two groups. In columns three and four, I study separately buys and sells. The difference between the two groups (illiquid and liquid funds) is only statistically significant for sells, but it is still very small economically (0.18% of the total shares outstanding). Moreover, it would contribute in the opposite direction, towards reducing the returns of illiquid funds. The conclusion is that the overlap in trades does not seem to mechanically drive the higher returns of illiquid mutual funds.

Conclusions

Funds invested into illiquid stocks outperform funds invested into liquid stocks (1.38% per year before fees, 1.18% per year after fees, risk-adjusted as in Carhart's 4-factor model). I find evidence this outperformance arises from stock selection skills of funds invested into illiquid stocks. The performance-illiquidity relationship holds better in cross-section than in time series, irrespective of the model used for risk-adjustment. This is evidence of skill, as illiquid funds do better than liquid funds at the same time, as opposed to a given fund increasing performance when it invests in illiquid stocks. Illiquid funds outperform liquid funds in subsamples, and by various tranches of size, age, turnover and fees. Illiquid funds are smaller, younger and they have slightly higher fees. Illiquid stocks are better at selecting stocks in a portfolio of matching characteristics. Liquid funds declare benchmarks with respect to which their returns look better. All funds are very close to their benchmarks in terms of illiquidity of their holdings. The FDR test identifies a higher proportion of funds with higher alpha, after fees, among the illiquid funds than among the liquid funds. The liquid stocks held by illiquid funds subsequently outperform the liquid stocks held by liquid funds. The overlap in trades by illiquid funds does not seem to mechanically drive the higher returns among illiquid funds.

1.6 Tables held by illiquid or liquid funds. At the end of quarter Q, I form 4 portfolios, illiquid stocks held by illiquid funds, illiquid stocks held by liquid funds, liquid stocks held by illiquid funds, liquid stocks held by liquid funds. I form the portfolios by aggregating the shares held by the funds. Then I compute the returns of these portfolios at the end of the previous quarter (Q-1), at the end of the formation quarter (Q), at the end of the following quarter (Q1), at the end of the second quarter following formation (Q1 to Q2). Returns are average returns over the months in the quarter. The returns are annualized and in percentages, and t-stats are in brackets. Panel A contains simple returns, and Panel B contains risk-adjusted returns, using the [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF] model that includes a liquidity factor. At the bottom of each panel, I present differences between returns of stocks held by illiquid funds, and returns of stocks held by liquid funds.

Returns (Panel A)

Illiquid stocks (score≥ 5)

Illiquid funds (Decile 10)

Liquid stocks (score<5)

Illiquid funds (Decile 10) Chapter 2: Opportunities and expected returns

Q-1 Q Q1 Q1 to Q2 Q-1 Q Q1 Q1
Chapter 2: Opportunities and expected returns

Introduction

The existence of asset mispricing has been shown by Grossmann and Stiglitz (1980) to be an unavoidable feature of financial markets. Indeed, as private information is usually costly to acquire, a market without mispricing would not provide any superior trading profits, and hence would not attract any privately informed traders. But in the absence of such traders, how could the market avoid any mispricing? The resolution of this paradox by Grossmann and Stiglitz ( 1980) is to introduce "noise" which allows asset mispricing. In this "noisy rational expectations" framework, some traders -often called by the literature "noise traders"

-introduce a random component to the asset order flow. Privately informed traders can then make superior profits by exploiting the mispricing created by noise traders.

Consistent with Grossmann and Stiglitz (1980), I define "opportunities" simply as the existence of mispricing of stocks. Under the interpretation that mispricing is generated by random price shocks, it is reasonable to expect that opportunities fluctuate significantly over time.

In this paper, I use time-varying opportunities to identify times when the benefits of private information acquisition are higher or lower. This in turn allows to identify time variation in the amount of adverse selection that traders face in the market, and according to theory (see for example [START_REF] Easley | Information and the Cost of Capital[END_REF]) this allows to expect predictability of risk premia based on how large opportunities are in the market. I then find empirical evidence in favor of this predictability.

Thus, consider an informed trader facing time-varying opportunities, and who needs to pay to acquire private information. She then may pay the price only to find that there are not many mispricings in the market at a given time. She may spend time and resources researching the stocks and find out that they are well priced. Ideally, she would pay the price to acquire (additional) private information at the time when there are plenty of mispricings in the market. In other words, she would pay to acquire private information when the benefit to private information is high.

How can a trader know when there are more opportunities in the market? First of all, let us consider the role of information. It is plausible that the stocks about which there is more information (whether public or private) are better priced. Let us take the example of stocks covered by many analysts and stocks not covered by analysts. Because analysts search for information about the stocks they cover, make earnings estimates and give recommendations (on a five-point scale: strong buy, buy, hold, underperform, sell), one would expect that the stocks covered by many analysts are well priced. Well covered stocks incorporate a large quantity of public information. They are usually bigger firms, that trade often, without frictions. On the other hand, neglected stocks incorporate less public information: there are no (or there are very few) analysts covering them. It is still possible that they incorporate some public information (for example, if there is public information about a well covered company in the mining sector, this should also affect the price of a neglected company in the same mining sector). Neglected stocks may also incorporate private information, but it is difficult to know how much private information exists about a stock at a given time. So unless one knows what type of information, and how much of it, exists about neglected stocks, ones prior is that neglected stocks should behave very much like covered stocks and so move up and down with them. An alternative view could be that neglected stocks are always riskier than covered stocks (because investors fear adverse selection), but in this case we should see a risk premium: we should see that a portfolio that goes long neglected stocks and short covered stocks has a positive risk premium. The data does not support this view: a neglected-minuscovered portfolio that is size neutral and equally weighted has an annual mean of -0.64%.

This portfolio has a monthly standard deviation of 3.53%, suggesting that neglected stocks comove with other neglected stocks, and covered stocks comove with other covered stocks.

This comovement is very important, as it means that neglected stocks all move up and down at the same time, possibly with the same factor(s).

Whenever an informed trader sees that neglected stocks are not very different from covered stocks, she can infer that there are not many mispricings in the market. It may not be worth it to pay the price to acquire additional private information, because the benefit to private information is small. However, when she sees that neglected stocks differ from covered stocks, she may be more willing to acquire private information: there are potentially more mispricings that she can exploit. In addition, these mispricings are probably concentrated in the neglected stocks (because between neglected stocks and covered stocks, the former are likelier more mispriced). I will refer to the moment when the returns of neglected stocks diverge from the returns of covered stocks as opportunities being high in the market. An investor, seeing that the returns of neglected stocks diverge from the returns of covered stocks, also knows that there are potentially more mispricings in neglected stock. He knows that informed traders will pay the price to obtain (additional) information and that they will trade on this information. Investors will thus fear adverse selection and require a higher expected return to hold stocks where there are potential mispricings.

The intuitions above can be explained in the context of the model in [START_REF] Easley | Information and the Cost of Capital[END_REF]. In a seminal paper, they build a model in which they allow for differences in the composition of information between public and private information. They show that these differences affect the cost of capital, with investors demanding a higher return to hold stocks with greater private information. In my tests, I identify stocks with higher private information as neglected stocks at the moment when returns of neglected stocks have diverged from the returns of covered stocks (I measure divergence as the absolute value of the difference between returns of neglected stocks and returns of covered stocks; I call "high opportunities" the times when this absolute value is higher than its mean). This is because at that point informed traders will acquire more private information in neglected stocks as they believe neglected stocks are mispriced. I test the prediction of the model, that subsequent returns of neglected stocks are high and I find this is true. Moreover, I am able to extend the results beyond neglected stocks to other stocks with difficult valuation (stocks with high volatility, distressed stocks, illiquid stocks, young stocks). While it is difficult to claim that only one particular theoretical framework explains my findings, I will show that my empirical findings are consistent with an information risk (as in the Easley and O'Hara (2004) model ), and thus it does not constitute an efficient market anomaly. I am able to reject the most likely alternative stories (delay, market sentiment), and I will also present some direct evidence as the difference in the probability of informed trading (PIN).

My main contribution is to show that, when opportunities are high, subsequent returns of stocks with difficult valuation is higher. For example, small stocks have returns higher with 1.32% per month when previous opportunities are high as compared with when previous opportunities are low. For stock with high volatility, the difference is 1.83% per month. For neglected stocks, the difference is 1.05% per month. The results are robust to different constructions of the opportunities measure. Also, they are robust to the exclusion of the month of January. Because of the documented January effect, which is more pervasive in small stocks, I test whether it is driving the results, but it is not the case. When I analyse two different subsamples (dividing the test period into two parts), I find that the results are stronger in the second part. I test whether there is a risk story in the sense of a conditional CAPM. In a conditional CAPM, betas with respect to the market are higher in some states of the world.

I test if high opportunities increase subsequent betas with respect to the market. There does not appear to be a consistent relationship among all the stocks considered. However, in the case of small stocks and young stocks, the coefficient of the interaction term is positive and significant.

I also try to identify a group of investors that benefit from a period of high opportunities.

While I do find that mutual funds trade on average more when opportunities are higher, I do not find that mutual funds have higher subsequent returns if they trade more when opportunities are higher. I interpret these findings in the following way: while mutual funds identify the periods with high opportunities and they are trying to exploit them (they trade more), the average fund does not succeed in correctly identifying these opportunities. The main advantage of this measure of opportunities is that it is very easy to compute, based on returns data (as opposed to market microstructure data). Its main disadvantage is that is can be noisy. However, I am able to predict future returns on stocks with difficult valuation based on this opportunities measure.

There is a vast literature covering market frictions that affect the cross-section of returns.

These frictions reside in incomplete information as in [START_REF] Merton | A simple model of capital market equilibrium with incomplete information[END_REF], the idea that investors can not invest in stocks they do not know about, thus leading to inefficient portfolio choices;

or asymmetric information as in [START_REF] Wang | A model of intertemporal asset prices under asymmetric information[END_REF], [START_REF] Easley | Is Information Risk a Determinant of Asset Returns[END_REF], [START_REF] Dong | Time-varying arrival rates of informed and uninformed trades[END_REF], [START_REF] Easley | Factoring information into returns[END_REF]; or liquidity innovations, as in [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF]; or market sentiment as in [START_REF] Baker | Investor sentiment in the stock market[END_REF]Wurgler, (2006),(2007). [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] present an empirical characterisation of the severity of frictions affecting the stock. They construct a measure of price delay and show that delayed firms command a return premium as large as 12% per year, risk-adjusted for size, book-to-market, momentum, and liquidity.

I will focus mainly on the papers on asymmetric information. [START_REF] Easley | Is Information Risk a Determinant of Asset Returns[END_REF] use a market microstructure model to derive a measure of the probability of informationbased trading. They find that information does affect asset prices: a difference of 10 percentage points in the probability of information-based trading between two stocks leads to a difference in their expected returns of 2.5 percent per year. A quick calculation shows that, if I apply the results of [START_REF] Easley | Is Information Risk a Determinant of Asset Returns[END_REF] to my results, there should be an average 50 percentage points higher probability of information-based trading between neglected stocks when opportunities are higher as compared to when opportunities are lower

( 1.05×12×10 2.5
≈ 50, because for neglected stocks the premium is 1.05% per month).

Easley, Hvidkjaer and O'Hara (2010) build a zero-investment portfolio which is size-neutral, but long stocks with high probability of informed trading (PIN) and short stocks with low PIN. This factor earns a significant abnormal return.

There are possible alternative explanations for my results: price delays or market sentiment. [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] present an empirical characterisation of the severity of frictions affecting the stock. They argue that the price of neglected stocks is delayed. Also, [START_REF] Arbel | Generic stocks: An old product in a new package[END_REF] argues that information incorporation is delayed for neglected firms. My results are unlikely to capture a measure of price delay for three reasons: firstly, the substantial variation in average returns produced in [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] applies to a very small segment of delayed firms (about 0.02% of the market), while in my case the prediction occurs for a larger segment of the market, between 0.1% and 12% of the market, on average, depending on the sorting characteristic14 ; secondly, taking absolute value of the difference between neglected and covered, captures both increases and decreases in the price of covered stocks. If it is a delay story, then we should see the subsequent price of neglected stocks "catching up", that is increasing or decreasing, as the case may be. However, subsequent returns are only higher for neglected stocks following increased opportunities. Thirdly, [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] find that the lags on the most severely delayed stocks are of several weeks, while in may paper the premium still manifests a year after a period with high opportunities.

The other possible explanation, market sentiment, is proposed by Baker and Wurgler (2006) and ( 2007). They show that when beginning-of-period proxies for sentiment are low, subsequent returns are relatively high for small stocks, young stocks, high volatility stocks, unprofitable stocks, non-dividend-paying stocks, extreme growth stocks, and distressed stocks.

However, my opportunities measure is only weakly correlated with the market sentiment measure (around 20% at yearly level), and the inclusion of market sentiment in the regressions does not change either the coefficient or the significance of the coefficient on the opportunities measure. So I interpret that it is not market sentiment that I am capturing in the paper.

This chapter is organized as follows. Section 2.2 describes the theoretical model of [START_REF] Easley | Information and the Cost of Capital[END_REF] and its predictions. Section 2.3 shows how I build the opportunities measure.

Section 2.4 describes how I build the test portfolios. Section 2.5 presents results. Section 2.6

shows robustness tests. Section 2.7 concludes.

Easley and O'Hara (2004)

In their paper, there are informed traders and uninformed traders. Informed traders form their demand as Bayesians, they update based on their informed signals. Uninformed traders learn after seeing the price. From the equilibrium condition, it follows that:

E[v k -p k ] = δx k ρ k + (1 -α k )I k γ k + µ k α k I k γ k + (1 -µ k )ρ θk ,
where k is an asset, v k is the future value of the asset, p k is today's price, δ is risk-aversion, ρ k is the precision of the distribution of v k , α k is the fraction of the signals that are private, I k is the information set, γ k is the precision of the distribution of signals, µ k is the fraction of traders that receive private signals, and ρ θk is the precision of a variable that affects the demand of the uninformed trader. Figure A1 describes the setup of the model. It follows, by taking the derivative with respect to α k , that:

∂E[v k -p k ] ∂α k > 0.
It means that when there are many private signals in a stock, investors demand a higher expected return to hold that stock. This is because with many private signals they require a higher expected return as they fear they will be adversely selected. So, in comparing two stocks that are otherwise identical, the stock with more private information will have a larger expected excess return. This is because, when information is private, uninformed investors cannot perfectly infer the information from prices, and so for them these stocks are riskier.

The results of my paper are consistent to the model of [START_REF] Easley | Information and the Cost of Capital[END_REF]. While it is difficult to reject all alternative hypotheses, I manage to reject the most likely alternatives, market sentiment and price delay. I also present direct evidence that the PIN is higher in stocks with difficult valuation than in stocks with easier valuation, following high opportunities. Thus, in the context of the [START_REF] Easley | Information and the Cost of Capital[END_REF] stocks, but this may not necessarily be the case: neglected stocks may be neglected even by informed traders, in the sense that they have little private information about them. If there is a cost to obtain (additional) private information (such as time to research a company, etc.) then an informed trader may pay the cost only to find out the stocks are not very mispriced.

She will ideally pay this cost at times when the benefit to private information is high. Thus, I identify the stocks with more private information, as the neglected stocks (and by extension stocks with difficult valuation), at the time when the returns of neglected stocks diverge from the returns of covered stocks. If there is no information about neglected stocks, they should move up and down with the covered stocks. I remain agnostic about why a divergence of returns occurs between neglected and covered stocks. Should it occur because there is more private information in the stocks at some point, then neglected stocks should command a higher expected excess return. Even if there is a different reason for which the returns of neglected stocks diverge, this could still be a signal for informed traders to gather additional private information in these stocks. Investors, knowing that there will be more private information in the neglected stocks then demand a higher premium to hold neglected stocks for fear of adverse selection. So whatever the reason for which the returns of neglected stocks diverge from the returns of the covered stocks, we should have the prediction that neglected stocks (and stocks with difficult valuation) have a higher expected excess returns following a period when returns of neglected stocks diverge from the returns of neglected stocks. This is what I find in the data. I call this period, when returns of neglected stocks diverge from the returns of covered stocks, a period when opportunities are high. This is because the benefit of private information is high and thus informed traders have incentives to obtain additional private information. In other words, there are opportunities for them to be seized, once they pay the price and obtain additional private information. It is important to note, however, that these opportunities (mispricings) are likely concentrated in neglected stocks and stocks with difficult valuation.

There are three parameters that could be affected when there is more private information, in the model of [START_REF] Easley | Information and the Cost of Capital[END_REF]: µ k , α k , I k . Parameter µ describes the ratio of informed traders over all traders. It is inversely related with expected returns:

∂E[v k -p k ] ∂µ k < 0.
The intuition is that when there are more informed traders in a stock, the stock becomes better priced by their actions. Thus the stock becomes less risky (from an information risk point of view), and thus investors require a lower premium to hold the stock. In my tests, given that the expected returns are higher after higher opportunities, it means that either it is the same informed traders who acquire additional private information (so that µ does not change, but α increases), or that more traders in general acquire private information so that µ increases, but the effect of α (to increase the premium for fear of adverse selection) is bigger than the effect of µ (to decrease the premium because the stock becomes better priced, so less risky). I k , the set of signals (private and public), also changes when the number of private signals increases. Moreover, its influence on subsequent returns is negative, I find that small stocks have returns higher with 1.32% per month when previous opportunities are high as compared with when previous opportunities are low. For stock with high volatility, the difference is 1.83% per month. For neglected stocks, the difference is 1.05% per month. The results are robust to different constructions of the opportunities measure.

∂E[v k -p k ] ∂I k < 0,
Also, they are robust to the exclusion of the month of January. Because of the documented January effect, which is more pervasive in small stocks, I test whether it is driving the results, but it is not the case. When I analyse two different subsamples (1985-2000 and 2001-2015), I find that the results are stronger in the second part. I test whether there is a risk story in the sense of a conditional CAPM. In a conditional CAPM, betas with respect to the market are higher in some states of the world. I test if high opportunities increase subsequent betas with respect to the market. There does not appear to be a consistent relationship among all the stocks considered. However, in the case of small stocks and young stocks, the coefficient of the interaction term is positive and significant.

I also try to identify a group of investors that benefit from a period of high opportunities.

While I do find that mutual funds trade on average more when opportunities are higher, I do not find that mutual funds have higher subsequent returns if they trade more when opportunities are higher. I interpret these findings in the following way: while mutual funds identify the periods with high opportunities and they are trying to exploit them (they trade more), the average fund does not succeed in correctly identifying these opportunities.

The opportunities measure

This part describes the construction of the opportunities measure. The first measure is a size neutral measure, constructed like the long-short portfolios of [START_REF] Fama | The cross-section of expected stock returns[END_REF][START_REF] Wang | A model of intertemporal asset prices under asymmetric information[END_REF][START_REF] Khorana | Top management turnover an empirical investigation of mutual fund managers[END_REF] factors. I sort stocks every December by their size (market capitalization) in two bins, according to the NYSE stocks 50th percentile. Using the NYSE breakpoints insures there is the same number of NYSE stocks in every bin. I then sort into three bins by neglect (number of analysts), according to the NYSE stocks 30th and 70th percentile. If there are more stocks with the same number of analysts at the cutoff, I take all the stocks into the bin. I then intersect the bins and form 6 portfolios, equally weighted. My first concern is that there will be too few stocks in the big-and-neglected and in the small-and-covered bins.

Indeed, the small-and-neglected bin has an average of 73 stocks (with a minimum of 23); the big-and-covered bin has an average of 103 stocks (with a minimum of 67). However, I show in the robustness section that computing the opportunities measure in a way that circumvents this problem yields similar results. I compute the return in the following 12 months as nmc ff ew = 0.5 × (small neglected + big neglected) -0.5 × (small covered + big covered).

The advantage of this method is that the measure is size neutral (there is not a difference in size between the long and the short leg of the measure). Finally, because I am interested in deviations or returns of neglected stocks from the returns of covered stocks, I take the absolute value of the measure. This measure is denoted a nmc ff ew. This can be seen as having a middle band in the neglected-minus-covered measure. Whatever returns are within the band will appear as below the average of the absolute value measure. Whatever returns are outside the band will appear as above the average of the absolute value measure. In other words, the observations within the band represent times when returns of neglected stocks do not deviate from the returns of covered stocks. Observations outside the band represent times when returns of neglected stocks deviate from returns of covered stocks (so times when opportunities are high, as defined in this paper). Figure 2.1 presents this fact.

I describe below how I obtain the data for analyst coverage. I use the I\B\E\S database for the analyst data. I use the number of analysts that make earnings forecasts (in the Summary History, Summary Statistics category). At a given time for a stock I may have 6 analysts giving a 6-month forecast, 5 analysts giving a 1-year forecast and 2 analysts giving a 2-year forecast. In this case where I have multiple horizons, I take the maximum number of analysts among all horizons (in the above example 6). I interpret that there are (at least) 6

analysts covering the stock. I am aware that this number may be understating the number of analysts (in the case where the analysts giving recommendations for different horizons are themselves different), however on average I will still capture the differences between stocks with very few analysts and stocks with a lot of analysts. If a stocks is in the CRSP database, but not in the I\B\E\S database, I assign 0 analysts to it for the period of time it appears in CRSP. I check at CRSP and they confirm that, most likely, a stock that has information in CRSP and not in I\B\E\S is a stocks with 0 analysts, rather that a covered stock for which the number of analysts is unreported. I present several statistics for the opportunities measure. Figure 2.2 plots the opportunities measure in the left graph this is the absolute value (a nmc ff ew), which describes the return divergences between neglected stocks and covered stocks. The right graph plots the original neglected-minus-covered, before taking absolute value. We observe that there is variation in the series (which indicates comovement between the stocks at the long leg and comovement between stocks at the short leg.) Table 2.1 analyzes the opportunities measures and their components. The alternative measures are described in Section 2.6 (Robustness) and in table A1 of the Appendix. We first notice that neglected minus covered does not have a risk premium (the premium is -0.64% per year when portfolios are equally weighted and -2.84% per when portfolios are value weighted). Once I take absolute value, the average value of the measure is 28.91% per year. The standard deviation of the neglected-minus-covered is 3.53% months, indicating comovement of stocks (at the short leg, and at the long leg). If there is no comovement, randomly placing stocks into two portfolios produces a standard deviation close to 0 of the difference portfolio. The standard deviation of the neglected-minus-covered is in line with the standard deviation of other long-short portfolios when there is comovement between stocks (2.99% per month for HML, 3.72% per month for the traded liquidity of [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF], 4.58% per month for momentum (up-minus-down stocks), over the same period of time). The AR(1) coefficient of the opportunities measure is 0.6; it should be expected that there is some correlation between opportunities at the monthly level. Last in the table, I compute the percentage of observation above average. I do this to ensure that the average is not greatly influenced by a few extreme observations. For the opportunities measure, there are 38% observations above average, so I consider the mean to be representative.

In table 2.2, I analyze the correlation between nmc ff ew, a nmc ff ew and the original components neglected stocks (the long leg of the difference) and covered stocks (the short end of the difference). First of all, neglected stocks do move up and down with covered stocks in general, as their correlation is 0.84 (this is true for HML or SMB as well were the correlation between the long leg and the short leg is around 0.8 as well). The negative correlation between nmc ff ew and covered stocks (while there is no correlation between nmc ff ew and neglected stocks) means that the it is mostly the covered stocks who are driving the deviations between neglected and covered. However, it is unlikely this is a measure of delay as in [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] for three reasons: firstly, the substantial variation in average returns produced in [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] applies to a very small segment of delayed firms (about 0.02% of the market), while in my case the prediction occurs for a larger segment of the market, between 0.1% and 12% of the market, on average, depending on the sorting characteristic15 ; secondly, taking absolute value of the difference between neglected and covered, captures both increases and decreases in the price of covered stocks. If it is a delay story, then we should see the subsequent price of neglected stocks "catching up", that is increasing or decreasing, as the case may be. However, subsequent returns are only higher for neglected stocks following increased opportunities. Thirdly, [START_REF] Hou | Market frictions, price delay, and the cross-section of expected returns[END_REF] find that the lags on the most severely delayed stocks are of several weeks, while in may paper the premium still manifests a year after a period with high opportunities.

In table 2.3, I present the correlations between the opportunities measure and usual long-short portfolios. The biggest correlations are with HML (0.12) and with momentum (-0.12).

One constraint I face in the tests is the length of the sample. Asset pricing tests usually use long periods of times (staring in the 60's or even before that). I am constrained first by the availability of the I\B\E\S data, as analyst data begin only in 1976. An additional constraint is the decile creation by number of analysts -given the distribution of analysts, I am only able to obtain reasonable decile splits by number of analysts starting with 1983

(then using two years of data to estimate alphas further reduces the sample to 1985). Another concern is that, for the future, if all stocks become covered at some point, there might be the same problem of dividing into deciles. However, as I show in the robustness tests, the opportunities measure works even if I use the stocks covered by 1 analyst as neglected stocks (and not stocks with 0 analysts). In the future, even if the landscape changes, one could potentially use the stocks with the minimum number of analysts at that point as neglected stocks.

The test portfolios

This part presents the construction of the test portfolios. When opportunities are high in December t-1, monthly returns are higher in year t for stock with difficult valuation: small stocks, high volatility stocks, neglected stocks, young stocks, distressed stocks, illiquid stocks.

I define high opportunities as opportunities above the average of the time series. To obtain the test portfolios, I sort stocks in ten deciles in December t-1 based on size, average volatility in year t-1, analyst coverage (how many analyst estimates there are), book-to-market 16 , age (time since first listed on the exchange), illiquidity (I compute the Amihud (2002) measure).

16 To compute book-to-market, I use the method outlined on the website of Kenneth French, http://mba. tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/variable_definitions.html: "Book equity (BE) is constructed from Compustat data. BE is the book value of stockholders' equity, plus balance sheet deferred taxes and investment tax credit (if available), minus the book value of preferred stock. Depending on availability, we use the redemption, liquidation, or par value (in that order) to estimate the book value of preferred stock. Stockholders' equity is the value reported by Compustat, if it is available.

If not, we measure stockholders' equity as the book value of common equity plus the par value of preferred stock, or the book value of assets minus total liabilities (in that order)."

Each decile portfolio is a equally weighted average of the stocks in the portfolio. As in Baker and Wurgler (2006), I compute equally weighted and not value weighted returns because the effects are likely to be higher in small stocks and value weighing would obscure this. Figure 2.3 shows that the difference in subsequent returns when opportunities are high versus low is bigger for small stocks (Decile 1) than for the big stocks (Decile 10): the line is downward sloping. Figure 2.4 shows that the difference in subsequent returns when opportunities are high versus low is bigger for more volatile stocks (Decile 10) than for less volatile stocks (Decile 1): the line is upward sloping. Finally, Figure 2.5 shows that the difference in subsequent returns when opportunities are high versus low is bigger for neglected stocks (Decile 1) than for covered stocks (Decile 10): the line is downward sloping.

Results

Table 2.4 shows subsequent returns when opportunities at the beginning of the period are high (low). Opportunities are measured in December of each year and returns are measured each month over the following year. Stocks are sorted into deciles at the end of each year. I measure returns on the deciles over the following year, then redo the sorting. I append the series of returns to form a continuous return for each of the 10 deciles. The deciles are formed by size (first panel), by volatility in the previous 12 months (second panel), and by coverage (number of analysts) (third panel). Sorting by these characteristics produces portfolios of stocks that differ by difficulty of valuation. Small stocks are more difficult to value than big stocks, highly volatile stocks are more difficult to value than less volatile stocks and stocks with less analyst coverage (neglected) are more difficult to value than stocks followed by more analysts. I claim in the paper that stocks with more difficult valuation have higher expected returns following high opportunities. When returns of neglected stocks diverge from returns of covered stocks, traders want to pay the cost to become informed about stocks with difficult valuation. At those times, the benefit to private information is higher for stocks with difficult valuation. Investors then require a higher risk premium to hold stocks with difficult valuation because they fear adverse selection. The table presents averages of returns, for each decile, when opportunities are high (low), for each stocks decile by size, previous volatility and coverage. As predicted, the returns of small stocks are higher than returns of big stocks, when opportunities are high. Also, the returns of small stocks, when opportunities are high, are bigger than the returns of small stocks, when opportunities are low. In each of the three panels, the third row is the difference between the first and the second rows. These differences are plotted in Figures 2.3-2.5. Small stocks have higher returns with 1.32% per month when beginning of period opportunities are high, as compared to when opportunities are low (the premium is 1.83% per month for stocks with high volatility, and 1.05% per month for neglected stocks). We notice in the three panels that the high opportunities periods produce more dispersion in returns between stocks with difficult valuation and stocks with easier valuation than the periods with low opportunities.

In table 2.5 I conduct the same type of analysis as in the previous table, but in a regression set up. Specifically, I construct long-short portfolios (Decile 10-Decile 1) of stocks with difficult valuation minus stocks with easy valuation. The long-short portfolios are: small minus big; high volatility minus low volatility; neglected minus covered; value minus growth; illiquid minus liquid; young minus old. For each group, I run regressions of the form:

R difficult valuation,t -R easier valuation,t = a + b × Opportunities t-1 + j k=1 c j F j,t .
F j are factors. First, I run regressions on the opportunities alone (column 1). The results in the table are the coefficient on Opportunities and its t-stat. In the Fama-French 3-factor model (column 2), I use as factors MKTRF (market minus risk-free rate), SMB and HML.

Whenever small-minus big is on the left hand side, I omit SMB on the right hand side. Whenever value-growth is on the left hand side, I omit HML on the right hand side. In the Carhart model (column 3), I also include the momentum factor (stocks that went up minus stocks that went down) in addition to the Fama-French 3-factor model . In the Pástor and Stambaugh model (column 4), I also include the traded liquidity factor in addition to the Fama-French 3-factor model. This is particularly interesting as it allows for separation between information risk and liquidity risk. The results suggest that there is an information risk, in addition to the liquidity risk. I leave the liquidity factor on the right hand side even when illiquid minus liquid is on the left hand side because the liquidity factor quantifies innovations (and not levels) of liquidity 17 . The first panel shows the coefficients of beginning of period opportunities are positive and significant: subsequent returns of stocks with difficult valuation (in excess of stocks with easy valuation) are higher if beginning of period opportunities are higher. For example, returns of neglected stocks in excess of covered stocks are about 5.78% per year riskadjusted (0.2 × 28.91), due to beginning of period opportunities. Before adjusting for risk, returns of neglected stocks in excess of covered stocks are about 9.54% per year (0.33×28.91), due to beginning of period opportunities. One interesting observation is that for value minus growth stocks. The coefficient on beginning of period opportunities is smaller than for other long-short portfolios. I believe this happens because extreme growth stocks are also difficult to evaluate (just like distressed stocks are). So value minus growth is probably not the correct measure for stocks with difficult valuation and stocks with easy valuation. This is what [START_REF] Baker | Investor sentiment in the stock market[END_REF]Wurgler (2006), (2007) find as well in their tests for market sentiment.

Because I am concerned this might be a January effect 18 , I repeat the regressions taking out the returns of of stocks in January. The results, presented in the second panel, still hold.

I also split the sample in two periods: 1985-2000 and 2001-2015. In the first subsample, the coefficients are only a little smaller than in the second, and close to being significant. The results are stronger in the second subsample.

Overall, table 2.5 shows that there is a positive and significant relationship between opportunities at the beginning of the period and excess returns of stocks with difficult valuation over stocks with easy valuation. The positive relationship is valid before and after accounting for risk by means of the usual risk models: Fama-French 3-factor model, Carhart 4-factor model with momentum, Pástor and Stambaugh 4-factor model with liquidity.

In table 2.6, I explore whether the information risk manifests in a conditional way. I test if the t-1 opportunities, correspond to a higher β on the market at time t. In other words, I 17 M KT , R f , SM B, HM L come from the website of Kenneth French:http://mba.tuck.dartmouth.edu/ pages/faculty/ken.french/data_library.html; U M D and the traded liquidity factor come from CRSP.

18 January effect: investors sell their losing positions in December to create a tax-loss to offset capital gains. In January there is an increase in price generating a positive return. The January effect is more pronounced in small stocks than in big stocks test the regression:

R difficult valuation,t -R easier valuation,t = a + b × Opportunities t-1 + c × MKTRF t + d × MKTRF t × Opportunities t-1 .
If the conditional CAPM specified above holds, then coefficient d of the interaction term should be positive and significant. Of the 6 pairs of stocks with difficult valuation minus stocks with easy valuation, the coefficient is positive and significant only twice. I interpret the findings as not enough evidence that the true model is a conditional CAPM.

I explore whether there are some winners, that is some agents who benefit after a period of high opportunities. I direct my search towards mutual funds. Mutual funds are great players in the market, as they manage around $16 trillion as of 2014 (for comparison, US GDP in 2014 was around $17 trillion). In table 2.7, I run a univariate regression of average turnover across all funds on opportunities. Turnover is reported annually, for each fiscal year, by mutual funds. Because of the turnover definition19 it is difficult to to know how much a fund traded in a given month. Given the above constraint, I assign to each month the value of the fiscal year that includes that particular month. When I regress Average turnover across funds on the contemporaneous opportunities measure, the coefficient is positive and significant. That translates into a correlation of 0.4 between Average turnover and opportunities. There is evidence that mutual funds are trading more when opportunities are higher. I try to run an additional regression to test if the funds that trade more when opportunities are higher have higher subsequent returns, controlling for opportunities themselves. This is not the case. I interpret that, although mutual funds may be trying to seize opportunities, the average mutual fund is not successful in doing so.

An interesting statistic to evaluate is the probability of informed trading (PIN) separately for stocks with difficult valuation and for stocks with easy valuation when previous opportunities have been high. As I conjecture, when neglected stocks move away from covered stocks, more traders acquire information about neglected stocks (and stocks with difficult valuation in general). If this is true, then we should see an increased difference between PIN for stocks with difficult valuation and PIN for stocks with easy valuation, following a period of high opportunities. PIN is the measure introduced in the paper of [START_REF] Easley | Liquidity, Information, and Infrequently Traded Stocks[END_REF]. In their paper, there are four parameters that govern the trade process for a stock: α is the probability of an information event; δ is the probability that the information is bad news; µ is the arrival rate of traders who know the new information if it exists (i.e. the informed traders); is the arrival rate of uninformed traders. These parameters are estimated by maximizing the likelihood function 20 , conditional on the stock's trade data. Once these parameters are estimated, PIN is computed as: PIN = αµ αµ + 2

. To evaluate the relation between the PIN difference (of stocks with difficult valuation relative to stocks with easy valuation) and previous opportunities, I run the following monthly regressions:

PIN difficult valuation,t -PIN easier valuation,t = a + b × Opportunities t-1 .
The results of the above regressions are presented in Table 2.8. I only have a smaller sample of PIN, that ends in 2002. When previous opportunities are high, the increase in the difference in PIN between small and big stocks is positive and significant, albeit not very big

(1.78 percentage points for a one standard deviation increase in previous opportunities). For neglected and covered stock, the increase is 1.40 percentage points, and for young and old stocks the increase is 2.32 percentage points. There is no significant increase for illiquid and liquid stocks, or for high volatility and low volatility stocks. It may be that the PIN measure is more noisy for illiquid stocks and for high volatility stocks, but further test are needed.

Although the differences are small, there is some evidence that previous high opportunities are associated to bigger difference in the probability of informed trading between the stocks with difficult valuation and stocks with easy valuation. 20 The likelihood of observing B buys and S sells on a day of unknown type, and of total

time T, is L((B, S)|θ) = (1 -α)e -T ( T ) B B! e -T ( T ) S S! + αδe -T ( T ) B B! e -(µ+ )T [(µ + )T ] S S! + α(1 - δ)e -(µ+ )T [(µ + )T ] B B! e -T ( T ) S S! .
While the results presented are consistent with a theory of asymmetric information, it is hard to refute all alternatives. I attempt to rule out the most evident possibilities. I showed that the results are not driven by a delay story, nor by market sentiment, and that the spreads in returns between stocks with difficult valuation and stocks with easy valuation are robust to different factor specifications. I also test if different exposures to aggregate volatility may be driving the results, and I find it is not the case. [START_REF] Ang | The Cross-Section of Volatility and Expected Returns[END_REF] show that stocks that covary positively with a measure of aggregate volatility have lower expected returns. This is because stocks that do well when volatility is high are desirable for investors and so investors demand a low risk premium to hold these stocks. The results are presented in Table 2.9, and they show that introducing ∆VIX in the regressions does not change the coefficient on previous opportunities.

Robustness

For robustness, I consider several alternative ways to construct the opportunities measure.

First, I consider the same measure as above, but with value weighing of the returns within the 6 bins. Second , I take all the stocks with 0 analysts as the long leg, and for the short leg I take an equal number of stocks starting from the covered side. If there are more stocks with the same number of analysts at the cutoff, I choose randomly from the stocks with this number of analysts so as to keep the same number of stocks on the two legs. I consider both the equal weighted and the value weighted versions of the measures. Third, I take all the stocks with 1 analyst as the long leg, and for the short leg I take an equal number of stocks starting from the covered side. If there are more stocks with the same number of analysts at the cutoff, I choose randomly from the stocks with this number of analysts so as to keep the same number of stocks on the two legs. I consider both the equal weighted and the value weighted versions of the measures. The reason I consider stocks with 1 analyst is to have a more conservative measure. This shows the differences between stocks with very little coverage (as opposed to stocks with no coverage) and stocks with a lot of coverage. In total, I have 6 measures for opportunities. I describe the measures in table A1. In the paper, I perform the tests on the first measure (size neutral, equal weighted). In Appendix, I show in Tables A2 -A6 that the results hold with the alternative measures as well. The only exception is in Table A6, for the stocks sorted by previous volatility.

Conclusion

In this paper, I identify high opportunities in stocks with difficult valuation as times when the returns of neglected stocks diverge from the returns of covered stocks. At times when the returns of neglected stocks diverge from the returns of covered stocks, the benefit of private information is higher and informed traders will pay the cost to acquire more private signals in stocks with difficult valuation. Investors then require a premium to hold stocks with difficult valuation because they fear adverse selection.

I find that small stocks have returns higher with 1.32% per month when previous opportunities are high as compared with when previous opportunities are low. For stock with high volatility, the difference is 1.83% per month. For neglected stocks, the difference is 1.05% per month.

The results are robust to several ways of constructing the opportunities measure.

The results are not driven by market sentiment, and it is unlikely that they capture a price delay in stocks with difficult valuation. They are also robust to the introduction of a measure of volatility of the market.

I find that, consistent with the theory, following a period of increased opportunities, the PIN in stocks with difficult valuation is greater than the PIN in stocks with easier valuation.

I find that the average turnover of mutual funds is higher when opportunities are higher.

However, the average mutual fund does not have a higher alpha if it traded more when opportunities were higher.

Figures

Figure 2.1: The round, green points represent observations of nmc ff ew when a nmc ff ew is below its average. The diamond, red points represent observations of nmc ff ew when a nmc ff ew is above its average. 2.9 Tables Table 2.1: Statistics for the opportunities measures. The opportunity measure is always an absolute value (with prefix a ). The starred measure (***) is the one I use in most of the tests. nmc ff ew is neglected minus covered, size-neutral, equally weighted. Suffix vw means value weighted. nmc 0 ew is neglected minus covered, equally weighted, where neglected is all stocks with 0 analysts, and covered is an equal number of stocks starting from the covered end. nmc 1 ew is neglected minus covered, equally weighted, where neglected is all stocks with 1 analyst, and covered is an equal number of stocks, starting from the covered end. Table 2.2: Correlations between the opportunities measure (a nmc ff ew) and its components: nmc ff ew, the measure before taking absolute value, is nmc ff ew=0.5 × (neglected small + neglected big) -0.5 × (covered small + covered big) ; Neglected is 0.5 × (neglected small + neglected big); Covered is 0.5 × (covered small + covered big).

Mean

Neglected Covered nmc ff ew a nmc ff ew Neglected 1.00 Covered 0.84 1.00 nmc ff ew 0.00 -0.55 1.00 a nmc ff ew -0.05 0.11 -0.28 1.00

(1.73) (1.54) (1.12) (1.5) (1.27) (1.3) (1.21) (0.87) (0.77)
Table 2.5: Regressions of the form: R difficult valuation,t -R easier valuation,t = a + b × Opportunities t-1 + j k=1 c j F j,t . F j are factors. The results in the table show b (the coefficient on beginning of period opportunities), and t-statistics are in parentheses. In the FF3 (Fama-French 3-factor) specification, the factors are Mktrf, SMB, HML. Whenever I regress small-big on the left hand side, I omit SMB on the right hand side; whenever I regress value-growth on the left hand side, I omit HML on the right hand side. In the C (Carhart) specification, the factors are Mktrf, SMB, HML, MOM. In the PS (Pástor-Stambaugh) Table 2.9: Regressions of the form: R difficult valuation,t -R easier valuation,t = a + b × Opportunities t-1 + j k=1 c j F j,t + d × ∆VIX t . F j are factors. ∆VIX measures changes in the aggregate volatility. The results in the table show b (the coefficient on beginning of period opportunities), and t-statistics are in parentheses. In the FF3 (Fama-French 3-factor) specification, the factors are Mktrf, SMB, HML. Whenever I regress small-big on the left hand side, I omit SMB on the right hand side; whenever I regress value-growth on the left hand side, I omit HML on the right hand side. In the C (Carhart) specification, the factors are Mktrf, SMB, HML, MOM. In the PS (Pástor-Stambaugh) nmc ff ew Neglected minus covered. It is constructed as the usual portfolios of Fama-French, so that it is size neutral. I compare stocks to the 50th percentile of size of the NYSE stocks, and I form 2 portfolios. I form 3 portfolios by coverage (number of analysts), by comparing to the 30th and 70th percentiles of the NYSE stocks. I intersect the portfolios and I form 6 portfolios with equally weighted returns. Then nmc ff ew = 0.5(small neglected + big neglected) -0.5(small covered + big covered). a nmc ff ew*** The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. This is the measure used in most of the tests. nmc ff vw Neglected minus covered. It is constructed as the usual portfolios of Fama-French, so that it is size neutral. I compare stocks to the 50th percentile of size of the NYSE stocks, and I form 2 portfolios. I form 3 portfolios by coverage (number of analysts), by comparing to the 30th and 70th percentiles of the NYSE stocks. I intersect the portfolios and I form 6 portfolios with value weighted returns. Then nmc ff ew = 0.5(small neglected + big neglected) -0.5(small covered + big covered). a nmc ff vw

The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. nmc 0 ew Neglected minus covered. For the neglected leg I take all the stocks that have 0 analysts and I compute equally weighted returns. For the covered leg, I take the same number of stock from the NYSE stocks, staring from the covered end. I compute the cutoff and I then compare all common stocks in CRSP with the cutoff to populate the covered portfolio. a nmc 0 ew

The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. nmc 0 vw Neglected minus covered. For the neglected leg I take all the stocks that have 0 analysts and I compute value weighted returns. For the covered leg, I take the same number of stock from the NYSE stocks, staring from the covered end. I compute the cutoff and I then compare all common stocks in CRSP with the cutoff to populate the covered portfolio. a nmc 0 vw

The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. nmc 1 ew Neglected minus covered. For the neglected leg I take all the stocks that have 1 analyst and I compute equally weighted returns. For the covered leg, I take the same number of stock from the NYSE stocks, staring from the covered end. I compute the cutoff and I then compare all common stocks in CRSP with the cutoff to populate the covered portfolio. a nmc 1 ew

The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. nmc 1 vw Neglected minus covered. For the neglected leg I take all the stocks that have 1 analyst and I compute value weighted returns. For the covered leg, I take the same number of stock from the NYSE stocks, staring from the covered end. I compute the cutoff and I then compare all common stocks in CRSP with the cutoff to populate the covered portfolio. a nmc 1 vw

The opportunities measure that corresponds to the above long-short portfolio. It is the absolute value of the above long-short portfolio. Table A3: Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks. For neglected stocks I take all stocks with 0 analysts, and then I take an equal number of stocks starting from the end of the most covered stocks. Portfolios of the neglected minus stocks are equally weighted. Table A4: Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks. For neglected stocks I take all stocks with 0 analysts, and then I take an equal number of stocks starting from the end of the most covered stocks. Portfolios of the neglected minus stocks are value weighted. Table A5: Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks. For neglected stocks I take all stocks with 1 analyst, and then I take an equal number of stocks starting from the end of the most covered stocks. Portfolios of the neglected minus stocks are equally weighted. Table A6: Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks. For neglected stocks I take all stocks with 1 analyst, and then I take an equal number of stocks starting from the end of the most covered stocks. Portfolios of the neglected minus stocks are value weighted. I find that (1) managers do not take more risk when it is more profitable for them to do so;

(2) After the manager has experienced bad times, he does not take bets outside his style; (3) Bad performing mutual funds move closer to the style of good performing peer funds, but young funds differentiate themselves in style from old peer funds; recently hired managers differentiate themselves in style from veteran managers of peer funds; (5) When the average fund takes more risk alongside a style dimension, it does not simultaneously consider its risk on the other style dimensions (except for changes alongside momentum).

These findings suggest that mutual fund styles' are stable, consistent with the literature [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF].

Style and risk are intertwined. I refer to style changes as style drift, as in [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF], especially since style changes are not dramatic. I classify styles alongside four dimensions: size, book-to-market, past performance and liquidity. All these characteristics refer to the stocks the mutual fund is invested into. Mutual fund style does not have a uniform definition.

For example, CRSP has a style-based classification into Growth, Growth & Income, Hedged, Short and Income funds. A Growth fund should not be confused with a fund invested into growth stocks. A Growth fund, in the CRSP classification, is rather a fund invested into more risky assets in the pursuit of a higher return (that aims to "grow" the initial investment of the investor). Furthermore, Morningstar has a 3 × 3 style box with growth, blend and value on the x-axis, and large-cap, mid-cap, small-cap on the y-axis. Both definitions acknowledge there are funds with riskier investments than other.

In the same vein, I define the style of a mutual fund as its exposure to priced risk factors.

The understanding of where a fund is situated, in terms of risk exposure, gives investors a way to measure if the fund fits their risk appetite; it also lets them monitor if, when and how a mutual fund strays from a perceived style. If a mutual fund suddenly picks up in performance, it may be just because it invests into riskier stocks, and not because it became better at picking stocks. Using four dimensions of risk allows to look in what way a fund style drifts: a fund may shift towards more illiquid stocks, while not significantly changing its exposure to size, and thus earning the liquidity premium; an investor who monitors only size exposure may be unaware of the increased liquidity risk he now faces.

In the paper I use a holdings-based approached, as in [START_REF] Grinblatt | Performance measurement without benchmarks: An examination of mutual fund returns[END_REF], [START_REF] Daniel | Measuring Mutual Fund Performance with Characteristic-Based Benchmarks[END_REF]Wermers (1997), henceforth DGTW, Wermers (2012). It involves looking at the disclosed holdings of a mutual fund and giving each fund a score on each of the four dimensions (size, book-to-market, momentum, liquidity). The advantage of this approach over a returns-based approach (which would measure regression betas to factors like SMB and HML) is that it catches recent and temporary drifts in style; the returns-based method would need the style change to be more permanent for the coefficient to be significant.

The disadvantage is that the holdings data have a smaller frequency than the returns data, but the gains from using the holdings-based method outweigh the losses for the purpose of the paper.

The link between the holdings-based scores and risk exposures is given by the known fact that, on average, small stocks have a higher covariance with SMB, value stocks have a higher covariance with HML (Fama andFrench (1992, 1993)), stocks that went up have a higher covariance with UMD [START_REF] Carhart | On Persistance in Mutual Fund Performance[END_REF]), and illiquid stocks have a higher covariance with LIQ [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF]).

My paper contributes to the literature that studies the actions of mutual fund managers and 103 whether the interests of the fund manager are aligned with those of the investors. Mutual fund managers have career concerns that may make them act myopically, as in [START_REF] Chevalier | Risk Taking by Mutual Funds as a Response to Incentives[END_REF]. [START_REF] Khorana | Top management turnover an empirical investigation of mutual fund managers[END_REF] finds that promotions tend to follow high returns, and demotions follow low returns. Because the performance-flow relationship is convex [START_REF] Sirri | Costly Search and Mutual Fund Flows[END_REF]), managers have an incentive to gamble, as in [START_REF] Brown | Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry[END_REF].

Another strand of literature studies window-dressing. Unskilled managers that perform poorly are more likely to window dress by strategically purchasing winner stocks and selling loser stocks near quarterends, as in [START_REF] Agarwal | Window dressing in mutual funds[END_REF]. [START_REF] Lakonishok | Window Dressing by Pension Fund Managers[END_REF] find weak evidence of window-dressing in a sample of 769 pension funds. [START_REF] Musto | Investment Decisions Depend on Portfolio Disclosures[END_REF] finds that money market funds hold disproportionately more government securities before portfolio disclosure dates. Ng, and [START_REF] He | Quarterly Trading Patterns of Financial Institutions[END_REF] find that institutions tend to sell more poorly performing stocks during Q4 than during Q1-3, and buy these stocks back in Q1. [START_REF] He | Quarterly Trading Patterns of Financial Institutions[END_REF] find window-dressing only among institutions that manage other people's money, and no window-dressing among those managing their own money. [START_REF] Carhart | Leaning for the Tape: Evidence of Gaming Behavior in Equity Mutual Funds[END_REF] find that fund managers inflate quarter-end portfolio prices with last-minute purchases of stocks already held.

The closest paper in the literature is [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF]. He finds that managers that trade more frequently tend to manage portfolios with grater style drift; also, the value-weighted portfolio of the top decile of funds, ranked by their three-year trailing average active style-drift (ASD), outperforms the bottom decile by about 3 % per year, before costs, and about 1.6 % per year, after estimated execution costs and expense ratios. Another close paper, [START_REF] Brown | Staying the course: The impact of investment style consistency on mutual fund performance[END_REF] which uses returns rather than holdings, reaches a different conclusion, that style-consistent funds outperform other funds, in terms of their stock picking performance.

My paper shifts the focus to gain insights into when and how mutual funds change their style. I separate the style drift into several components, as in [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF]. The passive style drift (PSD) is the change in scores, year-to-year, that comes from the change in score as if the fund had employed a buy-and-hold strategy; the active style drift (ASD) results from the active change in holdings. The total style drift (TSD) is the sum of the two. In my setup, a positive style drift means more risk21 . In a departure from [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF], I aggregate the changes to obtain a single measure. Specifically, I define the total style drift as the change in size plus the change in book-to-market plus the change in momentum plus the change in liquidity scores. The advantage of the measure is that a positive number means an increase in total risk, even if the source of risk is not revealed by the measure. This offers a perspective to the investor about the change in risk. The disadvantage is that different risks have different risk premia, so they contribute differently to the risk-return relationship. For some tests, I analyze separately the active style drift alongside the four dimensions.

The first observation is that in 60% of the cases, the ASD is positive, indicating that managers do shift towards more risk quite often. PSD is negative (stocks in portfolio become less risky) also about 60% of the time, suggesting that the ASD might be to correct for the PSD. TSD is positive (more risk) 47% of the time.

The correlation between ASD and PSD is -0.44. The correlation between ASD and PSD is -0.40 when stocks in portfolio become less riksy, as opposed to only -0.17 when stocks in the portfolio become more risky. That shows that managers actively trade to counterbalance the effects of passive drift, but they do it more when the stocks become less risky, meaning they actively trade in the direction of taking more risk.

The chapter proceeds as follows: Section 3.2 describes the data, Section 3.3 describes the methodology, Section 3.4 presents the tests and the results, and Section 3.5 concludes.

Mutual fund data

My mutual-fund data come from the CRSP Survivor Bias Free Mutual Fund Database. I use a sample from 1991 through 2011. This allows me to have a sufficient number of funds each year. In selecting the sample, I follow [START_REF] Kacperczyk | Unobserved Actions of Mutual Funds[END_REF]. I focus on domestic equity mutual funds, so I take out balanced, bonds, money market, sector and international funds, as well as funds not invested primarily in securities. I select the funds that have the following codes in the CRSP objective code: EDCL, EDCM, EDCS, EDCI, EDYG, EDYH, EDYS, EDYI 22 . I also screen for some other words in the name of the fund 23 , and I exclude those funds from the sample. I take out observations for which the year for the observation is prior to the reported fund-started year (to remove the incubation bias, as in [START_REF] Elton | A First Look at the Accuracy of the CRSP Mutual Fund Database and a Comparison of the CRSP and Morningstar Mutual Fund Databases[END_REF] and [START_REF] Evans | Does alpha really matter? Evidence from mutual fund incubation, termination and manager change[END_REF]). To make sure they are invested mostly in equity, I exclude funds if the average invested in common stocks is lower than 80% or higher that 105%. I exclude index funds and ETFs. I then match the CRSP data with the Thomson Reuters database using MFLinks. When a fund has multiple share classes, I collapse the different share classes into one observation. For qualitative attributes (e.g. name, year it started), I retain the observation for the oldest fund. For the TNA, I sum the TNAs of the different share classes. For other quantitative attributes (e.g. returns, expense ratios, turnover ratios), I take the weighted average, where the weights are the TNAs of the individual share classes. I take out observations for a fund before it reaches at least $5 mil. TNA for the first time, also to mitigate the incubation bias. I take out observation where returns or TNA's are missing.

After applying all the filters above I retain a sample of 2,394 mutual funds over the period 1991-2011. (see Fama andFrench (1992, 1993) and Lakonishok, Shleifer and Visny (1994)), previous 12-month return (MOM) (see [START_REF] Jegadeesh | Returns to buying winners and selling losers: Implications for stock market efficiency[END_REF] and Fama and French (1996))

and liquidity (I use the ILLIQ measure of [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series effects[END_REF], a measure of price impact -sum of absolute daily return divided by daily dollar volumne, but the interested reader can also see [START_REF] Pástor | Liquidity Risk and Expected Stock Returns[END_REF], [START_REF] Acharya | Asset pricing with liquidity risk[END_REF]). The sort on liquidity is an addition to the DGTW sort. I compute cutoffs for the deciles constructed on each of the four dimensions. Subsequently, each stock in the CRSP database receives a score which is the number of the decile it belongs to, after comparing its score with the cutoff. The scores should be interpreted in the following way: on size, 1=big stocks and 10=small stocks; on BE/ME, 1=growth stocks and 10=value stocks; on momentum, 1=stocks that went down, 10=stocks that went up; on liquidity, 1=liquid stocks, 10=illiquid stocks. I then assign to each mutual fund a score on each of the four style dimensions, that is computed in the following way:

S i,t,M E = N j=1 w i,j,t × S j,t,M E .
This should be read: the score of fund i, at the end of year t, on size is the weighted average of the scores of stocks j, at the end of the year t, on size, where j represents the stocks that the fund is invested into, and w is the weight in each stock. For example, Fidelity Magellan had in December 1992 (2 years after Peter Lynch had retired) a score of 2.01 on size, 5.62 on BE/ME, 6.44 on momentum and 2.10 on liquidity. The last step is to assign a score, on each of the four style dimensions, to each mutual fund decile d. I compute the score as an equally-weighted average: The reason I compute equally-weighted scores is that I am interested in the behavior of the average fund.

At this point, every decile of mutual funds has a score for size, BE/ME, momentum, and liquidity, at the end of each year t.

I have a motivation behind using deciles. There is not enough variation is scores to be able to draw any conclusion, when the scores are assigned as the number of quintiles. This is also the result in DGTW. In their case, they subsequently look at 125 portfolios, formed by interacting 5 size portfolios with 5 BE/ME and 5 momentum portfolios. Had they used deciles and not quintiles, they would have had 10×10×10=1000 portfolios. At 5,000 stocks (grosso modo) a year in the market, there would have been only 5 stocks per portfolio. In their case, working with quintiles makes sense, but in my case I need a finer parsing in order to achieve some time-series variation in scores. Therefore I use deciles to assign style scores. An additional motivation is the fact that more than 50% of funds have as closest benchmark (measured using the methodology in [START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF]) one of the following indexes: S&P400 (mid-cap companies), S&P500 (largest 500 companies), S&P600 (small-cap companies), and value and growth variants of those. If a company benchmarked against S&P500 changes all of its holdings into the next 500 large companies, the size score would not change if the score is based on quintiles. It will move to the next score if the score is based on deciles (considering about 5,000 stocks in the market in a given year).

3.3.2 Active, passive and total style drift I use three measures of style drift for each fund. Passive style drift is the change in score as if the mutual fund had employed a buy-and-hold strategy between year t-1 and year t. Passive style drift is computed as follows:

P SD l t = N j=1 ( w j,t Cl j,t -wj,t-1 Cl j,t-1 ),
where t is the year, l is the style dimension, j is the stock, C is the score and w j,t is the portfolio weight on stock j on December 31 of year t assuming that the manager used a buy-and-hold strategy for the entire portfolio t-1 to t.

Active style drift is the change in score that resulted from active trades of the mutual fund between year t-1 and year t, and is computed as follows:

ASD l t = N j=1 ( wj,t Cl j,t -wj,t Cl j,t ),
where wj,t is the actual portfolio weight on stock j on December 31 of year t.

Total style drift is the total change in score between year t-1 and year t and is the sum of active style drift and passive style drift.

T SD l t = P SD l t + ASD l t Passive style drift, active style drift and total style drift are computed alongside each dimension (size, book-to-market, momentum and liquidity). For some tests, in order to gauge a shift in risk taking, I compute active style drift, passive style drift and total style drift for a particular fund as the sum of the four active style drifts (or passive, or total):

P SD t = 4 l=1 P SD l t ASD t = 4 l=1 ASD l t T SD t = 4 l=1 T SD l t 109
This is a departure from [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF]. In their paper, the comprehensive active style drift (or passive, or total) is the sum of the absolute values of the three measures (size, bookto-market, momentum). Here I take the sum of real values because I am interested in the direction of the change (towards more or less risk).

Tests and results

Table 3.1 contains the statistics for my sample of mutual funds.

Table 3.2 shows the average scores alongside the four dimension. Eyeballing the table, we notice the funds are invested into big, growth, liquid stocks, who did well in the previous year.

On average, the funds do not appear to have big risk exposures to a particular factor.

Table 3.3 shows the correlations between scores on the four dimensions. As they are all positive (except for correlations with momentum), it means that as the style of a mutual fund drifts towards more risk within a style dimension, it also drifts toward more risk in other dimensions. The correlations are bigger for mutual funds than for stocks in the CRSP universe.

For example, the correlation between BE/ME scores and size scores of stocks in CRSP is 0.20, while the same correlation for mutual funds is 0.33. This suggests that as a mutual fund moves more into value stock, it chooses the ones which also are smaller. It may be that funds are trying to increase risk simultaneously alongside several dimensions in order to capture several risk premia.

Table 3.4 presents the correlations between ASD, PSD and TSD. The correlation between ASD and PSD is -0.44. The correlation between ASD and PSD is -0.40 when stocks in portfolio become less riksy, as opposed to only -0.17 when stocks in the portfolio become more risky. That shows that managers do actively trade to counterbalance the effects of passive drift, but they do it much more so when the stocks become less risky, meaning they actively trade in the direction of taking more risk. The correlation between PSD and TSD is 0.57; when PSD is negative (stocks in portfolio become less risky), its correlation to TSD is 0.37;

when PSD is positive (stocks in portfolio become more risky), its correlation to TSD is 0.43.

Table 3.5 shows statistics of the style drift. In Panel 1 we see that the average total style drift (or score change) is 1.10. This is computed summing the changes alongside components (size, B/M, momentum and liquidity), then taking absolute values. I do this to show how total "risk exposure" changes. If, for example, a fund's score increases in one dimension, but decreases in other, the two will partially cancel. Therefore, we see that the change in total risk of a fund is modest (to gain perspective, if no score changes, the change is 0 and if all 4 scores change, in the same direction, into the following decile, the change is 4). Panel 2 tracks the changes alongside the 4 dimensions. The average passive style drift alongside size is 0.12. This number should be understood in the following way: if 12% of the stocks in a fund pass into the following decile for size within a year, the PSD is 0.12. Panel 3 shows how the 4 components participate to the annual style drift. Momentum is by far the biggest contributor, accounting for a half (or more) of each of ASD, PSD and TSD.

Hypothesis 1:

The manager takes more risk in response to incentives A mutual fund manager may want to increase the risk of the fund (which he can achieve through changing the style) when the performance-flow relationship becomes more convex.

The performance-flow relationship is both documented empirically [START_REF] Chevalier | Risk Taking by Mutual Funds as a Response to Incentives[END_REF], [START_REF] Sirri | Costly Search and Mutual Fund Flows[END_REF]Tufano (1998), Ferreira et al. (2012)) and predicted theoretically [START_REF] Berk | Mutual Fund Flows and Performance in Rational Markets[END_REF]). It can be summarized as follows: good performance is followed by large net inflows, bad performance is followed by not-so-large outflows. As a result, managers have an incentive to gamble. Huang, Wei, Yang (2007) find that, on average, the convexity changes over time for mutual funds (they compare the periods 1981-1989 and 1990-2001). Ideally, I would want to look at how convexity of an individual mutual fund changes through time, and then see if the fund has a higher active style drift when convexity is high. That would mean that a mutual fund takes more risk in an attempt to increase performance at a time when this will attract more flows. However, there is an empirical challenge: the regression does not have enough power to estimate the convexity for a particular fund over a short period of time. Therefore, closer to the approach of Huang, Wei, Yang (2007), I look at two periods, 1991-1999 and 2000-2011. I find that in the latter period the convexity of the performanceflow is higher. Like in the paper of Huang, Wei, Yang (2007), the action is coming from the low-performance segment: the sensitivity of flows with respect to low performance is lower between 2000-2011. Then I look at the average active style drift of mutual funds over the same two periods. I do not find evidence that the average active style drift differs between the two periods -ASD in 2000-2011 is 0.3517 as compared to 0.3317 in 1991-1999 but the difference is not statistically significant.

The following part explains the methodology used, while the results are in Table 3.6. I employ the type of regression used in the seminal work of [START_REF] Sirri | Costly Search and Mutual Fund Flows[END_REF]:

Flow i,q = α + β 1 LOW i,q-1 + β 2 MID i,q-1 + β 3 HIGH i,q-1 + β 4 log(TNA) i,q-1 + β 5 Category flow i,q + β 6 Volatility i,q-1
To compute flows I use the formula:

Flow i,q+1 = TNA i,q+1 TNA i,q -(1 + R i,q+1 ),
where R i,q+1 is the return of fund i in quarter q+1.

Elton, Gruber and Blake (2001) document a large number of errors in the CRSP database associated to mergers and splits in the CRSP database, which lead to extreme value of flows.

To alleviate this problem, I remove the bottom and the top 5% of flows.

The factors LOW, MID and HIGH are constructed so as to reflect different slopes on different intervals of performance. Therefore, the difference between the coefficients on HIGH and LOW can be interpreted as the convexity of the performance-flow relationship (see Fig.

3.1). The factors are constructed in the following way: at each quarter-end and within each category (given by an Investment Objective Code), I sort all funds according to their past 12-month performance. I assign a rank from 0 to 1 (0 for the least performing funds, then 0.1, then 0.2 and all the way up to 1, for the best performing funds). Then, for each fund, in a given quarter, I have:

112 LOW i,q =min(0.2, rank i,q ) MID i,q =min(0.6, rank i,q -LOW i,q ) HIGH i,q =rank i,q -(LOW i,q +MID i,q )

Figure 3.1: The regression of flow on performance produces three different betas: on the low performance segment (β 1 ), on the medium performance segment (β 2 ) and on the high performance segment (β 3 ); the measure of convexity is given by the difference between β 3 and β 1 and is denoted γ.

To obtain the Category flow, I assign to each fund the Investment Objective Code from the Thomson-Reuters database. Because of the way I have selected the sample, the funds fall into one of the categories: Aggressive Growth, Growth, Growth and Income. Category flow is the average of flows into a particular category. Volatility is the standard deviation of returns over the previous 12 months.

As a complementary test, in table 3.7 I regresses style drift (ASD, PSD and TSD) on the measure of convexity of the performance-flow relationship (γ) and controls. To obtain γ, for every group of mutual funds (defined as funds with the same Investment Objective Code (IOC))

I run a 3 year rolling regression of flows on past quarter LOW, MID, HIGH factors (performance ranks), and controls. γ is the difference between the coefficient on HIGH and LOW.

Thus, a group of funds will have the same γ in a given year. In the regression of style drift on γ (table 3.7) the sign of the coefficient on γ is correct -positive, the value is 0.183 -meaning that there is more risk taken when convexity is higher, but the coefficient is not significant.

TSD is negatively related to manager's tenure, past performance of fund and past flows. A new manager takes more risk; also, he takes more risk when he had performed poorly, or when the fund had experienced outflows. This is consistent to the manager having incentives to gamble. The negative relationship between PSD and manager's tenure, past performance of fund and past flows appears puzzling at first. The explanation is that the drift in momentum represents the most significant share of the drift (63% in PSD, 51% in TSD). If, for example, past performance of a fund is high, it means the fund is invested in stocks that did well, so it has a high score on momentum. As it is with momentum, we would expect those stocks to continue to do well for the following year, so then the drift in momentum would be small. As momentum drift is on average the highest contributor to style drift, we will expect the style drift of the fund to also be small. Hence the negative relationship I find between PSD and past performance.

Hypothesis 2:

The manager takes more risk after bad times, or takes bets outside his style when he lags behind his peers Brown, Harlow, Stark (1996) and [START_REF] Chevalier | Risk Taking by Mutual Funds as a Response to Incentives[END_REF] show that funds tend to gamble.

They increase their risk after experiencing bad performance and outflows. I look if the style changes in the direction of taking more risk by regressing ASD on past performance (rank within a peer group defined as funds with the same IOC) and past outflows. Table 3.7 shows that managers do not seem to change their style in the direction of more or less risk after they have experienced bad periods.

I further look if managers that lag behind their peers take bets outside their style. [START_REF] Chevalier | Risk Taking by Mutual Funds as a Response to Incentives[END_REF] and [START_REF] Sias | Institutions and Individuals at the Turn-of-the-Year[END_REF] find that managers who fall behind their peers tend to react by engaging in riskier strategies than their peers. [START_REF] Wermers | A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios[END_REF] suggests they might take bets outside their style. For example, a manager that is primarily invested into large stocks may take on additional risk by investing in small stocks once he lags the other managers invested into large stocks. The results are presented in table 3.8. I do not find evidence that this is happening. In fact, the difference in active style drift between the worst performing decile (1) and the best performing decile (10) is almost never significant. The only difference is for value funds, where I find the opposite -that value funds that perform poorly actually increase their value bets, while value funds that perform well increase their growth bets.

Table 3.9 shows that managers that performed the worst tend to move closer to the style of the best performing peer funds (57% of times they move closer along the size dimension, 65% of times they move closer along the book-to-market dimension and 60% of the times they move closer along the liquidity dimension.)

Hypothesis 3:

The manager wants to be close to the style of his peers I test if the worst performing funds move closer in style to the best performing funds; if the youngest funds move closer in style to the oldest funds; and if the newest hired managers move closer in style to the most veteran managers. The peers are the funds in the same category (value, growth, large, small) as given by the Investment Objective Code.

To obtain the percentage of times the worst funds move closer in style to the best performing funds I sort funds according to the last 12-month performance at time t. Then I look at the percentage of times for which:

| S l t,worst -S l t-1,best S l t-1,worst -S l t-1,best | < 1,
where S l t,worst is the score at time t, alongside dimension l of the worst performing decile. In other words, I look if at time t the worst performing funds got closer to the style of the best performing funds at time t-1. Because the time t style of the best funds would be simultaneously unbeknownst to the worst funds, they would try to get closer to the last known style of the best funds, so time t-1. I do this for every dimension and for the worst performing vs. the best performing funds, for the youngest vs. the oldest funds and for the newest hired managers vs. the most veteran managers.

Hypothesis 4:

There is a new manager to the mutual fund I do not find evidence that the the tenure of the manager at the fund means moving into more or less risk as counted by the ASD (Table 3.7). However, as seen above, the newest hired managers differentiate themselves in style from the most veteran managers (in 63% of cases for ME, in 57% of cases for BE/ME, in 67% of cases for MOM and in 62% of cases for LIQ) (Table 3.9).

3.4.5 Hypothesis 5: Do mutual funds change their style simultaneously across several dimensions, or do they tackle each dimension separately?

The first hint mutual funds may tackle the dimensions simultaneously comes from comparing the correlations between scores for mutual funds with the correlations between scores for the stocks in CRSP. Table 3.3 shows the correlations between scores on the four dimensions. As they are all positive (except for correlations with momentum), it appears that as a mutual fund drifts towards more risk within a style dimension, it also drifts towards more risk in other dimensions. The correlations are bigger for mutual funds than for stocks in the CRSP universe. For example, the correlation between BE/ME scores and size scores of stocks in CRSP is 0.20, while the same correlation for mutual funds is 0.33. This suggests that as a mutual fund moves more into value stocks, it chooses the ones which also are smaller. It may be that funds are trying to increase risk simultaneously alongside several dimensions in order to capture several risk premia.

I explore this further in more detail. For simplicity, I describe the case where there is positive ASD alongside BE/ME. I want to see what happens with ASD alongside another dimension, say ME. There are three possibilities:

• The mutual fund pays no special attention to ME when increasing its BE/ME score;

• The mutual fund simultaneously increases (decreases) its BE/ME score;

• The mutual fund maintains its BE/ME score.

To distinguish between these alternatives, I identify cases of positive ASD BE/ME between In some cases, when the average fund increases its score on a dimension (i.e. takes more risk), it actually decreases its score on other dimensions (i.e. reduces its risk). However, the evidence is not strong. The results are presented in (Table 3.11). The strongest evidence is for changes alongside momentum: when a fund manager actively buys stocks that did well, he simultaneously reduces his score alongside size, book-to-market and liquidity. This is consistent with the manager decreasing risk on the other dimensions to compensate for the increase in risk on one dimension.

I further look if the results differ by manager tenure and by past flows. The results are similar for managers with shorter and longer tenure.

The results are similar differ if the funds have experienced inflows or outflows (Table 3.12 and Table 3.13).

Table 3.14 regresses future flows (6-month) on the style drift and controls. I want to see if investors adjust their invested money after seeing changes in style. It turns out this is not the case.

Table 3.15 regresses future performance on style drift and controls. I want to see if style drift is indicative of future performance. This is not the case. There is a negative, albeit not strong, relationship between size and future performance. This is consistent with [START_REF] Pástor | On the Size of the Active Management Industry[END_REF] who predict that future performance of funds that grow in size decreases as there will be fewer opportunities for them to exploit.

Conclusion

This paper analyzes patterns of style changes in mutual funds. Style change is decomposed into three components: passive style drift (the "natural" style drift as if the manager had used a buy-and-hold strategy), active style drift (actual trades of the mutual fund manager) and total style drift (the sum of the two). The changes in style are computed using a holdings approach. It implies looking at the holdings of the funds and giving scores on size, bookto-market, momentum and liquidity. I look at changes in ASD as a measure of risk change (positive ASD means more risk). I also look at individual ASD along the four dimensions.

I find that funds are invested, on average, into big, growth, liquid stocks that did well.

I cannot distinguish whether invested into stocks that did well means skill or last-minute selling of losers. There is a -0.44 correlation between ASD and PSD, suggesting that a large part of active trades are performed to undo the effects of passive style drift. In a regression Table 3.6: The performance-flow relationship using quarterly data in the whole sample 1991-2011 (1); and then in two subperiods (2) and (3). In column (4) I test whether the difference in coefficients is significant. I regress quarterly flows on the low, mid and high measures of performance, log(TNA), average flows to the category, and volatility of returns. I remove the bottom and the top 5% of quarterly flow observations. I perform [START_REF] Fama | Risk, return, and equilibrium: Empirical tests[END_REF] regressions. Because I regress quarterly flows on performance measured over the past 12 month, the errors are likely to be autocorrelated, so I report the Fama-MacBeth errors with Newey-West (1987) correction for autocorrelation and heteroskedasticity.

( Table 3.8: This table investigates if funds that lag behind their peers take bets outside their style. I look at groups of funds: value funds are benchmarked against a value index, and so on. At the end of each year t I sort funds from a group into deciles, where decile 1 is the worst performing, and decile 10 is the best performing, based on year's t performance. Then I compute the average style drift between the end of t-1 and the end of t alongside each decile. I then take averages across years. "10-1" is the difference in style drift between deciles, and the t-stat is the for this difference. The "10-1" difference is significant when the t-stat is bigger (in absolute value) than the critical value (CV).

Value funds

Growth funds

Style Decile 1 Decile 10 Table 3.11: Simultaneous ASD on several dimensions. This should be interpreted as follows: when a fund actively changes its BE/ME score (read on the left side of the table), it actively changes at the same time its ME, MOM and LIQ scores (read the first three columns on the top of the table) in addition to the market average along the BE/ME score. To compute the market average I create an alternative portfolio; For each stock a mutual fund holds at t-1, I look at the portfolio of all stocks in CRSP (held by mutual funds) with the same score (e.g. if a stock i held by the mutual fund has score 2 on BE/ME, I look at all stocks in CRSP with score 2 on BE/ME; I denote these stocks the alternative portfolio, with the weights given by the market capitalization normalized to sum up to 1). I compute the average score on ME for the alternative portfolio. Then I compute ASD ME of the actual mutual fund, and ASD ME of the alternative portfolio (as if the fund moves from the real to the alternative portfolio between t-1 and t). Column (1) on the top of the table is the difference between ASD ME of the fund and ASD ME of the alternative portfolio.

(1)

(2)

(3) (4)

(5) Table 3.12: Simultaneous ASD on several dimensions, for funds in the bottom decile sorted by past 12-month flows. This should be interpreted as follows: when a fund actively changes its BE/ME score (read on the left side of the table), it actively changes at the same time its ME, MOM and LIQ scores (read the first three columns on the top of the table) in addition to the market average along the BE/ME score. To compute the market average I create an alternative portfolio; For each stock a mutual fund holds at t-1, I look at the portfolio of all stocks in CRSP (held by mutual funds) with the same score (e.g. if a stock i held by the mutual fund has score 2 on BE/ME, I look at all stocks in CRSP with score 2 on BE/ME; I denote these stocks the alternative portfolio, with the weights given by the market capitalization normalized to sum up to 1). I compute the average score on ME for the alternative portfolio. Then I compute ASD ME of the actual mutual fund, and ASD ME of the alternative portfolio (as if the fund moves from the real to the alternative portfolio between t-1 and t). Column (1) on the top of the table is the difference between ASD ME of the fund and ASD ME of the alternative portfolio.

(1)

(2)

(3) (4)

(5) Table 3.13: Simultaneous ASD on several dimensions, for funds in the top decile sorted by past 12-month flows. This should be interpreted as follows: when a fund actively changes its BE/ME score (read on the left side of the table), it actively changes at the same time its ME, MOM and LIQ scores (read the first three columns on the top of the table) in addition to the market average along the BE/ME score. To compute the market average I create an alternative portfolio; For each stock a mutual fund holds at t-1, I look at the portfolio of all stocks in CRSP (held by mutual funds) with the same score (e.g. if a stock i held by the mutual fund has score 2 on BE/ME, I look at all stocks in CRSP with score 2 on BE/ME; I denote these stocks the alternative portfolio, with the weights given by the market capitalization normalized to sum up to 1). I compute the average score on ME for the alternative portfolio. Then I compute ASD ME of the actual mutual fund, and ASD ME of the alternative portfolio (as if the fund moves from the real to the alternative portfolio between t-1 and t). Column (1) on the top of the table is the difference between ASD ME of the fund and ASD ME of the alternative portfolio.

(1)

(2)

(3) (4)

(5)

Conclusion

This thesis makes a small contribution to the literature that studies if mutual funds managers have skill, that is if they can identify and benefit from potential opportunities and mispricings in the market. The research has shown that the average manager is not skilled, so that the literature has converged to identify special groups of managers, by some characteristics, who are skilled. In the first chapter, it is shown that managers who invest in illiquid stocks perform better than managers that invest into liquid stocks, even accounting for an illiquidity premium.

The intuition is that, on the one hand, there are potentially more mispricings in illiquid stocks than in illiquid stocks. On the other hand, transaction costs are also higher in illiquid stocks.

Only managers skilled enough to identify the most most mispriced stocks "survive" in illiquid stocks. The second chapter documents a predictability pattern in returns: after a period in which returns of neglected stocks diverge from the returns of covered stocks, subsequent return of stocks with difficult valuation (small stocks, neglected stocks, illiquid stocks, young stocks, etc.) are higher. In this chapter, the period when returns of neglected stocks diverge from the returns of covered stocks is denoted "high opportunities". This pattern is consistent with a theoretical model where investors demand a higher premium to hold stocks with difficult valuation (after a period of high opportunities) because they fear adverse selection (if traders search for more information about the stocks with difficult valuation). The third chapter describes instances when a mutual fund manager changes her investment style. Abstract : The first chapter shows that mutual funds that hold illiquid stocks ("illiquid funds") outperform funds that hold liquid stocks ("liquid funds"). There is evidence this outperformance arises from stock selection skills of illiquid funds. The stocks held by illiquid funds outperform portfolios matched by characteristics. Liquid funds declare benchmarks that make their benchmarkadjusted returns appear larger. A portfolio of stocks held by illiquid funds subsequently outperforms a portfolio of stocks held by liquid funds. The second chapter documents a predictability pattern in returns. This chapter identifies high opportunities in stocks with difficult valuation as times when returns of neglected stocks diverge from returns of covered stocks. Subsequent returns of stocks with difficult valuation are higher when beginning of period opportunities are high, as compared to when beginning of period opportunities are low. This is consistent with an information risk theory, where investors demand a higher premium to hold stocks with higher probability of informed trading, because they fear adverse selection. The third chapter explores instances when mutual funds change their style (style is regarded as risk exposure alongside usual factors). Mutual funds do not take more risk when it is more profitable to do so. After performing badly, mutual funds move closer to the style of good performing peer funds. Young funds' styles diverge from the style of old peer funds. Recently hired managers diverge in style from veteran managers of peer funds. When the average fund takes more risk alongside a style dimension, it does not simultaneously consider other style dimensions.

Chapitre 1 :

 1 Liquidité, performance et compétence parmi les fonds d'investissement En 2014, les fonds d'investissement des Etats-Unis ont géré environ 16 billion dollars. Les fonds actifs ont géré la plupart de cet argent, 83%. Les chercheurs étudient depuis longtemps si les fonds actifs sont compétents. Comme le fond moyen ne semble pas d'être compètent, les chercheurs essaient identifier des groups particuliers de fonds, qui ont des certaines cariv actéristiques communs, et qui surpassent les indices.

  vii (2009) trouve que 31% des fonds déclarent leurs indices d'une façon opportuniste. Les fonds liquides pourront choisir de déclarer des indices par rapport auxquels leur rendements sont meilleurs, parce qu'ils sont moins compétents que les fonds illiquides. C ¸a serait possible que les fonds illiquides détiennent des actions beaucoup moins liquides que celles des indices. Dans ce cas, les rendements ajustés pour l'indice des fonds illiquides contiendraient une prime pour illiquidité, qui pourrait le faire paraître plus compétents. Si c'est le cas, alors on aurait besoin des indices qui prennent en compte la liquidité des actions. Pour tester ça, je calcule le score d'illiquidité pour les indices. Je trouve qu'il n'y a pas une différence économiquement significative entre les scores d'illiquidité pour les fonds et pour leurs indices. Cela indique que les indices existants sont suffisants pour tenir compte de la différence de liquidité entre les actions des fonds.

  4: There is a new manager to the mutual fund . . . . . . . 3.4.5 Hypothesis 5: Do mutual funds change their style simultaneously across several dimensions, or do they tackle each dimension separately? . . . . 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U.S. mutual funds managed close to $16 trillion. Active funds managed most of this money, 83% 1 . The academic literature has long been investigating if active funds have

  8 , and is the benchmark to which the mutual fund is the closest in terms on holdings. As the data on the website of Antti Petajisto goes only until 2009, I carry forward the benchmark to the following years (the declared benchmark does not change as often), but for the "minimum-distance" benchmark, I restrict the sample to 2009, as this latter benchmark changes between periods. I use the following indexes: S&P500, S&P400, S&P600, S&P500/Barra Value, S&P500/Barra Growth, Russell Midcap, Russell Midcap Growth, Russell Midcap Value, Russell 1000, Russell 1000 Value, Russell 1000 Growth,Russell 2000, Russell 2000 Value, Russell 2000 Growth, Russell 3000, Russell 3000 Value, Russell 3000

Figure 2 . 2 :Figure 2 . 3 :

 2223 Figure 2.2: The left graph contains the opportunities measure; Right graph contains the same opportunities measure, but before taking absolute value.

Figure 2 . 5 :

 25 Figure 2.5: Subsequent returns when opportunities are high minus subsequent returns when opportunities are low by analyst coverage deciles (1=low analyst coverage, 10=high analyst coverage).

  This paper studies when and how mutual funds change styles. While not an exhaustive list, a mutual fund may change its style in the following instances: (Hypothesis 1) the manager responds to incentives; (Hypothesis 2) after bad times; (Hypothesis 3) the manager wants to be closer to the style of his peers; (Hypothesis 4) there is a new manager to the mutual fund; (Hypothesis 5) funds change their style simultaneously across several dimensions (as opposed to tackling each dimension separately).

22

  Please see the Survivor-Bias-Free US Mutual Fund Guide published by CRSP for a description of these codes 23 Canadian, Emerging, Europe, Global, International, Int'l, Japan, Regional, Transatlantic, World Trends, Air Transportation, Automotive, Basic Materials, Biotechnology, Broadcast, Chemicals, Commodities, Computer, Consumer Goods, Consumer Services, Defense, Electronics, Energy, Export, Food, Gold, Health, Industrial, Leisure, Medical, Oil & Gas, Paper, Pharmaceuticals, Precious Metals, Property, Real Estate, Retail, S&L, Sectors, Semiconductors, Software, Tech, Telecommunication, Television, Transportation, Utilities, ING Solution, Lifecycle, LifeCycle, LifePath, LIVESTRONG, Lifetime, RealRetirement, Retirement, Retiremen-tReady, RetireSMART, Balance, Dow, Futures, OTC, Sovereign, State Bond, Tax Aware, Tax-Efficient, fund scores I use a methodology motivated by DGTW. In December of each year 24 , I sort all stocks listed on NYSE on four separate dimensions: size (ME), book-equity-to-market-equity (BE/ME)

S

  24 once a year because book value is only computed yearly 107 is the number of funds in decile d.

t

  MOM ASD LIQ ASD BM ASD MOM ASD LIQ ASD ME ASD BM ASD LIQ ASD ME ASD BM ASD statistics in parentheses * p < 0.05, * * p < 0.01, * * * p < 0.001

t

  MOM ASD LIQ ASD BM ASD MOM ASD LIQ ASD ME ASD BM ASD LIQ ASD ME ASD BM ASD statistics in parentheses * p < 0.05, * * p < 0.01, * * * p < 0.001

t

  MOM ASD LIQ ASD BM ASD MOM ASD LIQ ASD ME ASD BM ASD LIQ ASD ME ASD BM ASD statistics in parentheses * p < 0.05, * * p < 0.01, * * * p < 0.001

Titre:

  Trois essais dans la gestion des actifs Mots clés : Fonds d'investissement actifs ; Allocation d'actifs ; Risque de l'information ; Liquidité ; Prédictibilité des rendements ; Gestion de portefeuille Résumé : Le premier chapitre montre que les rendements des fonds investis dans des actions illiquides ("fonds illiquides") sont mieux que ceux des fonds investis dans des actions liquides. Cette différence provient des capacités de fonds illiquides de sélectionner les actions. Les actions détenues par les fonds illiquides ont une meilleure performance que des portefeuilles qui ont les mêmes caractéristiques. Les fonds liquides déclarent des indices de référence par rapport auxquels leurs rendements sont plus importants. Un portefeuille d'actions détenues par les fonds illiquides a une meilleure performance qu'un portefeuille d'actions détenues par les fonds liquides. Le second chapitre documente une prédictibilité des rendements. Dans ce chapitre, les périodes d'opportunités sont les périodes où les rendements des actions faisant l'objet d'une analyse régulière par les analystes (les actions suivies) s'écartent de ceux des actions qui ne sont pas suivie (les actions négligés). Les rendements ultérieurs des actions faciles à évaluer sont plus importants quand les opportunités étaient grandes, par rapport aux périodes où les opportunités étaient limitées. Ce comportement est cohérent avec un modelé où les investisseurs exigent une prime pour supporter le risque de sélection défavorable. Le troisième chapitre explore les moments où les fonds d'investissement changent leur style d'investissement (le style est défini comme exposition au risque, prenant en compte les facteurs de risque habituels). Les fonds ne prennent pas plus des risques quand il serait plus rentable de le faire. Après avoir eu des mauvais rendements, les fonds se rapprochent du style des fonds similaires, mais qui ont eu des bons rendements. Le style de jeunes fonds s'écarte du style de fonds anciens. Les nouveaux gérants des fonds s'écartent du style de fonds avec des anciens gérants. Quand un fond prend plus de risque d'une côté, il n'essaye pas d'aborder systématiquement les autres côtés du risque. Title : Three Essays in Asset Management Keywords : Active mutual funds ; Asset allocation ; Information risk ; Liquidity ; Predictability ; Portfolio Management

  Morningstar Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.9 Sensitivity of flows to performance . . . . . . . . . . . . . . . . . . . . 1.4.10 Illiquid stocks bought by illiquid funds vs. illiquid stocks bought by liquid funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.11 Overlapping trades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mutual fund data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Mutual fund scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Active, passive and total style drift . . . . . . . . . . . . . . . . . . . . 3.4 Tests and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	Introduction	xv
	Chapter 1: Liquidity, performance and skill in mutual funds

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Data and variable construction . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Illiquidity -the Amihud measure . . . . . . . . . . . . . . . . . . . . . 1.3.2 Risk-adjusted returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Characteristic benchmarks -stock picking . . . . . . . . . . . . . . . . 1.3.4 Benchmark-adjusted returns . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Liquidity of the benchmarks . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Cross-section vs. time series . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Performance and illiquidity . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Illiquidity and size, age, turnover or fee . . . . . . . . . . . . . . . . . . 1.4.4 Stock-picking skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5 Benchmark-adjusted returns and liquidity of the benchmarks . . . . . . 1.4.6 Is it an investable strategy? After fee returns . . . . . . . . . . . . . . 1 1.4.7 False Discovery Rate (FDR) . . . . . . . . . . . . . . . . . . . . . . . . 1.4.8 1.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2: Opportunities and expected returns 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Easley and O'Hara (2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The opportunities measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The test portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3: When and How Do Mutual Funds Change Their Style? 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2

  In this sense the tests are conservative.

I use a sample of equity mutual funds from CRSP Mutual Funds funds over 1983-2014. For holdings I use Thomson Reuters. I find that illiquid funds outperform liquid funds by 1.38% per year (t-stat 2.93). Performance is risk-adjusted as in

[START_REF] Carhart | On Persistance in Mutual Fund Performance[END_REF]

model. The results are robust to sorting funds by size, age of the fund, turnover or fee. They also hold for sub-

Table 1 .

 1 in Table1.4 and 1999-2014 in Table1.5. The results seem to be driven by the second part of the sample. In the second 10. Illiquid funds are smaller by almost $325 million (or with 27%) than liquid funds, in terms of assets under management. Illiquid funds are younger with almost 4 years (or with 2%) than liquid funds. Illiquid funds are more expensive, both in terms of expense ratio and management fee, than liquid funds, although the difference is very small (they are with 2.7%

	subsample, Decile 10-Decile 1 is 1.56% per year (Carhart's risk-adjusted, before fees), with a
	t-stat of 2.28.
	1.4.3 Illiquidity and size, age, turnover or fee

Above I study if risk factors may be driving the results. I further study if any characteristic of the funds may explain the results. I test if illiquid funds outperform liquid funds, holding constant their size, age, turnover or fee. In separate tests, I first sort in quintiles of size (or age, or turnover, or fee). I will further describe the case with size, but I follow the same methodology for age, turnover and fee. For each size quintile, I then sort into quintiles by illiquidity. Within each size quintile I compare Carhart's risk-adjusted returns before fees between illiquid and liquid funds. I find that illiquid funds outperform liquid funds by more than 1% per year in each size quintile. The same is true when I first sort by age, turnover or fee. The results are presented in Tables 1.6-1.9.

Even is these characteristics of funds do not drive the results, there are differences in size, age, turnover and fee between illiquid and liquid funds. The evidence is presented in

Table 1 .

 1 1: Summary statistics for mutual funds. For illiquidity 1=most liquid, 10=most illiquid

		TNA	Age	Illiquidity	Expense ratio	Mgmt fee	12B-1 fee	Turnover
	Year Funds	(mil.)	(years)	decile	(%)	(%)	(%)	(%)
	78 265.99	20.94	2.17	0.93			74.35
	89 291.14	20.21	2.22	0.94			70.60
	89 346.72	21.52	2.07	0.92			73.69
	99 450.78	21.94	1.97	0.91			74.79
	108 549.31	21.09	1.90	0.95			85.44
	109 478.85	22.29	1.86	1.04			77.11
	107 496.06	22.72	1.92	1.10			75.83
	113 433.39	23.28	1.86	1.13			73.85
	164 663.44	25.29	1.82	1.04		0.31	55.25
	181 701.65	26.95	1.66	1.06		0.26	64.18
	243 668.37	21.38	1.62	1.07		0.30	65.50
	397 562.08	16.37	1.73	1.20		0.38	70.10
	412 598.82	16.01	1.70	1.23		0.41	75.43
	475 663.83	13.94	1.78	1.20		0.43	77.49
	633 761.13	13.28	1.80	1.22	0.72	0.44	83.28
	730 798.96	11.96	1.80	1.25	0.73	0.43	83.96
	786 999.11	12.40	1.70	1.25	0.73	0.48	96.03
	902 1150.84	13.15	1.67	1.26	0.75	0.45	96.48
	796 944.55	13.65	1.57	1.30	0.74	0.46	88.68
	1,049 738.71	12.70	1.66	1.38	0.71	0.46	88.02
	1,315 724.04	12.93	1.70	1.39	0.72	0.45	85.13
	1,231 892.66	13.24	1.82	1.35	0.73	0.44	79.83
	1,096 972.05	13.33	1.88	1.31	0.74	0.41	77.56
	1,000 1252.63	14.89	1.95	1.26	0.74	0.39	75.19
	967 1416.11	15.07	1.95	1.22	0.73	0.37	79.85
	1,109 1175.77	14.82	1.81	1.18	0.67	0.36	94.51
	1,071 1011.44	15.20	1.76	1.19	0.65	0.35	89.50
	885 1291.40	16.83	1.89	1.17	0.71	0.34	75.64
	1,260 1277.43	16.61	1.92	1.14	0.72	0.35	71.40
	1,201 1354.54	17.71	1.94	1.12	0.72	0.35	65.44
	1,133 1605.64	18.75	2.00	1.09	0.73	0.35	62.20
	1,061 1882.73	19.83	2.03	1.08	0.73	0.35	59.41
	Total 2,532

Table 1 .

 1 2: Regression of risk-adjusted returns, before fees, on illiquidity score; in each panel, the first column contains fund fixed-effects; the second column contains time fixed-effects; the third column shows Fama-MacBeth regressions; the forth column shows Fama-MacBeth regressions that put more more weight on periods when there are more funds. t-stats are in parentheses and are based on heteroskedasticity-robust errors that are clustered by month. Table 1.3: Alphas per deciles of illiquidity. Alpha Ch bf is with respect to Carhart model; Alpha PS bf is with respect to Pástor and Stambaugh; Alpha FF5 bf is with respect to the 5-factor Fama and French model; Alpha NM bf is with respect to Novy-Marx. t-stats are in parentheses. All alphas are before fees. This is for the entire sample 1983-2014. Table 1.4: Alphas per deciles of illiquidity. Alpha Ch bf is with respect to Carhart model; Alpha PS bf is with respect to Pástor and Stambaugh; Alpha FF5 bf is with respect to the 5-factor Fama and French model; Alpha NM bf is with respect to Novy-Marx. t-stats are in parentheses. All alphas are before fees. This is for the subsample 1983-1998. Table 1.5: Alphas per deciles of illiquidity. Alpha Ch bf is with respect to Carhart model; Alpha PS bf is with respect to Pástor and Stambaugh; Alpha FF5 bf is with respect to the 5-factor Fama and French model; Alpha NM bf is with respect to Novy-Marx. t-stats are in parentheses. All alphas are before fees. This is for the subsample 1999-2014. Table 1.6: Alphas with respect to Carhart, before fees. First I sort into quintiles by size, then into quintiles by illiquidity, within each size quintile. t-stats are in parentheses. Table 1.7: Alphas with respect to Carhart, before fees. First I sort into quintiles by age, then into quintiles by illiquidity, within each age quintile. t-stats are in parentheses. Table 1.8: Alphas with respect to Carhart, before fees. First I sort into quintiles by turnover, then into quintiles by illiquidity, within each turnover quintile. t-stats are in parentheses. Table1.9: Alphas with respect to Carhart, before fees. First I sort into quintiles by fees, then into quintiles by illiquidity, within each fee quintile. t-stats are in parentheses.Table1.10: Differences in size, age, fee, turnover between funds invested into illiquid stocks and funds invested into liquid stocks. Size is in million dollars; Age is in years; Fee, Mgmt fee, 12B-1 fee and Turnover are in percentages per year. t-stats are in parentheses.Table1.11: Characteristics benchmark adjusted returns; the first column is with respect to 5 × 5 × 5 sorted benchmark by size, book-to-value and past returns; the number of shares is kept constant between 2 reporting dates. The second column is with respect to 3 × 3 × 3 × 3 sorted benchmark by size, book-to-value, past returns and illiquidity; the number of shares is kept constant between 2 reporting dates. The third column is with respect to 5 × 5 × 5 sorted benchmark by size, book-to-value and past returns; the weights are kept constant between 2 reporting dates. The fourth column is with respect to 3 × 3 × 3 × 3 sorted benchmark by size, book-to-value, past returns and illiquidity; the weights are kept constant between 2 reporting dates. t-stats are in parentheses.Table1.12: Benchmark-adjusted returns, in column 1 and minimum-distance benchmarkadjusted returns in column 2. The benchmarks are those declared in the prospectuses of funds; minimum-distance benchmarks are those to which holdings of mutual funds resemble the most, as in[START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF] Table1.13: Name, abbreviation (used in this paper, as in[START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF]), ticker, style and illiquidity score of the most popular indexes; 1=most liquid; 10=most illiquid)

		Panel A: Carhart risk-adjusted returns, before fees
	Fund FE Time FE Fama-MacBeth	Fama-MacBeth w
	0.001* 0.0003**	0.0003**	0.0003**
	(1.85)	(2.55)	(3.00)	(2.75)
	Panel B: Pástor-Stambaugh risk-adjusted return, before fees
	Fund FE Time FE Fama-MacBeth	Fama-MacBeth w
	0.0003 0.0002**	0.0002**	0.0002*
	(0.59)	(2.03)	(2.12)	(1.84)
	Panel C: Fama-French 5 risk-adjusted return, before fees
	Fund FE Time FE Fama-MacBeth	Fama-MacBeth w
	0.0005 0.0002**	0.0002**	0.0002*
	(0.86)	(1.98)	(2.14)	(1.95)
	Panel D: Novy-Marx risk-adjusted return, before fees
	Fund FE Time FE Fama-MacBeth	Fama-MacBeth w
	-0.0008 0.0012**	0.0018***	0.0018***
	(-0.96)	(2.93)	(5.12)	(5.24)

Table 1 .

 1 14:The difference in liquidity score between funds and their benchmarks. Column 2 is with respect to the benchmark declared by the fund in its prospectus; column 3 is with respect to the minimum-distance benchmark, as in[START_REF] Cremers | How active is your fund manager? A new measure that predicts performance[END_REF], the benchmark to which the fund resembles the most in terms of holdings. The illiquidity score is measured on a 1-10 scale, 1=most liquid, 10=most illiquid.Table1.15: Alpha with respect to Carhart's model, after fees. First column is for a 1-month holding period; second column is for a 3-month holding period, third column is for a 6-month holding period, fourth column is for a 12-month holding period Table1.16: False Discovery Rate(BSW, 2010). The proportion of funds that are 0-alpha, positive-alpha and negative-alpha, after fees, in the whole sample (Column 1), in the liquid funds (Column 2) and in the illiquid funds (Column 3).

			Difference	Difference from
		Illiquidity score	from benchmark	benchmark-min
	Most liquid	1.05	-0.06	-0.05
	Decile 2	1.10	-0.01	0.00
	Decile 3	1.16	0.04	0.05
	Decile 4	1.23	0.11	0.11
	Decile 5	1.34	0.18	0.19
	Decile 6	1.51	0.26	0.27
	Decile 7	1.74	0.38	0.39
	Decile 8	2.19	0.35	0.38
	Decile 9	2.76	0.32	0.31
	Most illiquid	3.84	0.65	0.57
	Decile 10-Decile 1		0.72***	0.62***
	t-stat		(13.73)	(12.09)

Table 1 .

 1 17: Morningstar ratings for Decile 10 (Illiquid) and Decile 1 (Liquid) funds. The Morningstar Ratings are given on a 1-5 scale, where the 5-star funds are the best performing relative to the funds in their category over a period of 3, 5 or 10 years. The sample is 2000-2014, which insures there are at least 50 funds in each decile.

		Observations Morningstar Rating
	Illiquid	180	3.09
	Liquid	180	3.06
	Difference		0.03
	t-stat		(0.82)

Table 1 .

 1 18: Returns of portfolios of illiquid stocks (score≥5) in the left quadrants, or liquid stocks (score< 5) in the right quadrants

  Table1.19: Average trades of mutual funds, as percentage of shares outstanding. In the first column I average absolute trades over the group of illiquid funds, and over the group of liquid funds. In the second column, I average using the signed trades. In the third and fourth column, I consider separately buys and sells.

	Illiquid funds (Deciles 6-10) Liquid funds (Deciles 1-5) Difference t-stat	to Q2 Average stock Holdings -0.07 1.77 12.36 13.27 Holdings 15.66 18.27 14 13.18 t-stat (-0.01) (0.43) (3.15) (3.49) t-stat (3.94) (4.72) (3.73) (3.56) Liquid funds (Decile 1) Liquid funds (Decile 1) trades abs 1.36% 1.23% 0.13% (1.27)	Q-1 Q Q1 Q1 to Q2 Q-1 Q Q1 Q1 to Q2	Holdings 4.93 -0.14 9.62 -1.28 Holdings 18.64 16.63 12.19 11.63 Average stock t-stat (0.49) (-0.01) (0.88) (-0.1) t-stat (5.85) (5.14) (3.25) (3.75) Difference holdings -5 1.92 2.73 14.56 Difference holdings -2.98 1.63 1.8 1.54 t-stat (-0.52) (0.23) (0.27) (1.33) t-stat (-0.58) (0.32) (0.36) (0.32) trades 0.42% 0.40% 0.02% (0.18)	Illiquid stocks (score≥ 5) Illiquid funds (Decile 10) Liquid stocks (score<5) Illiquid funds (Decile 10) Average buys Average sells Q-1 Q Q1 Q1 to Q2 Holdings -10.94 -9 2.56 4.27 t-stat (-8.82) (-7.74) (2.38) (3.92) Liquid funds (Decile 1) Q-1 Q Q1 Q1 to Q2 Holdings -6.82 -7.92 -7.04 -19.35 t-stat (-0.6) (-0.95) (-0.6) (-1.49) Difference holdings -4.12 -1.09 9.61 23.63 t-stat (-0.45) (-0.16) (1.03) (2.29) Risk-adjusted returns, Pástor-Stambaugh model with liquidity (Panel B) Q-1 Q Q1 Q1 to Q2 Holdings 4.72 7.24 3.96 3.35 t-stat (4.76) (8.23) (4.46) (3.63) Liquid funds (Decile 1) Q-1 Q 2.14 (3.35) 1.21 (1.08) Q1 Q1 to Q2 Holdings 8.37 6.21 2.15 t-stat (9.79) (8.71) (3.72) Difference holdings -3.65 1.03 1.81 1.45% 1.04% 1.27% 0.85% 0.17% 0.18% t-stat (2.78) (0.91) (1.71) (1.38) (2.72)

Table 2

 2 Table2.4: Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks, size neutral, equally weighted.

	.3: Contemporaneous correlation between the opportunities measure and usual long-
	short portfolios
			Opportunities
		nmc ff ew	(a nmc ff ew) MKTRF SMB HML UMD LIQ
	nmc ff ew	1
	Opportunities
	(a nmc ff ew)	-0.29	1
	MKTRF	-0.31	-0.05	1
	SMB	0.21	0.08	0.21	1
	HML	-0.09	0.12	-0.29 -0.20	1
	UMD	0.46	-0.12	-0.18 0.01 -0.13	1
	LIQ	0.01	-0.03	-0.03 -0.02 -0.03	0.03	1

  specification, the factors are Mktrf, SMB, HML, traded liquidity.

	All sample:
	Opportunities	Opportunities	Opportunities	Opportunities
	(alone)	(FF3)	(C)	(PS)
	small-big 0.49***	0.5***	0.47***	0.52***
	(5.14)	(5.23)	(5.04)	(5.38)
	high volatility-low volatility 0.41***	0.24**	0.18**	0.26***
	(2.79)	(2.51)	(2.05)	(2.66)
	neglected-covered 0.33***	0.2***	0.2***	0.22***
	(3.87)	(2.91)	(2.93)	(3.09)
	value-growth 0.1	0.18***	0.13**	0.20***
	(1.43)	(2.80)	(2.25)	(3.12)
	illiquid-liquid 0.18**	0.17**	0.16**	0.18**
	(2.19)	(2.24)	(2.09)	(2.3)
	young-old 0.34***	0.26***	0.23***	0.26***
	(3.77)	(4.07)	(3.75)	(3.97)
	Without January:
	Opportunities	Opportunities	Opportunities	Opportunities
	(alone)	(FF3)	(C)	(PS)
	small-big 0.35***	0.35***	0.35***	0.37***
	(4.3)	(4.34)	(4.39)	(4.55)
	high volatility-low volatility 0.29**	0.17*	0.16**	0.19**
	(2.02)	(1.9)	(1.98)	(2.07)
	neglected-covered 0.25***	0.14**	0.15**	0.16***
	(3.12)	(2.37)	(2.47)	(2.58)
	value-growth 0.05	0.12**	0.11*	0.14**
	(0.72)	(2.02)	(1.83)	(2.23)
	illiquid-liquid 0.11	0.11*	0.11*	0.12*
	(1.63)	(1.86)	(1.83)	(1.91)
	young-old 0.22**	0.18***	0.18***	0.18***
	(2.57)	(3.05)	(3.11)	(3.00)
	1985-2000:
	Opportunities	Opportunities	Opportunities	Opportunities
	(alone)	(FF3)	(C)	(PS)
	small-big 0.49**	0.54**	0.54**	0.53**
	(2.01)	(2.28)	(2.3)	(2.27)
	high volatility-low volatility 0.48	0.32	0.33	0.32
	(1.41)	(1.51)	(1.53)	(1.51)
	neglected-covered 0.46**	0.25	0.25	0.25
	(1.97)	(1.53)	(1.52)	(1.53)
	value-growth 0.08	0.22	0.2	0.22
	(0.43)	(1.64)	(1.61)	(1.64)
	illiquid-liquid 0.13	0.05	0.05	0.05
	(0.68)	(0.27)	(0.27)	(0.27)
	young-old 0.32	0.28**	0.27**	0.28**
	(1.5)	(2.03)	(2.02)	(2.02)
	2001-2015:
	Opportunities	Opportunities	Opportunities	Opportunities
	(alone)	(FF3)	(C)	(PS)
	small-big 0.48***	0.48***	0.42***	0.47***
	(4.89)	(4.86)	(4.55)	(4.65)
	high volatility-low volatility 0.39**	0.27**	0.17*	0.3***
	(2.33)	(2.49)	(1.91)	(2.79)
	neglected-covered 0.3***	0.23***	0.21***	0.24***
	(3.64)	(3.04)	(2.84)	(3.15)
	value-growth 0.11	0.11	0.07	0.15**
	(1.4)	(1.56)	(1.03)	(2.03)
	illiquid-liquid 0.19**	0.23***	0.2**	0.23**
	(2.03)	(2.68)	(2.33)	(2.53)
	young-old 0.34***	0.26***	0.17**	0.24**
	(3.34)	(3.43)	(2.16)	(2.57)

Table 2 .

 2 6: Regressions of the form: R difficult valuation,t -R easier valuation,t = a + b × Opportunities t-1 + c × MKTRF t + d × MKTRF t × Opportunities t-1 . Coefficient d of the interaction term is presented in the table. t-statistics are in parentheses. Table 2.7: Average turnover of all mutual funds when opportunities are higher. Table 2.8: Coefficient in regressions PIN difficult valuation,t -PIN easier valuation,t = a + b × Opportunities t-1 . The first column contains b from this regression; in the first column, b is standardized (one standard deviation in previous opportunities is correlated to b standard deviations increase in PIN difference); in the third column, one standard deviation in previous opportunities is correlated to b percentage points increase in PIN difference.

	Interaction

Table A1 :

 A1 specification, the factors are Mktrf, SMB, HML, traded liquidity. Description of opportunities measures. The starred measure (***) is the one mostly used in the tests.

			Opportunities	Opportunities	Opportunities
		Opportunities	(FF3)	(C)	(PS)
	small-big	0.51***	0.52***	0.49***	0.55***
		(5.05)	(5.11)	(4.98)	(5.32)
	high volatility-low volatility	0.43**	0.26**	0.2**	0.3**
		(2.67)	(2.57)	(2.15)	(2.82)
	neglected-covered	0.35***	0.23***	0.23***	0.25***
		(3.82)	(3.06)	(3.07)	(3.33)
	value-growth	0.1	0.18**	0.13**	0.15**
		(1.3)	(2.58)	(2.06)	(2.39)
	illiquid-liquid	0.2**	0.2**	0.18**	0.21**
		(2.27)	(2.39)	(2.23)	(2.49)
	young-old	0.34***	0.26***	0.23***	0.27***
		(3.46)	(3.93)	(3.63)	(3.97)

Table A2 :

 A2 Subsequent returns when opportunities at the beginning of the period are high (low). Deciles are constructed by size, average volatility in the previous year, or analyst coverage. Opportunities are measured as returns of neglected stocks minus returns of covered stocks, size neutral, value weighted.

							Deciles
		Opportunities	1	2	3	4	5	6	7	8	9	10 Dec10-Dec1
		High	2.1	1.31	1.2	1.24	1.38	1.27	1.22	1.21	1.28	1.09	-1.01
	Size	Low	0.68	0.54	0.67	0.69	0.72	0.75	0.86	0.88	0.86	0.87	0.19
		Difference	1.42	0.77	0.53	0.55	0.66	0.52	0.36	0.33	0.42	0.22
		t-stat (2.17) (1.19) (0.82) (0.89) (1.04) (0.89) (0.64) (0.6) (0.8) (0.45)
		High	1.43	1.56	1.51	1.48	1.58	1.60	1.62	1.60	1.84	1.92	0.49
	Volatility	Low	0.82	0.84	0.85	0.89	0.8	0.87	0.75	0.74	0.62	0.45	-0.37
		Difference	0.61	0.72	0.66	0.59	0.78	0.73	0.87	0.86	1.22	1.47
		t-stat (2.06) (2.00) (1.62) (1.33) (1.64) (1.39) (1.52) (1.36) (1.66) (1.62)
		High	1.74	1.66	1.48	1.26	1.48	1.69	1.52	1.51	1.44	1.36	-0.38
	Coverage	Low	0.72	0.67	0.62	0.63	0.61	0.82	0.7	0.72	0.81	0.83	0.1
		Difference	1.02	0.99	0.86	0.63	0.87	0.87	0.82	0.79	0.63	0.53
		t-stat (1.71) (1.57) (1.31) (0.97) (1.35) (1.39) (1.33) (1.35) (1.17) (0.95)

Table 3 .

 3 9 shows that the worst performing funds tend to change their style to resemble the style of the best performing funds (in 57% of cases for ME, in 65% of cases for BE/ME, and in 60% of cases for LIQ). On the other hand, the youngest funds differentiate themselves away in style from the oldest funds (in 58% of cases for ME, in 62% of cases for BE/ME, in 63% of cases for MOM and in 63% of cases for LIQ). The newest hired managers also differentiate themselves in style from the most veteran managers (in 63% of cases for ME, in 57% of cases for BE/ME, in 67% of cases for MOM and in 62% of cases for LIQ).

  If the ASD ME of the actual mutual fund is not different from the ASD ME of the alternative portfolio, it means the fund pays no special attention to ME; if the ASD ME of the actual fund is different from the ASD ME of the alternative portfolio, it means the mutual fund is paying special attention to ME when it changes its BE/ME score.

time t-1 and t. For each stock a mutual fund holds at t-1, I look at the portfolio of all stocks in CRSP (held by mutual funds) with the same score (e.g. if a stock i held by the mutual fund has score 2 on BE/ME, I look at all stocks in CRSP with score 2 on BE/ME; I denote these stocks the alternative portfolio, with the weights given by the market capitalization normalized to sum up to 1). I compute the average score on ME for the alternative portfolio.

Then I compute ASD ME of the actual mutual fund, and ASD ME of the alternative portfolio (as if the fund moves from the real to the alternative portfolio between t-1 and t).

Table 3 .

 3 2: Average scores alongside the four styles. Each year in December, I average across all funds, then I average across all years. 10=small stocks, 1=big stocks; 10=value stocks, 1=growth stocks; 10=stocks that went up, 1=stocks that went down; 10=illiquid stocks, 1=liquid stocks.Table3.3: Correlation between scores on the four dimensions. Panel A is for mutual funds, Panel B is for all CRSP universe.

	Size score 2.56
	B/M score 3.63
	Momentum score 6.32
	Liquidity score 2.56

Table 3 .

 3 4: Correlations between ASD, PSD and TSD. ASD stands for active style drift, PSD stands for passive style drift, TSD stands for total style drift.Table3.5: This table shows averages of style drift. Panel 1 shows what the average (absolute value) of style drift is. For example, the year-to-year TSD for a fund is on average 1.10. Panel 2 shows what the average (absolute value) style drift is on the four different components. Panel 3 shows how the different components participate to the style drift.

		ASD	PSD	TSD
	ASD	1
	PSD -0.4439	1
	TSD 0.4767 0.5761	1
	PSD<0 (stocks become less risky)
		ASD	PSD	TSD
	ASD	1
	PSD -0.4027	1
	TSD 0.6989 0.3733	1
	PSD≥ 0 (stocks become more risky)
		ASD	PSD	TSD
	ASD	1
	PSD -0.1767	1
	TSD 0.8099 0.4343	1

  Table3.10: Regressions of ASD on PSD. Regression (1) is Fama-MacBeth; regression (2) is Fama-MacBeth where the average is weighted by the number of funds in each year; regression (3) is OLS with year fixed effects and White standard errors; regression (4) is OLS with year fixed effects and errors clustered by fund p < 0.05, * * p < 0.01, * * * p < 0.001

	10-1 t-stat CV Style Decile 1 Decile 10 10-1 t-stat CV Coefficient estimation TSD ME -0.0790 -0.0794 -0.0004 0.00 -2.10 TSD ME 0.0172 -0.0793 -0.0965 -1.08 -2.10 TSD BM 0.2358 -0.2996 -0.5355 -3.97 -2.10 TSD BM 0.2144 -0.1181 -0.3325 -3.28 -2.10 PSD Constant R 2 Standard errors Fixed effects Observations t statistics in parentheses	TSD MOM -0.6701 0.6747 1.3448 5.35 2.10 TSD MOM -0.7888 0.4212 1.2100 3.83 2.10 -0.563 * * * -0.564 * * * -0.555 * * * TSD LIQ -0.0947 -0.0297 0.0650 0.90 2.10 TSD LIQ -0.0451 -0.0119 0.0332 0.40 2.10 PSD ME -0.0649 -0.1643 -0.0994 -2.37 -2.10 PSD ME 0.0031 -0.1491 -0.1522 -2.30 -2.10 PSD BM 0.0028 -0.2867 -0.2895 -3.42 -2.10 PSD BM 0.3865 0.0905 -0.2960 -4.96 -2.10 PSD MOM -0.3826 0.9078 1.2904 3.99 2.10 PSD MOM -1.6207 -0.4431 1.1776 3.45 2.10 PSD LIQ -0.0890 -0.0974 -0.0084 -0.20 -2.10 PSD LIQ -0.1562 -0.2443 -0.0881 -1.44 -2.10 ASD ME -0.0141 0.0849 0.0990 1.24 2.10 ASD ME 0.0141 0.0698 0.0557 0.85 2.10 ASD BM 0.2331 -0.0129 -0.2460 -2.51 -2.10 ASD BM -0.1722 -0.2087 -0.0365 -0.49 -2.10 ASD MOM -0.2875 -0.2331 0.0544 0.23 2.10 ASD MOM 0.8319 0.8643 0.0324 0.20 2.10 ASD LIQ -0.0057 0.0677 0.0734 1.08 2.10 ASD LIQ 0.1110 0.2324 0.1214 1.59 2.10 Large funds Small funds Style Decile 1 Decile 10 10-1 t-stat CV (1) (2) (3) ASD ASD ASD 10-1 t-stat CV (-15.40) (-15.16) (-48.84) 0.0564 0.0528 0.0908 * * * (0.58) (0.51) (8.50) 0.28 0.27 0.3 FM WFM OLS FM FM White Style Decile 1 Decile 10 Year 11763 11763 11763	TSD ME -0.0295 -0.0996 -0.0701 -2.65 -2.10 -1.65 -2.10 TSD ME -0.2057 -0.2917 Clustered by fund TSD BM 0.1939 TSD MOM -0.8435 TSD LIQ -0.0515 PSD ME -0.0038 PSD BM 0.2272 PSD MOM -1.2698 -0.1695 -0.3635 0.6466 1.4901 -0.0433 0.0082 -0.0917 -0.0879 -0.0687 -0.2959 0.3491 1.6190 -3.98 -2.10 5.80 2.10 -0.66 -2.10 -4.49 -2.10 -6.17 -2.10 4.76 2.10 (4) ASD -3.74 -2.10 TSD BM -0.1956 -0.3855 4.99 2.10 TSD MOM 0.6057 1.3264 0.18 2.10 TSD LIQ -0.1104 -0.0692 -4.27 -2.10 PSD ME -0.3308 -0.3165 -4.88 -2.10 PSD BM -0.1407 -0.4792 4.87 2.10 PSD MOM 0.2905 1.5932 -0.555 * * * (-39.37) 0.0908 * * * (7.43) 0.3 OLS 0.0859 0.1899 -0.7207 -0.0412 -0.0143 0.3385 -1.3027 Year 11763	PSD LIQ -0.0672 -0.0810 -0.0138 -1.55 -2.10 -0.45 -2.10 PSD LIQ -0.3665 -0.1213 -0.2452	ASD ME -0.0257 -0.0079 0.0177 0.33 2.10 0.50 2.10 ASD ME 0.1250 0.0248 0.1002	ASD BM -0.0333 -0.1009 -0.0676 1.02 2.10 -1.06 -2.10 ASD BM -0.0549 0.0937 -0.1486	ASD MOM 0.4263 0.2975 -0.1288 -1.13 -2.10 -0.71 -2.10 ASD MOM 0.3151 -0.2669 0.5820	ASD LIQ 0.0157 0.0377 0.0220 0.57 2.10 0.53 2.10 ASD LIQ 0.2561 0.0521 0.2040

*

Table 3 .

 3 14: Regression of future flows on style drift and controls. Errors are clustered by date. p < 0.05, * * p < 0.01, * * * p < 0.001Table 3.15: Regression of future performance on style drift and controls. Errors are clustered by date.

		(1)	(2)	(3)
		Fol.6m flows Fol.6m flows Fol.6m flows
	ASD	-0.0358
		(-0.68)
	Rank	0.392	0.277	0.343
		(1.44)	(1.11)	(1.35)
	Past.6m flows	-0.287	-0.287	-0.287
		(-0.67)	(-0.67)	(-0.67)
	Log(TNA)	-1.705	-1.705	-1.703
		(-1.20)	(-1.20)	(-1.20)
	Age	-0.479	-0.514	-0.501
		(-1.10)	(-1.06)	(-1.07)
	Tenure	0.365	0.370	0.367
		(1.22)	(1.20)	(1.21)
	PSD		0.0965
			(0.63)
	TSD			0.0444
				(0.51)
	Constant	10.01	10.17	10.06
		(1.19)	(1.17)	(1.18)
	Fund FE	Yes	Yes	Yes
	Observations	9359	9359	9359
	t statistics in parentheses

* * p < 0.05, * * p < 0.01, * * * p < 0.001 134

M KT , R f , SM B, HM L, U M D, L come from CRSP; RM W and CM A come from the website of Kenneth French:http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html; and HM L * , U M D * and P M U come from the website of Robert Novy-Marx

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/variable_ definitions.html. The calculation is used for[START_REF] Davis | Characteristics, Covariances, and Average Returns: 1929 to 1997[END_REF], "Characteristics, Covariances, and Average Returns: 1929[START_REF] Carhart | On Persistance in Mutual Fund Performance[END_REF]", Journal of Finance

The DGTW benchmarks are available via http://www.smith.umd.edu/faculty/rwermers/ftpsite/Dgtw/coverpage.htm

http://www.petajisto.net/data.html

The indexes have the following codes in Compustat: S&P500 is I0003, S&P400 is I0016, S&P600 is I0019, S&P500/Barra Value is I0018, S&P500/Barra Growth is I0017, Russell Midcap is I0149, Russell Midcap Growth is I0145, Russell Midcap Value is I0147, Russell

is I0155, Russell 1000 Value is I0030, Russell 1000 Growth is I0154, Russell 2000 is I0123, Russell 2000 Value I0121, Russell 2000 Growth is I0033, Russell 3000 is I0135, Russell 3000 Value is I0133, Russell 3000 Growth is I0131. For the Russell Indexes I have the option to select the prices with dividends and I use them.

For each time period of 3, 5 and 10 years, Morningstar ranks the performance of a mutual funds within its category, and the 10% best performing funds receive 5 stars. Then an overall rating is computed in the following way: if a fund has between 36-59 months of returns, then the overall rating is 100% the 3-year rating; if a fund has between 60-119 months of returns, then the overall rating is 60% the 5-year rating + 40% the 3-year rating; if a fund has 120 or more months of returns, the overall rating is 50% the 10-year rating + 30% the 5-year rating + 20% the 3-year rating. There is a heavier weight on longer streams of returns.

The decile of the smallest stocks contains 1% of the market; the decile of the highest volatility stocks contains 9% of the market; the decile of the most neglected stocks contains 2.8% of the market; the decile of the highest book-to-market stocks contains 12% of the market; the decile of the most illiquid stocks contains 0.1% of the market; the decile of the youngest stocks contains 5.1% of the market.

The decile of the smallest stocks contains 1% of the market; the decile of the highest volatility stocks contains 9% of the market; the decile of the most neglected stocks contains 2.8% of the market; the decile of the highest book-to-market stocks contains 12% of the market; the decile of the most illiquid stocks contains 0.1% of the market; the decile of the youngest stocks contains 5.1% of the market.

From the Survivor-Bias-Free US Mutual Fund Guide published by CRSP: Turnover ratio = "minimum (of aggregated sales or aggregated purchases of securities), divided by the average 12-month Total Net Assets of the fund".

The scores are assigned such that a bigger score means higher risk exposure along that dimension; 10=small stocks, 1=big stocks; 10=value stocks, 1=growth stocks; 10=stocks that went up, 1=stocks that went down; 10=illiquid stocks, 1=liquid stocks.

Acknowledgements

I am grateful to the people of the Finance Department for the high quality research atmosphere and their readiness to discuss research ideas. Special thanks go the members of my committee.

I am grateful to my advisor, Laurent Calvet for his constant guidance and encouragement. I thank Thierry Foucault and Denis Gromb for their comments and general help along the way.

The finance PhD students group at HEC has been constantly growing over the years. I thank them all for feedback, discussions and for the collegial atmosphere in our office.

My warmest gratitude goes to my family, to whom I dedicate this thesis. Writing it would not have been possible without their support. I thank my parents, Rodica and Tudorel S ¸tefan, who encouraged early pursuits of knowledge. My husband, Ioanid, has been my source of encouragement and constant reminder that the highest return comes from investment in human capital. Our children, Andrei, Alexandru and Matei, who manifest the most genuine curiosity, are a constant source of happiness.

Thank you all!

iii Cette intuition peut être expliquée dans le cadre du model de Easley et O'Hara (2004).

Ils construisent un modèle où ils permettent d'avoir de différences dans la composition de l'information entre l'information publique et l'information privée. Ils démontrent que ces différences affectent le coût du capital, et que les investisseurs exigent un rendement supérieur pour détenir des actions avec plus d'information privée. Dans mes tests, j'identifie les actions avec plus d'information privée comme les actions pas suivies au moment où les rendements des actions pas suivies se sont éloignés des rendements des actions suivies (pour mesurer cette différence j'utilise la valeur absolue de la différence entre les rendements des actions pas suivi et les rendements des actions suivies ; je dénote comme "opportunités grandes" les périodes ou cette valeur absolue est plus grande que la moyenne). A ce moment, les traders informes vont acquérir plus d'information privée concernant les actions pas suivies, parce qu'ils pensent que les actions pas suivies n'ont pas les prix corrects. Je teste cette prédiction du model, comme que les rendements ultérieurs des actions pas suivies sont plus importants, et je la confirme.

En plus, je réussis à étendre les résultats en outre les actions pas suivies, pour les actions qui sont difficiles à évaluer (actions volatiles, actions illiquides, actions jeunes). Alors qu'il est difficile de montrer qu'un seul model explique mes résultats, je démontre que mes résultats sont compatibles avec un modèle de risque d'information (comme celui de Easley et O'Hara (2004)) et qu'elles ne constituent pas une anomalie du marché efficace. Je réussis à rejeter les explications alternatives les plus évidentes (retard, sentiment du marché), et j'apporte des preuves aussi en ce qui concerne la probabilité des transactions avec information (PIN).

Acknowledgements iii

Résume en français iv

Appendix

(49% of the score change occurs alongside momentum, with the other three accounting for the remaining 51%). Funds do not change their riskiness when they have more incentives to do so, nor after bad times. However, bad performing mutual funds move closer to the style of good performing peer funds, young funds differentiate themselves in style from old peer funds, and recently hired managers differentiate themselves in style from veteran managers of peer funds. When the average fund takes more risk alongside a style dimension, it does not pay special attention to its risk on the other style dimensions. Funds do not take bets outside their style when they lag behind their peers. Last, changes in riskiness (ASD) do not indicate superior future performance.