Raphaël Hekimian
email: raphael.hekimian@yahoo.fr

The French banking sector during the interwar: What lessons can be drawn from the stock market?

Keywords: JEL Classification: G21, G01, N20 Banking crisis, Financial History, Great Depression

The aim of this paper is to provide new insights on the French banking crisis of the1930's. This crisis is usually considered in the literature to have been relatively more limited in France than in other European countries. One feature of the French banking system at that time was the specialization of its activities: French banks were, for the most part, either deposit or business banks. The literature highlights the fact that business banks faced the greatest difficulties because they invested in foreign markets. The purpose of this article is to test this hypothesis with a new dataset of stock prices by estimating the risk on i) the aggregated banking sector; ii) on two subsamples, one including only deposit banks and the other one, only business banks and iii) on the individual series. We find that during the 1930's, business banks were indeed more risky than deposit banks, relative to the overall market

Introduction

The recent global financial crisis of 2007-2008 highlighted the importance of banks in the development and the propagation mechanisms of the US real estate crisis into the global economic crisis. In 2016, European banks raised fears with regards to their solvency and their potential systemic risks. During the summer, Italian banks such as Banca Monte dei Paschi raised concerns because of its exposure to bad loans. Especially after UK's brexit, analysts fear the threat of Italy being forced to leave the Eurozone. 1 In late September, it is the Deutsche Bank (DB) that worries international finance. After the US Department of Justice demanded a 14 billion dollars claim to settle allegations of mis-selling mortgage securities, the DB, hedge funds reduced their exposure to the largest German private bank in late September. It resulted in growing concerns on the whole European banking system followed by a decrease in large European banks' share prices. 2 Earlier this year, banks stocks already suffered from investors' uncertainty on both sides of the Atlantic, and especially European and French banks: in January 2016, Société Générale and Banque Nationale de Paris' shares dropped by roughly 20%, caused by investors' fear about both energy prices and low interest rates. 3 Moreover, concerns about a potential relapse of the financial system due to the banking sector's fragility flourished all over the French press. 4 The most relevant episode of such a long period of international financial stress in economic history is most likely the 1930s. In particular, the French case during the interwar outlines several interesting similarities with the recent times in terms of banking system. In addition to a low regulatory environment, French banks benefited from a powerful central bank with large gold reserves, able to play the lender of last resort if necessary. However, one striking difference lies in a much more specialized banking system: most of the big banks had one main activity among either the industrial and commercial sectors or in deposits.

During the Great Depression, banking systems went under a lot of pressure. The Austrian banking crisis of 1931 is often seen in the literature as the trigger of the Central European crisis and the aggravation of the depression in Western Europe. 5 The banking sector during the interwar has been recently studied for several countries. We can cite, among others, Billings and Capie (2011) who state that the British banking system resisted to the exchange-rate crisis thanks to the robustness of the joint-stock commercial banks that permitted the British economy to remain stable. Turner (2014) confirms this result with a very long-term analysis of the British banking system, emphasising its stability in the 1930s. On the contrary, Battilossi (2009) studies the interwar banking crisis in Italy and attributes the instability of this sector, consisting of universal banks, to the weaknesses of their governance. In the case of France, the literature usually states that the banking crisis of the 1930s was limited. Its impact on the origins of the 1930s economic crisis in France is not really examined. Instead, the origins of the 1930s crises, well summarized in Mouré's famous book, 6 opposes Alfred Sauvy, who attributes French difficulties to the Sterling crisis of 1931 and the misalignment of the Franc's exchange rate, 7 and Jacques Marseille who outlines an endogenous crisis of the French industry, unable to match the domestic market with the productive capacity. The role of the banking sector is therefore not so much highlighted in this debate. 8 The aim of this paper is to understand the role of French banking sector in the 1930s crises. Accordingly, we use a new dataset of individual stock prices for ten French banks with high market capitalization, using different levels of analysis, from aggregated to individual, in order to assess investor risk perceptions on this sector. We show that thanks to its specialization, the French banking system proved resilient to the economic downturn of the 1930s.

The remainder of the paper is as follows: Section 2 reviews the literature on French banks during the interwar and the consequences of both the economic expansion of the 1920s and the crisis of the 1930s. Section 3 presents the data and Section 4 provides an empirical study of the movements of bank share prices relative to the overall market, at both aggregated and individual levels. Section 5 concludes.

Historical background

In this section, we first focus on the features of the French banking sector during the interwar, before drawing the course of events that we divide in two sub-periods that have different impacts: (i) the economic expansion of the 1920s, and (ii) the downturn of the 1930s.

A specialized French banking sector

One of the main evolution of the French Banking system occurred during the period 1848-1875. According to Bouvier (1973), this evolution was a quantitative "revolution", since the founders of the "new" banks only imported the innovations of the decades 1820's and 1830's coming from Great Britain.9 This revolution applied to the size of the banks with on the one hand, the volume of their total equity (capital and reserves), and on the other hand, the volume of their deposits. These "new" banks were then much larger than during the first half of the 19th century. Indeed, they sought to increase deposits and at the onset of the World War I, the four largest banks had expended their deposit and current accounts from 285 million francs in 1860 to over 5.5 billion in 1913 (Bouvier, 1973). The French banking system is depicted by the author as having constant features from the end of the 19th century up to the World War II. According to the author, the French system differed from both the system prevailing in Grand Britain or in continental Europe. In France, powerful banks, as defined as having large gathered resources, were commercial and deposit banks with a national network (Crédit Lyonnais, Comptoir National d'Escompte, Société Générale and Crédit Industriel et Commercial). In those banks, capital was not so high but deposits were very important 10 and devoted to short term credit with mainly discount operations. Henri Germain, founder of the Crédit Lyonnais, insisted on the fact that short term resources should correspond to short term uses.

Especially for the period before 1914, these banking principles only allowed small per unit benefits considering the low level of interest rates and the stability of prices thanks to the Gold Standard. But overall gains allowed to maintain profits and dividends at a high level. Bouvier (1973) characterises those banks as having small links with large industrial firms, even if some could be both board members of entities in the two sectors.

The literature usually distinguishes commercial and deposit banks from business banks with large investments in the industrial sector, looking for investments in foreign markets. 11 But the distinction between these two groups of banks (all of which had been created between 1852 and 1875) only rose after the difficulties of the 1880's. Before the crash of the Union Générale,12 all of the large banks had both merchant and deposit activities, and could then be referred as "Universal" banks. In fact, this banking model was dominant in the continental Europe, particularly in Germany and to some extent, in Belgium,13 while the British system had already made a clearer separation between investment and commercial banks. The distinction between the two activities in the French banking model occurred at the end of the 19th century and operated until 1945. This separation between deposits and business activity is, as we will see, often seen as an explanation of the resilience of large deposit banks. Levy-Leboyer and Lescure (1991) explain that from the 1880's, the second stage of France's industrialization provided new opportunities for the banking system. However, the authors note that local and regional banks benefited more from those new investment opportunities than large national banks, more worried about their liquidity. Moreover, the remarkable growth of the "Belle époque" in France from the late 19th century and up to World War I, should be more attributed to the now mature capital market than from the banking system efficiency.

Another feature of the French banking system during the interwar was its freedom, much greater than what it became after 1945, and somehow comparable to what it is today. Indeed, the laws of 1863 and 1867 on joint stock companies allowed banks to be freely constituted and without any control from institutions. The State did not legislate on the banking sector before the early 1940's, when the "bank regulation act" of 1941, allowed the Banque de France to limit discount facilities and therefore control liquidity, but also when the four largest deposit banks were nationalized in 1945.

The impact of the French economy over banks between the wars

The interwar period can clearly be divided in two phases (i) an economic expansion in the 1920s. and (ii) a long downturn in the 1930s, with different consequences on French banks.

The 1920s: industrial growth, inflation and monetary instability

On the real economy side, the French economy of the 1920s is characterized by a strong industrial growth. The French industrial production doubled from 1921 to 1929 and its growth rate was the highest among the European countries. 14 This expansion was driven by a transfer from low (e.g. textile, leather) productive sectors to high (e.g. steel, chemicals, mechanical industries productive sectors. However, even though the productive industries were boosted by the Great War, the economic consequences for France were overall critical. In fact, Caron and Bouvier (1979) show that if the revenue of those industrial firms rose during the war, their benefits did not because most of the revenue was kept for self-financing. In terms of banking policy, this industrial growth had consequences: in the early 1920s, business banks got closer to domestic industries in order to benefit from the reconstruction and the modernization of French equipment. They increased their capital in 1920 (among others, Banque de Paris et des Pays Bas, Banque de l'Union Parisienne and Banque de l'Indochine). Industrials started to sit on some banks' board, while financiers kept a large majority (Bouvier 1979).

The monetary aspect of the period has been well studied and is very interesting to understand its implications on banks' policy. When WW1 started in 1914, France, along with Great Britain, abandoned the Gold Standard to follow expansionary monetary policies in order to finance the war effort. According to Blancheton (2000), France financed the war mostly by issuing debt (74%), the rest being financed by an increase in taxes (15%) and by the advances of the Banque de France (11%). The situation of public finance did not recover after the war because the French Treasury (Mouvement Général des Fonds) anticipated that Germany would pay for war damages as France did to Germany after the Franco-Prussian war in 1871. At that time, both the Central bank and the Treasury still thought that the return to the pre-war parity of the Franc could be manageable. They tried to adopt a deflationary monetary policy, by containing the circulation of money under a certain ceiling. 15 Once they finally figured out that Germany would never be able to pay the entire amount of the reparations, the Treasury faced its obligations by using indirect advances of the Banque de France (via commercial banks) as shown by Blancheton (2000). This increased the monetary base velocity and led to speculative attacks against the Franc in 1925-26. The monetary consequences of the war were then heavy and numerous: (i) the end of the Gold Standard, (ii) the convertibility of the paper Franc suspended, (iii) inflation in the fiduciary circulation, (iv) the State indebted towards the Banque de France and finally, (v) difficulties for the Franc on the foreign exchange. 16 What were the consequences on the banking sector? First, a share of the traditional customer base of French banks, the bond holders, was hit by inflation. Therefore, banks reaching out to other new clients: the sellers and producers, and firms in particular. On the asset side, if the nominal deposits did not increase faster than prices, the depreciation of the Franc affected banks' resources. After a constant growth during the Belle Époque, the increase of bank money slowed down during the 1920s, before decreasing during the depression. According to Bouvier (1979), the deposits of the top four French commercial banks decreased from 36 to 26 billion francs from 1931 to 1936. However, business and commercial banks did not equally suffer from inflation. It was easier for deposit banks, thanks to their large national network, to follow inflation by raising the nominal value of their deposits (and therefore their corresponding volume of credit).

A second consequence was the tendency of the banking sector to increase their activity of security issuers on the stock exchange and the corresponding securities services (holding securities, coupon and dividend detachment, tax levy and so forth). In fact, the share of the volume of issued securities from private companies accounted for the majority of the total during the period 1924-1932, while for the periods 1915-1923 and 1933-1938, the share of State and local government securities were higher. This is also confirmed by Hautcoeur (1994), who highlights this evolution in the French banking activity during the interwar: the inflation experienced in the early 1920s made banks looking towards other profits. In particular, Hautcoeur (1994) states that while during the pre-war period, the securities issuing activities were dedicated to business banks, the drop in deposits made also commercial banks turning into these activities, especially because listed companies' financial operations increased substantially during the 1918-1929 period. Yet, Bouvier (1979) relativizes this idea by stating that the securities service had high costs.

A third effect of the monetary instability lies in the activity of banks on the Foreign Exchange market. According to Bouvier (1979), the "stabilization" of the French franc in 1928, by a devaluation of four fifth of its prewar parity, pushed French banks to multiply operations on the foreign exchange market. In fact, the large fluctuations due to the end of the Gold Standard made this market more profitable for speculators,17 as well as hedging activities against currency risk essential . Moreover, France did not put in place foreign exchange controls, even during the 1930s. According to Bouvier (1979), the year 1928 registered the record level for the item Banquiers et correspondants which reached 22% of the asset side of the balance sheet. It was even higher for business banks: from less than 4% in 1914, the weight of this item went up to 8, 5% in 1923, 20% in 1926-30 and reached 23,5% in 1939. The author depicts the interwar period as being very important in terms of banking operations' internationalization.

The 1930s: banking crisis and economic depression in the literature

The economic crisis of the 1930s did not come forward before the early month of 1931, but lasted longer than many other countries (Caron and Bouvier, 1979). In the literature, the main banking crisis started in late 1931-early 1932 as a consequence of the Sterling crisis of September 1931. Bouvier (1979) studies the sequence of events through the length of deposit volumes for the largest commercial banks. According to the data of the Crédit Lyonnais, the highest volume of deposits held by the four largest commercial banks18 reached its peak in June 1931. In the following months, deposits started to decrease, which coincided with the Hoover moratorium on reparations and war debts, and the Sterling crisis of September. The slump in deposits slowly accelerated in 1932 and the following years, reaching a trough in September 1936 before the devaluation of the French Franc and the subsequent end of the Gold Block. On the credit side, a reversal trend occurred at the beginning of the 1930s: from 30 billion francs in 1920, it reached 79 in 1929, 61 in 1934 and 74 in 1938. The author claims that the increase in the late 1930s is more the result of the growing inflation after 1936 than a real surge in economic activity.

An important feature of the French banking crisis of the 1930s is the resistance of large banks with regards to failures. Indeed, 276 joint-stock banks 19 failed between 1929 and 1937 but among them only one was considered large, the Banque Nationale de Crédit. The addition of small local bankers and maisons de coulisse 20 increased the number of failures to 670.

However, important banks also experienced difficulties. The Banque de l'Union Parisienne (BUP) is a famous case, detailed in Bonin (2001). The bank suffered from its investment in Central and Oriental Europe. After the failure of the Austrian Creditanstalt, a confidence crisis took place while the BUP was investing in Hungary, Austria, Romania and Czechoslovakia. Despite a drop of 600 million francs in the deposits, the bank benefited from the solidarity of the Parisian place, 21 on the request of the Minister of Finance, to face its obligations in late 1931. A fund was created by six banks (among others the Crédit Commercial de France) to help the BUP to deal with these cash-flow issues. Levy-Leboyer (1995) shed lights on the international money market to explain the trigger of the banking crisis: the increase of interest rates in the US, provoking the distress of Wall Street in late 1929, was putting the European capital markets in danger. American capital flew back to the US and French banks also suffered from those movements. Between 1930 and 1935, the contraction of credit was of the same magnitude than in Germany and in Belgium and twice as high as in Netherlands and in Switzerland (Levy-Leboyer, 1995). But the dramatic distress of 1931, when German and Austrian banks failed and the convertibility of the Sterling pound to gold got suspended, was not seen as contagious for the French banking system. Indeed, the reserves of the biggest banks increased substantially in the early 1930s (from 973 million francs to over 5 billion from 1928 to 1932 for the Crédit Lyonnais). In addition, long-term interest rates started to decrease with the stabilization of the Franc in 1928, and went from 7% to 3.5% in 1931, while short-)term interest rates went below 2% in 1930-32, i.e, below the levels of UK and US. 22 However, in 1932 the cost of credit in France went above the levels of UK and US, and even above the other Gold-Bloc countries (Belgium, The Netherlands, Switzerland, Italy and Poland). The outflow of capital to London and New-York in 1933-34, probably due to investors seeking for profitability after the suspension of the US dollar's convertibility to gold in 1933, 23 raised the difficulties of the French banking system and hence, reinforced the economic crisis up to the devaluation of the French franc in 1936.

While the literature generally supports the idea that the French banking crisis was not as deep as in other countries, Lescure (2004) mitigates, however, this view. According to him, the overall banking system resisted quite well to the crisis from a macro-financial point of view. But Lescure shows the large national banks, for the most part, did not experience the worst difficulties while local and regional banks suffered from lots of failures. 19 A joint-stock bank combines features of a general partnership, in which owners of a company split profits and liabilities, and a publicly-traded company, which issues stock that shareholders are able to buy and sell on an exchange. 20 Small entities trading securities on the Over the Counter market of the Paris' Bourse. 21 Banks that could be referred as "private" banks in the sense they are not joint-stock companies but rather old family banks: in French: Maisons de Haute Banque. The six banks are: Demachy, Hottinguer, Mallet, Mirabaud, Neuflize and Vernes. See Bonin (2001). 22 Levy-Leboyer quotes sources from the League of Nations. 23 After the US's departure from gold, American stock prices started to rise again.

The resilience of the banking sector was then explained by the strength of large banks, specialized and featured by a balance sheet's structure devoted to liquidity, while universal and decentralized smaller banks failed. The author adds that the severity of the crisis' issue cannot be answered only by looking at failures. Indeed, numerous banks such as the Banque de l'Union Parisienne or the Banque Nationale de Crédit, were restructured or dissolved and re-founded without any juridical procedures.

The French banking crisis of the early 1930s as seen by the Central Bank

In this sub-section, we go through the minutes of the Conseil Général of the Banque de France in order to provide (i) an in-depth investigation the role of the Central Bank in the management of the crisis and (ii) a first insight on market sentiments at the time.

First of all, the French monetary authorities mention two episodes of banking crisis. The first one occurred from October 1930 to January 1931. In the minute of the Conseil Général of December 26 th , 1930, we can read: "The banking crisis, which brutally occurred at the end of October, caused numerous failures among banks related to our establishment. No matter how much we supported the ones who asked for our intervention, we could not avoid the failure of banks that had either suffered from losses, or invested their deposit into activities that, according to our statutes, may not justify our intervention". 24 The scope of the crisis seems however limited. Only twelve failures are mentioned: 8 for local and regional banks, four "important" in Paris, among which the Oustric25 bank and the Société Financière de Paris. Only those last two hold the Central Bank's attention. It is said that the liquidation for these two private banks will take some time, but "according to the available information, large losses should not be feared".

The second stage of the banking crisis took place with the Sterling crisis of September 1931. The Central Bank uses the movements in its commercial portfolio to describe the timing of the two episodes of banking crisis: "The first credit crisis (from October 1930 to January 1931) increased the portfolio from 4.7 billion to 7.4 billion francs. The recovery, which occurred during the first semester of 1931, gradually decreased the amount of the portfolio at 4 billion francs on July 1 st 1931. The second credit crisis (September 1931) provoked a movement of a similar magnitude. The portfolio went from 4.2 billion to 6.7 billion within a month. This increase of 2.5 billion is made of 1 billion francs of commitments only for the Banque Nationale de Crédit (...). Since November 1 st , the portfolio constantly decreased until reaching its level of the first semester of 1930, before the first credit crisis occurred."26 A description of the portfolio is then presented in detail. After mentioning three banks that could generate risk because of their very specialized activities (i.e. Marret Bonnin and Messein Bedarrides, specialized in the diamond business, and the Banque d'Extension Commerciale & Industrielle, specialized in refinancing commercial paper), it is clearly said that: "Besides those three banks, the composition of the portfolio does not contain any particular risk". Here we will focus on the first three (and main) cases in terms of "commitments" to the Banque de France.

Banque de l'Union Parisienne:

The bank, which as an equity capital of 200 million francs at that time, is engaged towards the Central bank to the amount of 391 million francs: "The discounted bills, insignificant during the first semester of 1931, increased following the treasury needs due to massive deposits withdrawals. The maximum was reached on February 16 th with 421 million francs and it seems like it will be quickly reduced." The Central bank does not seem to be worried about this case: "The situation is improving, especially thanks to recent cash inflows, rising stock prices and finally with the upcoming merger with the Crédit Mobilier".

Banque Nationale de Crédit:

This bank has already been in liquidation since February 26 th , and the amount engaged is of 145 million francs: "Discounted bills that amounted to 200 million in the course of 1930, reflected twice but in different moments, particularly sharp increases, owing to numerous refund claims from customers. In the aftermath of the first crisis during winter in 1930-31, commitments rapidly returned to their previous value, thanks to restored trust and confidence from depositors. In contrast, a much more serious panic took place at the end of September 1931, which led to a sudden dramatic increase in commitments. Between September, 16 th and October, 16 th 1931, pledges went from 291 to 1.497 million. Since then, they have been gradually reduced to their current amount of 257 million, the latter being broken down into 185 million various commercial prints and 72 million prints representing receivables' fundraising. These commitments are guaranteed as follows: on the one hand, those that were assigned before December, 31 st 1931, amounting to 108 million, a guarantee totaling 205 million has been given to the Bank of France and provided by the main credit institutions. On the other hand, commitments subsequent to December, 31 st 1931, currently about 144 million, are guaranteed up to one-fifth of their amount, by blocked funds in a particular account opened at the Banque Nationale de Crédit. The ensemble is supported by a pool of securities whose value seems to be set to 40 million. Hence, commitments do not put the Banque at endue risk."

Crédit Commercial de France:

"After moving around 50 million francs, the engagements quckly raised during the last quarter of 1931. The maximum was reached on November 1 st with almost 523 million francs. Since that date, this amount is in constant decline. Commercial paper and bank acceptations are related to the Northern and Eastern textile industry, as well as large firms in the chemical and metalworking industry".

The Crédit du Nord is also mentioned for having important difficulties during the second semester of 1931. Its engagements rose from 63 to 605 million francs between July the 1st and November the 1st, following the panic of depositors and the worsening of the textile industry crisis."

According to the minutes of August 25 th , by the summer of 1932, the French banking crisis was over: "For the last two month, it (the portfolio of discounted bills) shows a relative stability after the large decrease of the first months." From 6.5 billion on January 19 th , it went down to 3.2 billion in late August. The Central bank explains this reduction by "the disappearance of the banking crisis, which was the reason for easing access to liquidity". The descriptions detailed above confirm the view of a contained banking crisis, but also a crisis that only hit certain type of banks, more devoted to lend to industrial businesses. In the following sections, we aim at completing this picture by examining stock market's perceptions on the banking sector which, to the best of our knowledge, has not yet been done with high quality data.

Data

To empirically address the issue of the stability of the French banking sector during the interwar, we rely on stock price data instead of data either on balance sheets or on failures used by the existing literature. Yet, as shown by Lescure (2004), data on failures are incomplete while balance sheets can only be studied in a descriptive way since data are not available on a regular frequency for a sufficient sample of banks.

In this paper, we propose to use a new monthly bank share index including ten highly capitalized banks listed at the Paris Stock Exchange from 1919 to 1939. The index is built by collecting both individual stock prices for each of the ten banks and their corresponding number of shares listed on the official list of the Paris' Stock Exchange. The included banks are the following: Banque de France, Banque d'Algérie, Banque de Paris et des Pays Bas, Banque de l'Union Parisienne, Comptoir National d'Escompte, Crédit Commercial de France, Crédit Foncier de France, Crédit Lyonnais, Banque de l'Indochine and Société Générale. The choice of this sample can be justified by several reasons. First, these banks correspond to joint-stock banks. Even if the literature on the French banking shows that private banks, also called Maisons de Haute Banque, account for an important share of the banking operations in Paris at that time, data on those banks are not published and they are not listed on the Exchange. Second, securities of highly capitalised firms are usually very liquid: they are traded every day hence we are able to collect transaction prices for each of our observations. In addition, those banks are all listed on both the spot and the forward markets. Therefore they are more prone to speculation than securities only traded on the spot market. Finally, the heterogeneity between the considered banks provides additional information. As highlighted in the previous section, the French banking sector is specialized. In our sample, three banks correspond to deposit and commercial banks: Crédit Lyonnais, Comptoir National d'Escompte and Société Générale. Three are business banks: Banque de Paris et des Pays Bas, Banque de l'Union Parisienne and Banque de l'Indochine. The three last remaining cannot be included in either of the last two groups: the Banque de France is the central bank; the Banque d'Algérie is not a central bank, but is the one bank authorized to issue notes in the wide Algerian department and in the French protectorates of Tunisia and Morocco; the Crédit Foncier de France is a mortgage loan bank with close ties with the State.

The index is weighted by market capitalization for two main reasons: i) using market capitalization instead of prices alone allows to adjust from the firm's operations on capital such as stock splits or seasonal public offerings without calculating adjustment coefficients; ii) the standard stock price index for the overall Parisian market for our period of interest is the monthly cap-weighted index of Le Bris and Hautcoeur (2010), 27 which includes the top forty market capitalization for each year over the period 1854-2007. It is then obvious to choose the same type of index (cap-weighted) to run our study on a sectorial index relative to the overall market.

Finally, we also collected monthly prices of what is considered as the risk-free asset of the time at the Paris' Bourse: the Rente 3%. This will allow us to measure excess returns relative to the risk-free asset, which is a more precise way to study risk within the portfolio theory framework.

For all our series in levels, we log-differenciate them in order to get returns. The series in level are mostly integrated at the order 1 (I(1)). It is not surprising given the macroeconomic regime of either expansion or recession during the interwar. Especially if one wants to run estimations on both sub-periods, the stationary nature of the series has to be checked. Augmented Dickey-Fulher and Perron tests (not reported) allows us to use the return series as they are all I(0).

The French banking sector seen by the stock market

In this section we aim at study the risk of the French banking sector during the interwar. We first measure this risk at an aggregated level in order to qualify the sector as a whole in terms of risk. As a second step, we divide our sample between business and deposit banks to assess the investor's behaviour with regards to the specialization of banking activities. Finally, we study the risk relative to the overall market at the firm's level.

The aggregated banking sector

A first glance at the data in level gives us an overlook of out three series. Figure 1 represents the share index of the overall market, of the banking sector and the risk-free security index over the period 1919-1939 in base 100 in 1919.

Both the overall and the bank-share indices seem to fluctuate together, while the Rente 3% only vary very slightly. It is interesting to observe how the data capture historical events that should have an impact on the series. We can see that the stabilization of the French franc boosted the banks stock prices, as well as the devaluation of 1936. On the contrary, the sterling crisis seems to accelerate the decrease in stock prices in late 1931. However, the impact of the Wall Street crash of October 1929 over the banking sector index does not seem straightforward.

In order to assess the stability of the banking sector, we rely on the methodology of Reinhart and Rogoff (2009), also used in Turner (2014) for the English case. The method consists in using bank-share prices and bank-share prices relative to the overall stock market, and is considered by the author superior than the study of failures. Even though Turner (2014) run its analysis of the English banking stability over a much longer period (1830-2010) and by using stocks' annual returns, we also compare the returns of our banking sector index relative to the overall market, but on monthly basis.

Figure 2 shows three main episodes (circled in dotted lines) of negative excess returns of our bank-share index (R banks ) relative to the index of the overall market (R cac40 ): i) in early October 1931, right after the sterling crisis of September; ii) in June and August 1936, right before the devaluation of the franc and iii) in September 1939, France's in the WWII. Those events are indeed destabilizing for banks, however this first result should be mit- igated by the magnitude of the banks' excess negative returns relative to the market. In Turner (2014), the only crisis considered systemic is the recent one of 2007-8. According to the author's calculation, bank stocks fell by almost 80% when the overall market fell by "only" 30%. In our case, the worst negative return occurred in 1931: bank stocks fell by 18% when the market fell by 15%.

This result leads us to reject the systemic hypothesis. To provide a more in-depth analysis, we estimate the risk of the banking sector relative to the overall market by using the portfolio theory. We estimate several equations in the Capital Asset Pricing Model (CAPM thereafter) in order to get the estimated beta of the banking sector, β banks .

β banks = cov(ER cac40 , ER banks ) var(ER cac40 )
With ER i the difference between the return of stock or index i and the return of the risk free asset. This calculation amounts to estimate the following regression, using the Ordinary Least Squares (OLS) estimation procedure:

ER banks = α + βER cac40 + u t (1)
The purpose of this calculation is to assess the risk in the following way:

If β > 1: the banking sector is more volatile (i.e. risky) than the overall market.

If β < 1: the banking sector is less volatile than the overall market.

We rely on a CAPM framework mainly for data frequency reasons. Indeed, monthly intervals does not allow to measure Value-at-risk (VaR) with the usual 10 days horizon. In fact, according to Alexander (2009), it is not appropriate to base historical VaR models on weekly or monthly data. The issue is similar for example for Stressed VaR (SVaR), which should be relevant in a financial stressed period as the 1930s. However, it has to be calculate on a minimum basis of one week.

We estimate Equation ( 1) for (i) the full period as well as for (ii) the 1920s (overall expansion) and (iii) the 1930s (overall recession). The first striking observation is that regardless the considered period, the estimated coefficient β is lower than 1, suggesting that bank stocks are on average less risky than the overall market. However, our risk measure almost doubles between the two sub-periods, confirming the riskier investment environment driven by the Great Depression. Nevertheless, our review of the literature on French banks suggests that one should distinguish banking activities according to their specialization.

Banks' stocks according to their specializations

We calculate a stock index for aggregated investment banks and for deposit banks. Each sub-indices is measured by taking into account three banks: Banque de Paris et des Pays Bas, Banque de l'Union Parisienne and Banque de l'Indochine for the investment banks index, and Crédit Lyonnais, Comptoir National d'Escompte and Société Générale for the deposit banks index. Figure 3 illustrates the series' evolution in level. A first look at the series outlines the fact that, according to their specialization, bank stock prices do not move within the same magnitude. During the bull phase of the 1920s, investment banks invested more in industrial firms. It seems that, especially after the stabilization of 1928, those banks' share price skyrocketed. It is not surprising since stabilization implied a devaluation of the French franc at one fifth of the pre-war parity. It meant that French exporters had a comparative advantage over England firms, since the UK stabilized its currency at the pre-war parity in 1925. On the contrary, the dramatic slump following 1929-1930 could be explained by the investment of business banks in Central and Oriental European countries. After the sterling crisis of 1931 and the subsequent failure of the Creditanstalt in Austria, runs on business banks such as Banque de l'Union Parisienne occurred and the latter seems to be well captured in the data.

At the opposite, inflation in France in the early 1920s and the consequences thereof on deposits could be an explanation of the low level of deposit banks' share prices. Indeed, the bear phase of 1929-1939 less affected those banks, given that they were less invested in neither industrial firms nor foreign markets. This view is confirmed by the risk analysis. It is interesting to note that even during the boom phase of 1919-1939, investment banks were less risky than the overall market (β = 0,84). Nevertheless, during the depression, these same banks were clearly riskier than the market (β = 1,37). For deposit banks, stock prices variations are only half of the overall variation during the 1920s, despite the very low diversification that a three share portfolio would offer regarding the overall index that includes 40 stocks. This analysis corroborates the hypothesis that a specialized banking sector may help as a buffer to exogenous financial shocks. Indeed, only business banks needed intervention of either authorities or bank syndicates in order not to fail. To make comparisons with other banking systems, the work of Richard Tilly (1998) is very insightful. As the author writes: "Neither bank-oriented nor market-oriented financial systems escaped the crisis; and it is not easy to say which system proved the more resilient". The German case is quite interesting. Although German banks suffered a lot from the Government's debt and policy and the weakness of the Reichsmark, Tilly (1998) notes that the competition among universal banks in the 1920s reduced their margin and encouraged them to invest in riskier businesses. As for other countries like Austria, Italy or Belgium, where universal banking was widespread, the crisis of the early 1930s caused Government interventions. For Italy and Austria, the State's ownership continued after the war, whereas Belgium took steps to separate commercial and investment activities, as in the US. Only the German universal banking system survived. For the US case, the Glass-Steagall act response to the large banking crisis of 1929-1933 could also be seen as a confirmation of our hypothesis. However, the study of Kroszner and Rajan (1994) tempers this view by showing that the comparison between performances of securities underwritten by commercial and investment banks prior to the Act shows no evidence of the need to separate those activities. In our current analysis, the French case seems to differ from the American experience.

Individual stocks riskiness

As a robustness check, we run the same regressions with individual bank series. Table 3 reports the estimated betas for both the business and the deposit banks included in our sample.

Results on individual series confirm the ones detailed in the previous section: busi- ness banks stocks are all riskier than the overall market during the 1929-1939 period, while deposit banks stocks are all less risky, even during the depression. Only the coefficient β related to Crédit Lyonnais's stocks is slightly above 1. Moreover, this risk measure seems to suit investment strategies well: the Banque de l'Union Parisienne exhibits the highest beta. It was indeed more invested in Central and Oriental European markets than the Banque de Paris et des Pays Bas. The Banque de l'Indochine invested more in Eastern Asian markets and as such, has the lowest β among the three banks. Finally, the Crédit Commercial de France, which raised the portfolio of discounted bills of the Central bank after the stress of October 1931 (as seen in Section 2.2.3), is riskier than the overall market during the 1930s with a β of 1.05, compared to the one prevailing during the 1920s (0,53).

Conclusion

Thanks to a new set of stock price data, we have estimated in this paper investors risk perceptions, according to the activity of several French banks. Our results show that this estimated risk differs between business and deposit banks. They then add new insights on the picture of the French banking crisis of the 1930s by relying on a different framework than the usual failures analysis. Moreover, this study goes against the argument stating that universal banking provides a more stable and diversified financial system. Indeed, during the stressful episode of the early 1930s in France, the specialized structure of the French banking system did help deposit banks to avoid panics and bank runs.

In addition, the paper highlights the need for historical microdata in order to get lessons from past financial events. In particular, it provides an example of a specialized banking system resilient in times of economic and financial crisis.

However, this study needs to be completed. In order to go further, a first interesting way would be to use balance sheets data to investigate which items explain stock returns the best. For example, the level of deposits or participations in other firms would probably help to understand the difference in the risk of bank stocks according to their activity, i.e. to their balance sheets. Balance sheets data on the banks' debt structure would also allow us to estimate a market-based measure of risk such as the distance-to-default. As we already have stock prices, it would only require to assess the "default-point" by using short-term and long-term debt data. It should be particularly interesting for our period of interest to see how such measures behave across two very different macroeconomic regimes (i.e. the 1920s and the 1930s). Also, bank level data would allow us to calculate capital and liquidity ratios in order to evaluate investors' interest in the management policy of the banks as well as their market discipline.

Another way to assess the systemic risk of the banking system should also be considered: the connectedness. The Social Network Analysis should be investigated through the lengths of interlocking-directorates. Such a study is possible because the Desfossés Yearkbooks report the names and functions of all board members for every listed company at the Paris' Bourse. Recent studies, such as Billio et al. (2012) use both monthly data on stock returns and different measures of connectedness under the Principal Component Analysis framework, in order to assess the role of different financial institutions (banks, hedge funds, insurances...) in the transmission of shocks.

Figure 1 :

 1 Figure 1: CAC 40, banks and Rente 3%, 1919-1939 Source. Author's calculation.

Figure 2 :

 2 Figure 2: Monthly returns of the banking sector relative to the overall market Source. Author's calculation.

Figure 3 :

 3 Figure 3: Investment banks vs. deposit banks, 1919-1939 Source. Author's calculation.

Table 1 :

 1 Table 1 summarizes the results for the estimated betas. estimated β by periods Notes. Figures in parenthesis are t-stats. If t-stat > |1,96|, the coefficient is significant at a 5% threshold.

		Full period 1919-1929 1929-1939
	β	0,73	0,55	0,91
		(19,56)	(10,75)	(18,1)

Table 2 :

 2 Table 2 reports the estimated betas for the two sub-indices. Estimated β according to specialization Notes. Figures in parenthesis are t-stats. If t-stat > |1,96|, the coefficient is significant at a 5% threshold.

		Full period 1919-1929 1929-1939
	Investment banks	1,1	0,84	1,37
		(17,8)	(10,73)	(14,8)
	Deposit banks	0,66	0,49	0,82
		(18,3)	(9,55)	(17,7)

Table 3 :

 3 Estimated β per bank Notes. Figures in parenthesis are t-stats. If t-stat > |1,96|, the coefficient is significant at a 5% threshold.

		Full period 1919-1929 1929-1939
	Banque de l'Union Parisienne	1,3	0,87	1,75
		(10,7)	(8,9)	(7,9)
	Banque de Paris et des Pays Bas	1,08	0,78	1,38
		(14,5)	(7,4)	(13,9)
	Banque de l'Indochine	1,02	0,8	1,25
		(12,1)	(7,3)	(9,8)
	Crédit Lyonnais	0,8	0,6	1,02
		(17,4)	(8,6)	(18,1)
	Société Générale	0,48	0,38	0,56
		(11,8)	(6,5)	(10,1)
	Comptoir National d'Escompte	0,68	0,48	0,86
		(13,7)	(6,8)	(13,2)
	Crédit Commercial de France	0,79	0,53	1,05
		(12,8)	(5,6)	(14,2)

http://www.marketwatch.com/story/why-italys-bank-crisis-could-be-ticking-time-bomb-2016-0

Financial Times, September

th 2016. 3 http://money.cnn.com/2016/02/05/investing/bank-stocks-worse-than-oil/. 4 Les Échos, February 12 th 2016.5 Accominotti (2012) provides empirical evidences of the international contagion of the 1931 crisis.6 Mouré, K., Managing the franc Poincaré, 1998.7 Sauvy, A., Histoire Économique, 1984.

Marseille, J, Les Origines inopportunes, 1980.

The law allowing banks to be found as joint-stock companies was voted in 1826 (Copartnership Act) in England, in 1825 in Ireland, while Scottish banks already had a quasi-joint-stock status, allowing unlimited liabilities. See[START_REF] Turner | Banking in Crisis: The Rise and Fall of British Banking Stability, 1800 to Present[END_REF].

E.g. Crédit Lyonnais. in 1919: capital share of 250 million francs, deposit (à vue) over 1.5 billion francs. Source: Desfossés yearbooks 1918-1921.

Banque de Paris et des Pays-Bas, Banque de l'Indochine, Banque de l'Union Parisienne are the most cited ones.

The famous crisis of 1882, when the decline and failure of one bank put the Paris Stock Exchange under large liquidity difficulties. See[START_REF] White | The Crash of 1882 and the Bailout of the Paris Bourse[END_REF].

See Tilly (1998).

See Caron and Bouvier (1979).

Up to April 1925, the main objective of the monetary policy is to keep the fiduciary circulation under 41 billion francs. Because the authorities could not manage to stay beyond this ceiling, it will cause the great scandal of the "fake balance sheets", described in detail in[START_REF] Blancheton | Les faux bilans de la Banque de France dans les années 1920[END_REF].

See Hautcoeur and Sicsic (1999).

Even though the French Cambistes were already making arbitrages on foreign exchanges, but gains was potentially low.

Crédit Lyonnais, Société Générale, Comptoir National d'Escompte de Paris and Crédit Industriel et Commercial.

Author's translation.

This famous case is depicted in[START_REF] Sauvy | Histoire Economique de la France entre les deux guerres[END_REF].

Minute of the Conseil Général, March 17 th 1932. Author's translation.

The author would like to thank David Le Bris for sharing his data on the 1919-1939 period.


Pierre Bui Quang

Jonas Heipertz

Natacha Valla

Keywords: gross international investment positions, home bias, correlation puzzle, financial structure, macro-prudential regulation JEL codes: G11; G15

International portfolio diversification has been shown to be subject to several puzzles, notably the home bias in equity investment, and the correlation bias. Taken together, those facts suggest that not only do investors tend to prefer domestic equity to foreign equity, but that, when they venture into cross-border investments, they do so in countries where stock prices are most correlated with home markets -contradicting the intuition that international investments are used to diversify portfolios more optimally. Our paper deals mainly with the correlation bias. It uses a dataset on French external financial portfolio positions produced by the Banque de France that allows a security-by-security analysis of international positions. We show that although insurance companies and investment funds are indeed more exposed to highly correlated markets, the way they arrange their portfolios at the security-level is consistent with the existence of a diversification motive.

International equity portfolio diversification: a sectoral and security-by-security analysis Introduction Amidst the unprecedented increase in cross-border financial transactions that took place over the past couple of decades, two key features emerge. First, portfolio investments -in particular in equity -are heavily allocated in domestic assets. This is the well-known equity home bias (EHB) -first documented in French and Poterba (1991), [START_REF] Lewis | Trying to explain home bias in equities and consumption[END_REF], and more recently by [START_REF] Coeurdacier | Home bias in open economy financial macroeconomics[END_REF] for equity as well as debt instruments. Even though it has steadily reduced in the developed world (and especially for euro area countries as shown for instance by [START_REF] Coeurdacier | The geography of asset trade and the euro: Insiders and outsiders[END_REF] over the last two decades, the share of foreign equities is still on average one third of the share implied by the basic Capital Asset Pricing Model (see [START_REF] Coeurdacier | Home bias in open economy financial macroeconomics[END_REF]. Following [START_REF] Coeurdacier | Home bias in open economy financial macroeconomics[END_REF], three classes of theoretical explanations have been proposed: (i) hedging motives in frictionless markets from non-tradable income risk or real exchange rate risk, (ii) trade costs in international financial markets and (iii) informational frictions and behavioral assets.

Second, given home bias, one expects a rational investor to compensate for its over-exposure to domestic risk by privileging investments in destinations whose equity markets are weakly correlated to the domestic market. The opposite of this is actually observed. Higher correlations between domestic and foreign stock returns are associated with higher equity investments, a situation to which we refer to as correlation bias.

Several explanations have been proposed to explain this result. [START_REF] Portes | The determinants of cross-border equity flows[END_REF] have found weak support for the diversification motive by controlling for informational frictions. [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] have conjectured that the correlation bias is driven by endogeneity of stock return correlations to financial integration. In particular, highly financially integrated economies are more likely to exhibit both stronger correlations of stock returns and high levels of cross-border asset holdings, given that it comes with a decrease in transactions costs, regulatory barriers, and other financial frictions. Following this line of reasoning, [START_REF] Coeurdacier | International portfolio diversification is better than you think[END_REF] instrument current stock return correlations by correlations prior to the stock market liberalization of the 1980s, arguing to thereby capture variations in current correlations that are unrelated to financial integration. They find that investors are driven by the diversification motive and, ceteris paribus, tilt their portfolio towards countries that provide better hedge against domestic risk. Building on Coeurdacier and 1 Guibaud (2011), [START_REF] Balli | The determinants of bilateral cross-border bond and equity flows: a sectoral analysis[END_REF] replicate the econometric analysis at the sectoral level using CPIS1 data from the IMF on portfolio holdings by financial institutions, insurance companies, corporations, households, and the government. They can solve the correlation puzzle for most of the sectors, while financial institutions and corporations are found to exhibit a stronger diversification motive than households and the government. Pericoli, Pierucci and Ventura (2013) also find diversification motive using fractional regression techniques and controlling for trade relationships.

On the whole, the existing literature is characterized by two main features. First, the correlation bias questions the optimality of investors' choices, and so far this question has been dealt with by trying to identify the potential omitted financial frictions responsible for this result. Second, the majority of research on the correlation bias (with the exception of [START_REF] Balli | The determinants of bilateral cross-border bond and equity flows: a sectoral analysis[END_REF] investigates diversification of the aggregated country portfolio and does not take into account differential investment behaviours across investor types (with possibly different degrees of risk aversion or institutional constraints). While this approach is interesting per se, we argue that empirical results on international portfolio diversification based on aggregate country portfolios might be biased and not allow conclusions on diversification of more disaggregated, i.e. sectoral portfolios (see, e.g. [START_REF] Galstyan | The holders and issuers of international portfolio securities[END_REF].

Falling into the strand of this literature, our paper aims at analysing the correlation bias for French investors. We go further than the previous studies thanks to the use of a unique database on French holdings of securities provided by the Banque de France, that allows us to analyse equity portfolio choice for each investor type at the security level. With this level of detail, we are able to show that although French investors are positively biased toward highly correlated equity markets at the country level, the magnitude of this bias differs a lot across investor categories. As far as the financial sector is concerned for example, it is very strong for insurance companies, intermediate for investment funds, and non-existant for banks. This result is different from [START_REF] Galstyan | The holders and issuers of international portfolio securities[END_REF] who found that banks are more sensitive to gravity-like determinants (that are closely related to markets correlation) than other financial corporations. 2Furthermore, the security-by-security dimension of our database allows us to go beyond the endogeneity concerns put forward by the literature. Whereas previous studies used gravity-like and instrumental variables in order to control for endogeneity in country-to-country positions, we are able to consider the determinants of portfolio composition within a destination country. This approach enables us to show that the observed correlation bias does not exclude the existence of a significant diversification motive in portfolio choices, as even "biased" financial sectors are composing their portfolio in each destination country so as to reduce its correlation with their oversized domestic portfolio. 3The rest of the paper is organized as follows. Section 1 provides a description of the dataset and gives an insight on the profiles of the different investor types. Section 2 assesses the strength of the home and correlation biases of international portfolio choices of French investors. Section 3 moves to the security-by-security analysis of portfolio choice. Section 4 concludes.

Data and descriptive statistics

Our analysis mainly relies on the database PROTIDE provided by the Banque de France that contains French international portfolio investment positions by investor type at the security-level. 4 It provides information on security characteristics on the integrality of equity holdings by French residents at quarterly frequency from March 2008 to March 2014. Data on outstandings, valuation (both due to market price and exchange rate changes) as well as flows are included. We use the detailed information on security characteristics and on the type of investor to construct sectoral domestic and foreign portfolios in stocks (in particular excluding investment fund shares). We also use security valuation rates to construct sectoral portfolio return indices and security return correlations for our security-level empirical analysis. This dataset allows us to consider international portfolio diversification for seven investor types, both financial and non-financial, the aggregate of which corresponds to the total country-level stock portfolio of French residents. We distinguish four financial sectors, i.e. investment funds, banks, 5 insurance companies and other financial institutions, and three non-financial investors, households, corporations, and the public sector. Throughout this paper, we are particularly interested in the portfolio choices of investment funds and banks as they are by far the largest investors in non-French equities (with a portfolio amounting to respectively 205 Bn Euro and 128 Bn Euro in 2014Q1) but also in the choices of insurances and households, who are second-orderly important (25 Bn Euro and 16 Bn Euro respectively).

To shed light on sectoral investment strategies, we look at the characteristics of the average foreign stock investment and overall portfolio performance by investor type as shown in Table 1. Insurance companies and investment funds tend to hold large positions on a small number of securities, with an average position by security at 25.0 Mil. Euro and 32.6 Mil. Euro respectively. Insurance companies also tend to invest in highly capitalized stocks (16 Bil Euro on average). This suggests a preference for more liquid and less volatile stocks. On the other hand, banks invest on average smaller amounts in less capitalized stocks. The low median investment position across all investor types suggests that the vast majority of investments are small and that the high average is due to a few very large foreign stock investments, i.e. a fat-tailed distribution of stock investments. Stock portfoliso returns and volatilities suggest that insurance companies have the highest risk aversion accepting a relatively low average portfolio return of 2.6% for the lowest volatility of 11.38% in the group of financial investors. Investment funds' and banks' foreign stock portfolios both exhibit higher average returns, and higher volatilities. Within the group of non-financial investors, corporations seem to be most risk-taking investors, with average stock portfolio return and volatility standing at 3.9% and 12.99% respectively, followed by the public sector and households. Finally looking at the correlation of the foreign stock portfolio with the domestic one, we observe that banks achieve the least correlated foreign stock portfolio (0.45) among the financial investors followed by other financial institutions, investment funds and insurance companies. Again, this could reflect the level of sophistication of portfolio management of the different investor types. Within the non-financial investor group, corporations realize the lowest correlation (0.37) with their domestic stock portfolio, followed by the public sector and households. Table 1: Descriptive statistics -based on the total sample Furthermore, investor-type specific investment strategies are also suggested by the portfolio turnover, that we define here as the ratio of the absolute value of flows (investments and desinvestments) into securities over the amount outstanding (see Table 2):

τ d = i∈P F d |F di | S P F d (1)
where P F d is the portfolio of securities held by sector d, F di is the net investment of sector d in security i over one quarter and S P F d is the volume of the portfolio (where the max is taken over the ex ante and the ex post volume). We interprete this measure as a proxy for dynamism and sophistication of portfolio management. Across all investor types, the turnover of the foreign stock portfolio is higher than the turnover of the domestic stock portfolio. As Tesar and Werner (1995) have pointed out, this suggests that variable transaction costs are an unlikely explanation to the home bias. We also find that portfolio management tends to be more dynamic in markets that have a low correlation with the domestic market, so transaction costs are probably not an explanation for the correlation bias either (except for banks, but it will turn out that banks are not as biased toward correlated markets as other categories of investors). Last but not least, there exist important differences in portfolio turnover across investor types. Banks manage their stock portfolios, both domestic and foreign, most actively with a turnover of 3.39 and 4.16, respectively, while the turnover of stock portfolios managed by insurance companies is 2.51 domestically and 2.89 for the foreign portfolio. If we interpret these differences as the result of unequal financial expertise, they may be indicative of different propensities to be subject to informational disadvantage or familiarity effect that may contribute to explaining correlation bias. They may also be explained by the differences in regulatory rules applicable to each investor type.

Stylized facts: Home and correlation biases

Let us now investigate the two perennial puzzles of international portfolio choice at the sectoral level for our seven investor types, i.e. the home bias and the correlation bias.

In frictionless financial markets, the most basic CAPM model suggests that the representative investor should hold the market portfolio, i.e. the share of her financial wealth invested into domestic stocks should be equal to the share of domestic stocks in the world market portfolio. The divergence of the actual holdings of domestic stocks from the market portfolio is the most commonly used measure of the home bias (see for instance Coeurdacier and Rey, 2013). 6 Since we are predominantly interested in differences across sectors, it suffices here to proxy the degree of sectoral home bias by the share of domestic stocks in the sectoral stock portfolio (since the share of French stocks in the world market stock portfolio is the same for all investors). Figure 1 shows that the degree to which investors venture abroad is very het- 6 In particular the home bias of the country i equity portfolio is measured as EHB i = 1 -Share of foreign equity in country i equity holdings Share of foreign equity in the world market portfolio erogeneous over investor type. Banks clearly have the most internationalized portfolios with a relatively low share of 35.2% of domestic stocks in their portfolios. On the opposite, insurances and other financial institutions hold the large majority of their stock portfolio invested in domestic stocks, while investment funds are in between (43.4%). Non-financial investors hold a very low share of foreign securities, but this may be due to the fact that direct investments are excluded from the database, whereas there are no equivalent limitations concerning holdings in French equities. 7 Moving to correlation bias, we measure its magnitude for each investor as the difference between the average correlation of foreign position and the average correlation of a "representative" investor composed of all countries that participate to the CPIS (Figure 2a) :

CB d = K k=1 ω d,k ρ F R,k - K k=1 ω CP IS,k ρ F R,k (2)
where CB d denotes the correlation bias, ω d,k is the share of country k in the international equity portfolio of the resident investor d, ω CP IS,k is the share of country k in the international equity portfolio of countries that participate to the CPIS, 8 and ρ F R,k is the correlation between French and country k stock market returns. 9 The comparison with the CPIS allows us to neutralize all country-specific factors that impact the country's attractiveness for international capital, such as market size, financial openness, information availability or country risk. A positive value of CB d indicates that the average portfolio of international investors is less correlated to French stock market than the portfolio of investor d. However, a part of the correlation bias may be explained by the fact that the average CPIS investor is less integrated in the Eurozone than France. 10 We therefore also compute an alternative measure of the correlation bias. Figure 2b shows our measure of the correlation bias net of the effect of Eurozone inte- 7 Meaning that participating interests in domestic entities are not excluded. 8 The CPIS data aggregates stocks and investment fund shares into equity in the broad sense. In order to obtain a proxy of stock liabilities outstanding for a given country, we multiply the broad-sense-equity from CPIS with the proportion of stocks in French holdings of broad-sense-equity for this country. This assumes that the composition of broad-senseequity liabilities of a country is homogeneous across creditors. 9 Empirical correlations on yearly returns are measured over the past ten years. 10 Lane (2006) has shown the existence of a "Euro Bias" in the global bond portfolio of euro area member countries. gration. Two correlations biases are computed separately for inside and outside Eurozone investments, and are then averaged according to the weight of each portfolio in the investors' foreign position:

CB EZ d = ω d,EZ ( k∈EZ ω d,k ω d,EZ ρ F R,k - k∈EZ ω CP IS,k ω CP IS,EZ ρ F R,k ) + ω d,outEZ ( k / ∈EZ ω d,k ω d,outEZ ρ F R,k - k / ∈EZ ω CP IS,k ω CP IS,outEZ ρ F R,k ) (3)
where EZ (resp. outEZ) is the set of Eurozone countries (resp. the set of non Eurozone countries) and ω x,EZ (resp. ω x,outEZ ) is the weight of the Eurozone (resp. non Eurozone countries) in the international equity portfolio of investor x, x being either the resident investor d or the CP IS investor. Both measures show that French investors tend to be positively biased toward countries with stock markets correlated to the French one. Nonetheless, there exists important differences depending on investor types. Insurance companies appear as "champion correlators", whereas banks seem to diversify their home portfolio by investing in less correlated countries. Investment funds are in an intermediate position, with a positive but less pronounced correlation bias. The correlation bias decreases a lot, for all investors, when we consider separately investments inside and outside the Eurozone and is overall close to 0 in 2013. Still our previous observations remain true: insurance companies stand out as "champion correlators", investment funds have a lower but positive correlation bias, and banks hedge their domestic risk on international markets.

Finally, the joint analysis of these biases shows that investors with a strong correlation bias typically are those with a strong home bias. Thus, both puzzles are linked. This makes them even more puzzling since investors displaying a strong home bias should have more incentives to invest in uncorrelated countries as pointed out by Coeudacier and Guibaud (2011). This observation also weakens the interpretation of Coeurdacier and Guibaud (2011) holding financial integration responsible for the apparent correlation bias, as we may expect financial integration to affect all investors equally.

International diversification at the security level

If resident investors are facing cross-border constraints that prevent them from efficiently hedging against domestic risk when they would actually be willing to, then -everything else being equal -we should observe investors composing their portfolios in each invested country so as to minimize their covariance with the domestic portfolio. We formalize this idea in subsection 3.1, and provide an empirical analysis in subsection 3.2.

Model

We consider a mean-variance investor who can invest in three countries: the home country (H), the neighbor country (N) and the foreign country (F). Each country has issued n k securities (with k ∈ {H, N, F }). We are interested in the porfolio choice of the home investor. The return of this portfolio is given by:

α r = α H [α H1 r H1 + ... + α Hn H r Hn H ] + α N [α N 1 r N 1 + ... + α N n N r N n N ] + α F [α F 1 r F 1 + ... + α F n F r F n F ] ( 4
)
where α k is the share of the investor's portfolio invested in country k and α ki the share of the investor's country k portfolio invested in security i. The return of security i of country k is denoted r ki . For notational clarity, we drop the time index.

For simplicity, we assume that all securities have the same expected return equal to zero. Therefore, the objective of the risk-averse investor reduces to minimizing the variance of returns subject to her budget constraint. We rule out short-positions.

The optimisation program is written as follows:

min {α} 1 2 V ar[α r] subject to: k∈{H,N,F } α k = 1 (µ 0 ) ∀k, i α ki = 1 (µ k ) ∀k, α k 0 (θ k ) ∀k, n k α kn k 0 (θ kn k ) ( 5
)
where µ 0 , µ k , θ k and θ kn k are Lagrangian multipliers associated to the constraints. To further simplify, we assume that the "no-short-position constraints" are not binding (implying that all θ k and θ kn k equal to zero for all k, n k ). Moreover, we assume that the investor is constrained to invest a minimum share ( ᾱH ) of her portfolio in the home country and a minimum share (ᾱ N ) of her portfolio into the neigbor country N :

α H ᾱH (λ H ) α N ᾱN (λ N )
These constraints are associated with Lagrangian multipliers λ H and λ N that represent respectively home bias and correlation bias.

Before computing the solutions, we introduce some useful notations:

Ω kl = CoV ar[(r k1 ...r kn k ), (r l1 ...r ln l )] k, l ∈ H, N, F αl = (α l1 ... α ln l ) l ∈ H, N, F
Then, the investor's objective can be written as

V ar[α r] = k,l∈{H,N,F } α k α l α k Ω kl αl (6)
and the Lagrangian of the investor's problem writes :

L = 1 2 V ar[α r] + λ H (ᾱ H -α H ) + λ N (ᾱ N -α N ) + µ 0   1 - k∈{H,N,F } α k   + k∈{H,N,F } µ k 1 - i α ki (7)
The first-order conditions of this problem imply for αk :

α 2 k Ω kk αk + l =k α k α l Ω kl αl = µ k 1 k ∈ H, N, F (8)
Finally, re-arranging the last equation, we find that the security-level portfolio allocation of the resident investor in destination country k ( αk ) is given by:

αk = Ω -1 kk ( µ k α 2 k 1 - l =k α l α k Ω kl αl ), k ∈ {H, N, F } (9)
This equation allows us to analyse the implications of portfolio constraints on the investor's optimal security choice. In particular, we can directly assess the sensitivity of security-level portfolio allocation (within-country) to the correlation with the home portfolio of the investor: it increases with the share of the portfolio invested in the home market (α H ) and decreases with the portfolio share invested in another country (α N and α F ). Indeed, the sensitivity of within country portfolio allocation to security correlation with the home country is given by the term multiplying the variancecovariance matrix Ω kH : α H /α k (k ∈ {N, F }). To fix ideas, we analyse the sensitivity to security correlation in three cases in more detail (i) neither home nor correlation bias, (ii) only home bias, (iii) both home and correlation biases. We denote with a * (resp. **, ***) the optimal portfolio shares of the investor problem in case (i) (resp. (ii), (iii)).

• Within country portfolio allocation in both N and F is more sensitive to security correlation with the home portfolio if there is home bias: ᾱH

/α * * k > α * H /α * k (k ∈ {N, F }).
• For security-level portfolio allocation in country F , we also have ᾱH /α * * * F > ᾱH /α * * F . Therefore, the correlation bias further increases this sensitivity.

• For security-level portfolio allocation in country N , however we have ᾱH /ᾱ N < ᾱH /α * * N . Therefore correlation bias would decrease this sensitivity compared to home bias.

• Nonetheless, the security-level portfolio allocation in country N remains more sensitive to security correlation with home country in case (iii) than in case (i), as long as constraints on home investment are more severe than constraints in neighbor investment : ᾱH /α * H > ᾱN /α * N .

Estimation results

For each investor we estimate the following equation:

Y ijt = α jt + βρ it + γσ it + θµ it + δπ it + it (10)
for Y ijt > 0, where Y ijt is the share of the investor's equity portfolio in country j invested in security i at time t, α jt is a country-time fixed effect (j being the country of the issuer of i), ρ it is the correlation between the investor domestic portfolio return and security i, σ it is security i's volatility, µ it is its return, and π ijt is the share of security i in the market capitalisation of securities from country j held by French investors at time t. it denotes the error-term.

Considering our model in 3.1, we expect that :

1. Investors with higher home bias and correlation bias will have a significant (negative) value for β. There are two reasons for this. First, as is clear from equation ( 9), a higher home bias leads to a higher sensitivity of within-country portfolio allocation to correlation with the domestic portfolio. The second reason is more statistical: as ρ pit measures the correlation between security p and the domestic portfolio of investor i, we may also expect that ρ pit is a good proxy for the correlation of the same security p with the portfolio invested in neighbor country securities. Thus, β may capture -in addition to the willingness to hedge against over-exposure to domestic risk -the willingness to hedge against over-exposure to correlated risks. 3 confirms that investors who have a high correlation bias have more incentives to diversify their home equity portfolio at the security-level. Insurance companies are the strongest country-level correlators and the strongest security-level diversifiers. Thus on average, in a given invested country, they hold larger positions in securities that are less correlated with their home portfolio. Investment funds diversify less over securities, but have also less biased aggregate portfolios. As shown in section 2, banks on the contrary are already well diversified across countries (lowest home bias and correlation bias) and seem therefore less concerned about security-level correlation. We consequently speculate that banks' investment choice in foreign securities could be rather driven by motives similar to those that drive domestic investment and therefore other than diversification of their home portfolio. Moreover, coefficients on volatility suggest that all investors, with the exception of banks, aim to avoid volatility, where insurance companies show the highest concern about reducing volatility. We interpret the positive sign on return volatility for banks as evidence for a "search for yield" motive. Securities with higher past return volatility constitute a riskier investment but might promise higher returns in the future. Banks tend to buy low and sell high.

IC

Moving to the second econometric consideration about the model (that if we estimate equation ( 9) separately for each destination country, the estimated βs should be more negative in less invested countries), we find no clear-cut confirmation of our prediction. Table 4 below shows the correlation between the estimated β k for each destination country k and log of the ratio α H /α k (where α H is the share of the investor equity portfolio invested in France and α k is the share of the equity portfolio invested in country k) averaged over time. For most investor types, the estimated correlations are not significant, and it is not significant either on the total resident portfolio. But we do find significant negative correlations between β k and α H /α k for insurance companies and general government, whereas we find no investor type for which there exists a significant positive correlation. Hence, these results are overall consistent with our model.

Conclusion

This paper uses the dataset PROTIDE on sectoral holdings of securities in order to investigate the correlation bias of French investors based on an analysis of international positions at the sectoral and security levels. We show that the magnitude of the correlation bias strongly differs across investor types. In particular, French banks seem to positively contribute to hedging the French international equity portfolio against domestic risk, and this hedging property seems to have increased over time. The same cannot be said about insurance companies and investment funds: they contribute negatively to this hedging, as we have shown that they would be decreasing the average correlation of their international equity portfolio with the domestic market should they be investing identically to the world-average investor.

Nonetheless, for these investors, we find that the existence of a correlation bias does not rule out a significant diversification motive. Indeed, although they are more exposed to more correlated markets, they seem to compose their portfolio in each market so as to lower its correlation with their oversized domestic equity portfolio. This would further confirm that the "correlation puzzle" does not originate from some exotic preferences of investors, but rather from omitted variables in econometric specifications. It also indicates that the correlation puzzle may be overstated.

Taken together, these results suggest that there exists several portfolio management strategies for the financial sectors to satisfy their willingness to diversify their equity portfolios. Insurance companies and to a lesser extent investment funds seem to have adopted a "second-order" diversification strategy, that may be compared to the "home-grown" foreign exposure considered by Cai and

  Funds = investment funds, OFI = other financial institutions, HH = households, CORP = non-financial corporation, GG = general government, RES = All resident investors, Pf = portfolio. Note 2 : * Total volume of the international equity portfolio in 2014Q1.

Figure 1 :

 1 Figure 1: Sectoral home bias -Share of domestic stocks in total stock portfolio in 2014Q1

  (a) Total (b) EZ, Non-EZ separately

Figure 2 :

 2 Figure 2: Sectoral correlation bias

  Funds = investment funds, OFI = other financial institutions, HH = households, CORP = non-financial corporation, GG = general government, RES = all resident investors. Note 2: Investments in countries where the portfolio is composed of less than 7 securities are omitted Note 3: Standard errors are in parenthesis and * (resp. **, ***) denotes significance at the 10% (resp. 5%, 1 %) level

  IC=insurance companies, Inv Funds = investment funds, OFI = other financial institutions, HH = households, CORP = non-financial corporation, GG = general government, PF = portfolio. Note 2 : cov(τ, ρ) refers to the covariance between the correlation of foreign markets to French market and the turnover on the portfolio to foreign markets.

		Domestic PF Foreign PF Total PF	cov(τ, ρ)
	IC	2.51	2.89	2.63	-0.33
	Banks	3.39	4.16	3.91	0.23
	Inv Funds	1.93	3.00	2.63	-0.48
	OFI	3.08	3.47	3.21	0.099
	HH	2.10	2.63	2.16	-0.27
	CORP	2.02	3.44	2.13	-0.03
	GG	1.59	3.24	1.88	-0.28
	Note 1 :

Table 2 :

 2 Descriptive statistics -Investor profiles

Table 3 :

 3 Security-level regressionsTable

  Note 1 : IC=insurance companies, Inv Funds = investment funds, OFI = other financial institutions, HH = households, CORP = non-financial corporation, GG = general government, RES = all resident investors. Note 2: All observations (β k , log α H /α k ) are weighted by √ N k N k being the number of observations used to estimate β k .

		Estimated correlation	p-value
	Banks	0.09	0.566
	CORP	0.08	0.660
	GG	-0.53	0.004
	HH	0.13	0.406
	IC	-0.39	0.049
	Inv Funds	0.04	0.823
	OFI	-0.23	0.217
	RES	0.21	0.172

Table 4 :

 4 Correlation between α H /α k and β k

Coordinated Portfolio Investment Survey.

This difference can partly be explained by the fact that we included investment firms in the banking sector, whereas the "other financial corporation" sector in[START_REF] Galstyan | The holders and issuers of international portfolio securities[END_REF] includes not only insurances and investment firms, but also pension funds and investment funds.

We obtain no such result for non-financial ones.

Excluding direct investment positions.

Including investment firms, as the bulk of them are in practice subsidiaries of banks.

If we estimate the value of the coefficient β for each destination country separately, then βs corresponding to countries that are least invested should be higher.

 [START_REF] Cai | International diversification at home and abroad[END_REF]. Further research may be aiming at making clearer whether this kind of circumvention strategies should be explained by sectoral-specific constraints in international diversification -in particular, prudential constraints -or by familiarity effects. It is worth noticing however that our descriptive statistics would indicate that the latter is at work, in particular concerning insurance companies, as they appear as less "sophisticated" investors.