Effect of Euro crisis on the relative performance between the country and Euro area specific Fama and French Three factor model : evidence from Germany

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Masters of Finance – Asset management Thesis

Effect of Euro crisis on the relative performance between the

country and Euro area specific Fama and French Three

factor model

Evidence from Germany

Author:

Supervisor:

Erkin Ilkay Özdemir

mw. Dr. E. Eiling

A thesis submitted in fulfilment of the requirements

for the degree of Masters in Finance

at the

Faculty of Economics and Business

University of Amsterdam

Thesis coordinator:

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Statement of originality

This document is written by Erkin Ilkay Özdemir, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business of the University of Amsterdam is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

This study examines the effect of the Euro Sovereign Debt crisis on the relative performance of the Euro Area compared to the German Fama and French three-factor model in describing stock returns listed on the German equity index with the underlying assumption of increased European stock market integration. Using monthly data from 1993-2017, OLS time-series regressions for several test portfolios are done. The results show that the relative performance of the Euro Area model increased during the years 2003-2012 which could correspond to increased European stock market integration. However, the substantial decrease in absolute and relative performance of the Euro Area model in the years 2013-2017 could be caused by the Euro crisis due to stock market segmentation. In segmented markets, local factors matters more than global factors which favours the Country model. Possible explanations for European stock market segmentation are increased sovereign debt risk, political uncertainty, bad credit ratings and large volatile inflation which occurred in this period. The results are robust across the different number of size and BE/ME sorted test portfolios and industry portfolios.

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Acknowledgement

I would like to thank professor Eiling for her support and feedback during the last weeks of writing. Moreover, special thanks to Emile Massau for his support with programming issues.

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1. Introduction

Did the Euro crisis have an effect on the relative performance between the country and Euro area specific Fama and French Three factor model in explaining the variation in stock returns under the assumption of financial stock market integration in the Eurozone? This paper tries to answer the question by examining the variation in stock returns in Germany.

Many investment practitioners and researchers in the field of asset management use the Fama and French Three Factor model for understanding portfolio performance, portfolio construction and estimating future returns. It is therefore important to understand what the common factors that are used in the FF 3FM are, that may affect returns and whether the relative performance is sensitive to investment periods. Moreover, the choice for using the Euro Area and Country FF3F model instead of the Country and Euro Area CAPM is motivated by studies that examine global asset returns co-movements. For instance, Bekaert et al. (2009) emphasize the additional descriptive power of Fama and French global and local risk factors compared to local and global CAPM in describing stock returns. One important economic driver that might determine the construction of the risk factors is market integration. Stock market integration can be seen as a process in which (inter)national stocks are more and more explained by common instead of local factors. In case of fully integrated equity markets, the price of risk would be equal across these markets and driven by the same factors. Therefore, an increase in stock market integration in a certain area could require a global or region risk factor instead of a domestic risk factor. Europe is such a region in which a Region specific model could improve the performance of the Fama and French 3FM. The European countries have put much effort to become a strongly integrated region. The introduction of the European Monetary Union in 1992 has had a substantial positive effect on European stock market integration1. First of all, due to the implementation of central monetary and policy rules and legislation. On top of that, the start of the EMU led to a more common inflation level and interest rates and a more balanced fiscal policy across EMU members. From the Eurozone countries, Germany is an interesting country to investigate. First of all, because Germany actively participated in the European integration process since the beginning of the EU. Furthermore, Germany has always been the leading country in the European economic policy. Also, Germany put a huge effort in constructing a common market and an economic and monetary union.

The sample period for this research also incorporates the introduction of a single

1_{Bekaert et al. (2013) finds increased stock market integration for EU members by measuring the level of}

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currency. The adoption of the Euro cancelled the exchange rate risk and legal boundaries between EU countries and led to an increase in common risk for European investors. Nevertheless, in 2009 in the aftermath of the financial crisis, the PIGS countries (Portugal, Italy, Greece and Spain) were not able to refinance their government debt without the support of other Eurozone countries and the European Central Bank. This led to the European Sovereign crisis in 2009 which caused downward pressure on European financial markets. The effect of the Euro crisis on financial stock market integration is still unclear. In 2018, the political unrest in Italy again resulted in a strong increase in the short-term Italian government bond rate in a short period and showed similar symptoms as during the Euro crisis. The question is how this increased risk in Italy affects the stability in the European Union and thus the behaviour of investors. A less stable European Union could result in financial stock market segmentation due to increased political risk and weak institutions2. Nowadays, there is no clear view on the effect of the Euro crisis on the performance of the FF3F model in explaining returns. One study about the Euro area FF3F model is done by Moerman in 2005. He concludes that the domestic FF 3FM outperforms the Euro area FF 3FM in describing stock returns for Euro area participating countries. Nevertheless, since 2005, events such as the financial crisis and the Euro crisis has occurred which could affect the performance of both models and thus lead to different results compared to the findings of Moerman (2005). I would like to shed light on whether the Fama and French 3FM is sensitive to different time periods by analysing sub-periods and comparing the relative performance between the country and Euro area specific Fama and French 3FM in explaining the variation in stock returns of listed stocks in Germany before and after the occurrence of the Euro crisis in 2009 under the underlying null hypothesis of integrated stock market integration. The results will be compared to findings of Griffin (2002) and Moerman (2004). Moreover, it is important to do research on the relative performance between the country and Euro area specific Fama and French 3FM in explaining the variation in stock returns since the choice of a domestic or Euro area model can essentially affect expected return estimates and therefore result into wrong risk management decisions, portfolio management and cost of capital calculations.

The findings of this study show that the Country model outperforms the Euro Area model throughout the sample (1993-2017) in absolute terms, but the relative performance of the Euro Area model does increase in the period 1998-2007, possibly due to increased European

2_{La Porta et al. (1997) and Bekaert (1995) show that characteristics of less stable markets such as limited}

regulation and accounting structure, bad credit ratings and high inflation levels could lead to segmented (equity) markets.

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stock market integration. Moreover, a possible long-term negative effect of the Euro crisis on the performance of the Euro Area model is observed. This statement is derived from the fact that the performance of the Euro area model drops strongly in absolute and relative in the years 2013-2017 due to an increase in pricing errors and a decrease in adjusted 𝑅𝑅2s. The results are robust across different size, and BE/ME sorted portfolios and industry portfolios.

Section 2 gives an overview of the existing literature regarding this subject and short historical description of the German stock market index. Section 3 presents the parts that belong to the methodology of this research. Section 4 describes the data that is constructed and used, and Section 5 describes the summary statistics. In section 6, the results are projected and analysed including robustness checks, and in section 7, a general conclusion is given concerning the results in section 6.

2. Literature review

2.1 Fama and French factors

This section gives an overview of existing literature on the relationship between firm-specific factors and its explanatory power concerning stock returns. The purpose of this section is to give background information on the risk factors and the most recent discussion about its validity and additional factors besides the three factors proposed by Fama and French.

The first risk factor of the model, the market excess return, is the CAPM which is related to the market risk premium. The market portfolio is a value-weighted portfolio of a certain market that serves as a proxy for the systematic risk. The higher the beta of the stock, the more systematic risk that stock contains. According to Fama and Macbeth (1973), assuming an efficient market portfolio, there exists a positive relationship between the level of systematic risk of a certain asset and its average return. The second risk factor is the SMB portfolio return. The SMB factor mimics the size effect in which small firms tend to have lower returns than large firms. According to Fama and French (1992b), small-cap firms usually have higher earnings on their assets compared to large firms. The HML factor mimics the value effect in which high value firms tend to have higher earnings on their assets compared to growth firms (Fama and French, 1992b). According to Fama and French (1996), weak companies that generate low earnings persistently usually have high book-to-market ratios and positive coefficients on the HML factor.

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firm-specific factors in stock returns. First of all, Banz (1981) tested whether the market value of listed stocks on the New York Stock Exchange explain returns. He states that firms with smaller market value have on average higher excess returns compared to firms with larger market value. Fama and French (1993) provide an asset pricing model that expands the CAPM model by adding size and value factor to the market risk factor. They conclude that the three factors do significantly explain stock returns. Moreover, studies done by Haugen and Baker (1996) and Chan et al. (1991) show that book-to-market ratio of firms does explain cross-sectional stock returns.

Despite the increasing empirical evidence in favour of the Fama and French factors, there is still disagreement about the interpretation of these risk factors. For example, Lakonishok et al. (1994) researched the source of value strategies that yield higher returns. They argue that these value size equity effects are the result of an overreaction of investors instead of inherently riskier strategies. Another study, which tests the empirical power of the Fama and French 3FM, is done by Lewellen in 1999. Lewellen (1999) examined the relationship between expected returns, risk and book to market ratio at portfolio level by using time-series data and concludes that the book to market ratio significantly explains expected stock returns. Moreover, after controlling for risk, the book to market ratio is not able to explain expected returns which does contradict the results of (Lakonishok et al. 1994). Zhang (2005) investigated the underlying economic mechanism that result into higher risk in case of value firms compared to growth firms. He conclude that the combination of expensive reversibility and the countercyclical price of risk makes it more difficult for value firms to decrease or increase capital compared to growth firms (Zhang, 2005). There is also another group that criticizes the empirical validity of the factors. First of all, Ferson et al. (1999) question the use of attribute-sorted portfolio returns for exhibiting risk variables for a certain asset pricing model. They show by using fabricated data that these characteristic categorized portfolios become appropriate risk factors without any relationship with fundamental risk exposure (Ferson et al. 1999). Berk (1995) examined whether size-linked consistencies in asset pricing models are anomalies or inherently explain partially the unexplained part of the cross-section of expected returns. He concludes that small market capitalization firms with high book-to-market ratios automatically earn higher average returns. In other words, this holds for both economic risk exposure and anomalies. Daniel and Titman (1997) argue that the higher expected returns on high book-to-market and small book-to-market capitalization firms are not caused by the covariance of these stocks with the risk factors. They show that the characteristics of these firms explain the cross-sectional deviation in stock returns. Daniel, Titman and Wei (2001) show that this result is

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robust for international data. They show that firm characteristics instead of risk factors explain Japanese stock returns.

Foye et al. (2013) tested the performance of the Fama and French 3FM in explaining stock market returns of countries that joined the European Union in 2004. They find a poor performance by the market value factor in the case of emerging European markets. Fama and French (1998) tested, under the hypothesis of market integration, whether one set of international risk factors is able to describe expected domestic returns. They conclude that a combination of a world market factor with a world value factor better explain expected returns than in the case without the world value factor. Many studies examined additional risk factors besides the Fama and French factors. Liu (2006) researched the importance of a liquidity risk factor in the capital asset pricing model. He shows that liquidity is a relevant source of priced risk exposure and he also finds that the liquidity risk premium is significant in the Fama and French 3FM and the CAPM model. The results of Liu (2006) are supported by a research conducted by Acharya and Pedersen (2003). Acharya and Pedersen (2003) built a liquidity-adjusted capital asset pricing model in which a stock’s required return is related on its expected liquidity and the co-movement of that stock’s return with the liquidity of the market. They show that liquidity risk both economical and statistically significant influences asset prices. Moreover, studies assessed whether variables that proxy macroeconomic conditions improve the explanatory power of the Fama and French model. These studies are related to the ongoing debate regarding the ability of the Fama and French factors to capture the macroeconomic links related to systematic risk. For example, Hahn and Lee (2006) investigated whether the default spread and term spread, which proxy for long-term and short-term business cycles, can explain the variation in stock returns explain the systematic differences in size and high book-to-market portfolios similar to the HML and SMB factors. They conclude that small stock portfolios and high book-to-market stock portfolios indeed have higher factor loadings on the default spread risk factor and term spread risk factor (Hahn and Lee, 2006). As a result, adding the term and default risk as risk factors could improve the descriptive power of the Fama and French 3FM by capturing the economic links that are related to systematic risk. These findings could also indicate that the usual Fama and French factors indeed fail to capture the macroeconomics links related to systematic risks. In that case, the model could perform worse during extreme high or low business cycles such as bubbles and crises. Fama and French (2015) introduced the five factor asset pricing model in which two new risk factors are added, namely profitability and investment. They conclude that adding these factors improves the performance of the model in describing stock returns compared to the FF3F model.

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It can be concluded that the Fama and French risk factors do significantly explain cross-sectional stock returns. Nevertheless, there is still disagreement about the interpretation of these factors. Besides the disagreement, several studies provide evidence that other risk factors such as liquidity risk and factors that proxy credit market conditions improve the performance of asset pricing models in describing stock returns.

2.2 Domestic and International risk factors

This section gives insights about the current literature related to global and domestic asset pricing models and its performance in describing cross-sectional stock returns. Financial stock market integration can be seen as a process in which linkages between stock markets becomes stronger. As a result, the co-movements between stock prices across countries or regions are expected to increase. This increase in co-movements can be explained by a more common stochastic discount factor. A SDF discounts the future cash flows of a certain asset to determine the price at present3. In fully integrated stock markets, international risk factors are the only relevant factors in explaining stock returns compared to domestic factors.

In order to estimate the cost of capital of a certain firm, both the CAPM and international CAPM can be used. Koedijk et al. (2002) examined the difference in cost of capital estimations by using the multifactor Solnik-Sercu ICAPM model including the international market portfolio and exchange rate risk premium and the domestic CAPM. They conclude that the single factor CAPM estimate significantly different cost of capital for only five percent of the stocks in the sample compared to the multifactor international CAPM. They argue that this result is mainly caused by the fact that domestic factors play an important role in describing individual returns due to shortcoming integration and the home bias puzzle (Koedijk et al. 2002). The equity home bias refers to investors who mainly invest in listed domestic equities despite diversifying benefits from investing their wealth also in foreign equities4. The explanation for the home bias puzzle partly lies in increased transaction costs and legal rules that could decrease the gains from investing abroad. The results of Koedijk et al. (2002) are supported by the literature study of Karolyi and Stulz (2002). Karolyi and Stulz (2002) examined the importance of global factors for financial security demand and pricing. They show

3_{Bekaert et al. (2013) state that in integrated markets, there should be a common discount rate (stochastic}

discount factor) within a certain industry.

4_{Brooks and Del Negro (2004) state that a decline in home bias portfolio holdings could increase the correlation}

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that international asset pricing models are not able to fully explain the portfolio construction of investors, equity streams, and the correlations between countries. The main reasoning for this shortcoming is the home bias of investors which increases the importance of local factors. Another study on the performance of a regional asset pricing model is done by Morelli in 2010. He constructed a portfolio consisting of solely European stocks and performed a maximum likelihood factor analysis to observe the common factors that explain European stock returns with the underlying hypothesis of financial market integration. The results show that between some of the 15 countries, there exist common risk factors that are priced (Morelli, 2010). Finally, Eiling et al. (2012) investigated the importance of currency, country, industry and world market factors in global asset returns. They conclude that currency and industry factors outperform the other factors in explaining international asset returns. They also state that the superiority of the international industry factors over country factors is analogous to financial market integration (Eiling et al. 2012).

Apart from the methodological discussion on asset pricing models, more studies have been performed answering a practical question that is related to this research. First of all, Griffin (2003) examined whether country-specific or global versions of Fama and French’s three-factor model better explain time-series variation in international stock returns. By analysing the adjusted 𝑅𝑅2𝑠𝑠 and the alphas, he concludes that the domestic factor model explains much more time-series variation in returns together with lower pricing errors compared to the world factor model. Additionally, Griffin (2003) examined the explanatory power of international models that combine both country and foreign factors. He finds an increase in explanatory power but weak economic importance. The methodology of Griffin has been applied for the Euro area in 2004 by Moerman (2005). According to Moerman (2005), the country specific three factor outperforms the Euro area specific model in describing stock returns. Nevertheless, the relative performance of the Euro area model is increasing. In both studies, the underlying null hypothesis of stock market integration is formulated. The choice of the null hypothesis is taken because an increase in stock market integration due to centralized monetary and policy rules and legislation could improve the relative performance of the Euro area model compared to the domestic model. Therefore, in the following part, findings from existing literature with regard to the analysis of European stock market integration is provided.

Conclusively, both studies conclude that the Fama and French risk factors at country level outperform a global or Euro area model in describing cross-sectional stock returns. Nevertheless, Moerman (2005) stresses out an increase in the importance of a Euro Area model. This leaves room for a further investigation into both Fama and French 3 FM models.

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2.3 European stock market integration

The most important contribution of this section is to provide an overview of results regarding European stock market integration. Since European stock market integration is taken as the null hypothesis of this research, it is important to shed light on this subject. First of all, Mylonidis and Kollias (2010) assessed the cointegration between the four largest European stock markets, motivated by the introduction of the euro, and find little evidence for cointegration but they also state that it is still in the process. Additionally, they find stronger convergence for the German and French stock markets (Mylonidis and Kollias, 2010). Kim et al. (2005) also analysed the European stock market integration by examining the influence of the European Monetary Union. They show a significant increase in stock market integration caused by macroeconomic convergence which is associated with the establishment of the EMU. More evidence in favour of European stock market integration is provided by the study of Cappiello et al. (2010). They examined whether the co-movements between the Eurozone stock returns at industry and state level changed after the implementation of Euro. They find an increase in equity return co-movements. According to Cappiello et al. (2010), the convergence of overnight interest rates and bond yields show that money markets and bond markets are already integrated in the Euro Area. Also, Bartram et al. (2007) investigated the effect of the Euro implementation on financial market dependence between European equity markets in the period 1994-2003. They show an increase in stock market dependence for Germany, Italy, Netherlands, France and Spain. The increase in market dependence started in 1998 together with the determination of the European Union membership. One research conducted by Fratscher (2002), in which he analysed the integration process of the European equity markets since the 1980s, provides evidence on increased European stock market integration. He finds that European equity markets have become highly integrated since 1996 and that the Euro has become more important in global financial markets. The results of Fratscher (2002) are supported by the results of the study conducted by Hardouvelis et al. (2006). Also, Hardouvelis et al. (2006) tested the amount of integration between the equity markets of Eurozone countries during the 1990s. They observe an increase in European stock market integration caused by the anticipation of a monetary union. With the underlying assumption of increased European stock market integration, Adjaoute and Danthine (2004) examined European equity returns and find a long-term increasing trend in correlations among stock returns at both country and industry level and a decrease in country specific factors. Last but not least, Bekaert et al (2009) examined

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the correlations between international asset returns by constructing country and industry portfolios of developed markets. They do not find a significant increase in co-movements for most markets except for Europe.

Despite the substantial amount of evidence in favour of European stock market integration, a large macroeconomic event such as the Euro crisis could stagnate the integration process or lead to segmentation. Bekaert et al. (2013) stress out possible ways, without formulating a definite conclusion, how the sovereign debt crisis in the Eurozone could negatively affect the stock market integration in the Eurozone. They argue that an increase in both sovereign debt risk, political uncertainty and bad institutions together with worldwide risk aversion could play a role. These developments may influence the way foreign investors estimate risk which could lead to increased stock market segmentation (Bekaert et al. 2011). During the crisis, the PIGS countries reported large deficits and fiscal imbalances which led to increased political and economic risk for these countries. These developments were reflected in the sovereign bond rates and the spreads between country bond yields. The large spreads priced the differences in volatility and credit risk perceived by investors (Lane, 2012). In other words, these spreads indicate the factors that Bekeart et al. (2013) mentioned that could affect stock market integration. More papers examined determinants of stock market segmentation. Weak political and legal institutions significantly increases liquidity costs of trading according to Lesmond (2005). Increased illiquidity could further segment equity stock markets. Moreover, bad credit ratings and large volatile inflation could also negatively affect market integration (Bekaert et al. 1995). These factors occurred during the Euro crisis.

Conclusively, studies show that the Fama and French 3FM is able to explain a substantial part of the cross-sectional variation in expected stock returns despite some disagreement about the interpretation of the risk factors. Moreover, there is evidence for equity stock market integration in the Euro area. Taking into account the possible negative effects of the Euro sovereign debt crisis on European stock market integration, research on the relative performance between the domestic or Euro area Fama and French factors in explaining expected returns before and after the Euro crisis in 2009 adds value to existing literature.

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2.4 Motivation and research question

The Euro debt crisis led to an increase in risk aversion in combination with negative equity returns (Stracca, 2013). Moreover, the equity indexes in countries that are considered safe such as Germany and US experienced negative returns. This result could signal that the Euro crisis indeed affected the European stock market integration. Due to an increase in risk aversion, more (German) investors might only invest in stocks listed in Germany. Sorensen et al. (2007) show that an increase in global risk sharing is related to less home bias investment behaviour. Moreover, they argue that international risk sharing is positively related to financial integration. In other words, if the Euro crisis leads to European stock market segmentation, this could stimulate home bias behaviour by European investors due to less international risk sharing. This, in turn, could result in a stronger performance of a local Fama and French 3FM.

The discussed literature review provides background information regarding the following research question:

“Did the Euro crisis affect the relative performance between the Country specific and Euro Area Fama and French Three Factor Model in describing stock returns?”

The underlying null hypothesis of stock market integration is used. In other words, I expect that an increase in relative performance of the Euro Area model compared to the Domestic model throughout the sample period (1993-2017) could correspond to European stock market integration. On top of that, it is expected that the occurrence of the Euro crisis leads to European stock market segmentation which could negatively affect the relative performance of the Euro Area model in the period after the crisis (2012-2017).

3. Methodology

3.1 Germany stock market index

This section gives an overview on the trends and developments of Germany’s equity market index. The list of firms that are used in the sample are obtained from the constituent list of the German total equity market index given in Datastream. The reason behind the choice to choose the total market index is that this index covers 80% of the available stocks of that country, which means that almost 99% of the total market capitalization of the country is covered (Moerman, 2005). Therefore, the large coverage makes the results from this study more

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representative for the complete listed stock market of Germany. An important starting point is to analyse the historical trend of the total market equity index in order to observe trends. This analysis can be used for explaining results of the FF3F model in describing stock returns.

Figure 2.4

This chart shows the historical German equity market index level for the period January 1, 1992 -January 1, 2018

The sub-period time ranges are analysed as follows: • January 1992 - December 1997

• January 1998 - December 2002 • January 2003 - December 2007 • January 2008 – December 2012 • January 2013 – December 2017

The choice for the sub-period time ranges is similar to the analysis in section 6 in which sub-period regressions will be done. In the first two sub-periods from 1992-2002, a gradual increase in the index is observed. The increase becomes steeper during the years 1999 and 2000. One possible cause for this could be the dotcom bubble in 2000 in which a general overvaluation in listed equities all over the world occurred due to over-optimism in the financial markets. It is very likely that this bubble also existed on the German equity market. The steep crash in 2001 is another signal which could indicate that there was indeed a bubble on the market that crashed

0 200 400 600 800 1000 1200 1400 1-1992 1- 4-1993 1- 7-1994 1- 10-1995 1-1997 1- 4-1998 1- 7-1999 1- 10-2000 1-2002 1- 4-2003 1- 7-2004 1- 10-2005 1-2007 1- 4-2008 1- 7-2009 1- 10-2010 1-2012 1- 4-2013 1- 7-2014 1- 10-2015 1-2017 Ind ex l eve l Date

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in 2001. In the next sub period from 2003-2007, another trend is observed. The index experienced a period of gradual increase. This period is partially characterized as the housing bubble which resulted in a bubble that crashed in 2007 and preluded the global financial crisis. The index level reached its lowest point in 2008 when the worst period of the crisis was reached. In the years after that, the index experienced a small increase until the end of 2010. The sharp depreciation happened in a period when the Euro sovereign debt crisis started. This might be one of the factors that explain the drop in value.

3.2 Fama and French factors

Two versions of the Fama and French three factor model will be estimated. The methodology of Griffin (2003) and Moerman (2005) will be used. The most significant difference between the methodology of Griffin and the method of this research is that instead of global factors, the Euro area factors will be used for the composition of the Euro area FF 3FM. This section provides a detailed explanation of the models used in this research.

The Fama and French 3FM puts a link between the expected return on a certain stock or portfolio in excess of the risk free return to three different factors. The first factor is the excess return of the market portfolio. The second factor represents the difference between the return on a portfolio of small market capitalization stocks and the return of big market capitalization stocks (SMB, small minus big). The last factor represents the difference between the return on a portfolio of high book-to-market stocks and the return on low book-to-market stocks (HML, high minus low) which incorporates the value premium.

3.3 OLS Regression specification

The following OLS regression will be done:

𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖 = 𝛼𝛼𝑖𝑖+ 𝛽𝛽𝑖𝑖∗ � 𝑅𝑅𝑚𝑚𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖� + 𝑠𝑠𝑖𝑖∗ 𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ ℎ𝑖𝑖∗ 𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝜀𝜀𝑖𝑖𝑖𝑖 (1)

where 𝑅𝑅_{𝑖𝑖𝑖𝑖}, 𝑅𝑅_{𝑓𝑓𝑖𝑖} and 𝑅𝑅_{𝑚𝑚𝑖𝑖} are the stock or portfolio returns, risk free asset and the market portfolio return, 𝛽𝛽_𝑖𝑖, 𝑠𝑠_𝑖𝑖 and ℎ_𝑖𝑖 are the coefficients for the factors and 𝛼𝛼_𝑖𝑖 and 𝜀𝜀_{𝑖𝑖𝑖𝑖} the pricing error and the

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error term. This regression will be performed based on country specific factors and Euro area specific factors.

The methodology will be applied to the domestic three-factor regression model 𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖 = 𝛼𝛼𝑖𝑖+ 𝛽𝛽𝑖𝑖∗ 𝐷𝐷𝑅𝑅𝑆𝑆𝐷𝐷𝑖𝑖+ 𝑠𝑠𝑖𝑖 ∗ 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ ℎ𝑖𝑖∗ 𝐷𝐷𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝜀𝜀𝑖𝑖𝑖𝑖 (2)

Where 𝐷𝐷𝑅𝑅𝑆𝑆𝐷𝐷_𝑖𝑖 is the German stock market index excess return, 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆_𝑖𝑖 the German small minus big portfolio and 𝐷𝐷𝐻𝐻𝑆𝑆𝐻𝐻_𝑖𝑖 the German high minus low value portfolio.

The following regression model represent the Euro area three-factor regression model 𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖 = 𝛼𝛼𝑖𝑖+ 𝛽𝛽𝑖𝑖∗ 𝐸𝐸𝑅𝑅𝑆𝑆𝐷𝐷𝑖𝑖+ 𝑠𝑠𝑖𝑖 ∗ 𝐸𝐸𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ ℎ𝑖𝑖 ∗ 𝐸𝐸𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝜀𝜀𝑖𝑖𝑖𝑖 (3)

Where 𝐸𝐸𝑅𝑅𝑆𝑆𝐷𝐷_𝑖𝑖 is the euro area euro area market excess return, 𝐸𝐸𝑆𝑆𝑆𝑆𝑆𝑆_𝑖𝑖 the Euro Area small minus big portfolios and 𝐸𝐸𝐻𝐻𝑆𝑆𝐻𝐻_𝑖𝑖 the high minus low value portfolio of the Euro Area. The Euro area Three Factor Model is given by Kenneth French’s library. The risk factors for the German stock market index are calculated in the same way as Kenneth French’s methodology which is the standard Fama and French procedure5.

Different portfolio categories will be tested within these models. First of all, the six value-weighted portfolios will be regressed against the German and Euro area risk factors. The research will concentrate on size-sorted portfolios and BE/ME-sorted portfolios and the intersection of these rankings. The criteria that will be used to assess the relative performance of both models are the adjusted 𝑅𝑅2s of each regression and the alpha, also called Jensen’s alpha, which is a proxy for the pricing error. The model that produces the lowest pricing error could be on average the best model in describing stock returns. In addition to the pricing error analysis, the Gibson, Ross and Shanken F-test will be performed to test for joint significance of the alphas of all portfolios. If the F-test rejects the null hypothesis that the pricing errors of the test portfolios are jointly equal to zero, this could be evidence that the asset pricing model is not able to fully capture the average stock returns. Test portfolios constructed on size and book-to-market ratio are used to see whether the replicating portfolios SMB and HML are able to capture common risk factors in stock returns that are linked to size and book-to-market equity. Under the null hypothesis of European stock market integration, a decrease in relative

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performance of Euro area FF 3FM compared to the domestic FF 3FM model is expected after the Euro crisis. As mentioned before, the Euro crisis could have a reversal effect and thus lead to financial market segmentation. Consequently, an increase is expected in the pricing error of the Euro area model and a decrease in the pricing error of the country specific model after the Euro crisis.

3.4 K-ratio

In order to make the relative performance between the Euro and German FF 3FM more transparent, the methodology of Moerman (2005) will be used. Moerman (2005) proposes the ratio of the mean absolute alpha of model i over the mean absolute alpha of model j as a measure of the relative performance of model i to j.

𝑘𝑘

𝑖𝑖𝑖𝑖

=

1

𝑛𝑛∗∑ | 𝛼𝛼𝒑𝒑 𝑝𝑝,𝑖𝑖| 1

𝑛𝑛∗ ∑ | 𝛼𝛼𝒑𝒑 𝑝𝑝,𝑗𝑗|

In this case, model i corresponds to the Germany FF 3FM and model j corresponds to the Euro area FF 3FM. An advantage of this ratio is that it shows the relative performance of both models in one single number. If k is smaller than one, the mean absolute pricing error of the country model is smaller than the mean absolute pricing error of the Euro model. As a result, the country outperforms the Euro model. By calculating the k-indicator for different subsamples, trends in performance can be analysed. For example, the k-indicator value for two subsamples divided by the Euro crisis could show whether the Euro crisis could have an effect on the performance of both models. Logically, possible underlying economic mechanisms should be explained in order to understand relationships between the Euro crisis and the performance of both models. Finally, as part of robustness check, the average alphas will be calculated separately for size-sorted portfolios, value-size-sorted portfolios, financial and non-financial portfolios.

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3.5 Robustness check

As part of the robustness check, the test portfolios will be constructed by sorting the stocks in the sample by book-to-market and by its size. Moreover, the amount of tested portfolios will vary from 3 to 6 and to 10 in both BE/ME sorted and size-sorted portfolios. The sorted portfolios will be formed similar to the six value-weighted portfolios. The criteria to evaluate the results are similar to the main analysis, namely the adjusted 𝑅𝑅2s and the alpha. On top of that, additional portfolios based on industries will be created. Financial stocks will be assigned to the Financials portfolio, and non-financial stocks will be assigned to the Non-financials portfolio. The two industry portfolios will not be sorted on size and BE/ME due to the small amount of stocks per industry. Via these additional test portfolios, regressions on the Euro area and Country factors could indicate whether the results are similar between financial and non-financial industries. Historically more regulated sectors such as the financial sector could be less integrated with the financial sectors in other countries in the Euro area compared to other industries. Therefore, a higher performance of the Country model is expected in case of Financials in the beginning of the sample period. Also the increased regulation after the global financial crisis could result into a relative stronger performance of the country model compared to the Euro Area model for the financials. Moreover, this analysis will be done for five sub-periods, in which each sub period contains five years. The first sub period will cover the years 1993-1997. The second sub period will contain the years 1998-2002 ending before the start of the housing bubble. In January 1999, the Euro as a single currency was introduced. The Euro adoption led to a decrease in both information and transaction costs and an increase in standardization of pricing. All in all, the introduction of a common currency further improves transparency and stimulates financial integration. This could affect the performance of the models. The third sub period will contain the years 2003-2007 before the start of the financial crisis. In order to shed light on the performance of both models during crises, the performance of both models in this period can be compared to the preceding and succeeding period. The final two sub periods will contain the years 2008-2012 and 2013-2017. In all these sub periods will the test portfolios be regressed against the Euro area FF3F model and the Germany FF3F model. Similarly, the alphas and the adjusted 𝑅𝑅2s will be analyzed and compared with each other. Also F-tests will be conducted to test for joint significance of the intercept of the test portfolios. Finally, the regression results of this research will be compared to the researches of Griffin (2003) and Moerman (2005).

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3.6 GRS test

The GRS test is implemented by Gibbons, Ross and Shanken (1989) and assesses the efficiency of a given test portfolio. In this research, the GRS test is performed to analyse whether the alphas of the six value-weighted portfolio intercepts are jointly equal to zero for both the German and Euro Area three factor model. Moreover, in case of robustness checks, the GRS test will be done for the different size and BE/ME sorted test assets. If the risk factors fully explain excess returns of test portfolios, a pricing error equal to zero is expected. In other words, if the observed alphas are jointly significant from zero, the GRS test statistic should also be equal to zero. The higher the value of the alphas, the larger the absolute value of the test statistic.

The following null hypothesis is tested by running an OLS regression and obtaining the alphas and test whether these alphas are jointly significant from zero:

𝐻𝐻0 = 𝛼𝛼𝑖𝑖 = 0 𝑓𝑓𝑓𝑓𝑓𝑓 𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖

The equation corresponding to the Fama and French three factor model is built as follows6:

𝐺𝐺𝑅𝑅𝑆𝑆 = �_{𝑁𝑁� ∗ �}𝑇𝑇 𝑇𝑇 − 𝑁𝑁 − 𝑘𝑘_{𝑇𝑇 − 𝑘𝑘 − 1� ∗ [}

′

𝛴𝛴−1

1 + ′𝑘𝑘 Ω−1 𝑘𝑘

]~𝐷𝐷(𝑁𝑁, 𝑇𝑇 − 𝑁𝑁 − 𝑘𝑘)

In this research, the number of test assets is equal to N and the amount of time-series observations is captured by T. Furthermore, k measures the number of factors used in the model and 𝑢𝑢_𝑘𝑘 refers to a k-vector of factor average returns whereby Ω refers to the k*k covariance matrix factor returns. The GRS test under the null hypothesis is based on a central F-distribution in which N counts the degrees of freedom for the numerator and 𝑇𝑇 − 𝑁𝑁 − 𝑘𝑘 counts the degrees of freedom for the denominator. From a large GRS value can be concluded that the asset pricing model is ineffective in describing stock returns since a large value indicates that the calculated alphas are jointly significant different from zero and thus the worse the model performs.

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4. Data description

The methodology will be applied to listed stocks in Germany from the start of the European Monetary Union in 1992. The reason for including the period before the introduction of the Euro lies in the fact that many regulatory rules were implemented within the EMU in order to increase the financial integration across European countries. It is interesting to see whether these regulatory changes have an effect on the performance of both models. The sample runs from January 1993-January 2018. The starting point in 1993 is chosen because the European Monetary Union is founded at 7 February 1992. The first complete year since the foundation of the EMU is 1993. Moreover, increasing the sample period to the years before 1993 would result into less listed stocks per year. A Euro area investor will be taken as a perspective with obtaining data. In other words, the stock returns will be prepared in the Euro currency.

4.1 Variables

The sample for this research consists of all individual stocks listed in the total equity market index of Germany in Datastream. This index contains the 250 largest and most liquid stocks of Germany and should therefore be a useful representation of the German equity market. The data for the index could be obtained via the Datastream-code LTOTMKBD. Stocks that are not listed in a certain year are still taken into account for this research in order to control for survivorship bias and thus an overestimation of performance from historical data7. Table A provides an overview on the amount of stocks taken into account per year. The total return index, which includes dividend yields, is used for the market return of Germany.

Returns are calculated with the following formula:

𝑅𝑅𝑖𝑖 = _𝑃𝑃𝐷𝐷𝑖𝑖 𝑖𝑖−1+

𝑃𝑃𝑖𝑖− 𝑃𝑃𝑖𝑖−1

𝑃𝑃𝑖𝑖−1 ∗ 100

Here, 𝑅𝑅_𝑖𝑖 is the return on a certain firm’s stock, 𝐷𝐷_𝑖𝑖 the dividend of that stock in month t, 𝑃𝑃_𝑖𝑖 the closing stock price of that firm at the end of the month and 𝑃𝑃_𝑖𝑖−1 the closing price of that firm

7_{All the single stocks that are in the German total market equity constituent list are shown in the Appendix B}

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one month before. The market capitalization is obtained from Datastream and calculated as; Market Price –Year End * Common shares outstanding. The book-to-market ratios for each month is also obtained from Datastream and calculated as the inverse of the market-to-book value. The returns and book-to-market ratios are calculated within Matlab. The three month German government bond yield which can be seen as a proxy for the risk free asset, is retrieved from the OECD database. The short-term interest rate is the rate at which government bonds are issues or traded on the markets. In this study, the short-term interest rate is based on the three month German bond rate. The monthly short-term interest rates are the average of daily rates which is measured in percentages.

4.2 Fama and French Methodology

The Fama and French methodology will be applied for selection criteria and the formation of portfolios. First of all, the stock that belongs to a firm will be included in the analysis if the stock price for that firm is available for June of that year. The book-to-equity/ market-to-equity is defined as total shareholder’s equity on December t-1 divided by the total market capitalization of that firm on December t-1. The market capitalization that is used to sort stocks on their size is based on the market capitalization on March 31st_{. In the next step, all stocks that}

meet the selection criteria are ranked into three groups based on their BE/ME and two groups based on their market capitalization in September at country level. After the construction of these groups, the intersection of the six BE/ME and market capitalization rankings will be transformed into six size and book-to-market value weighted portfolio returns in order to simulate the underlying risk factors that are related book-to-market value and size of firms. An important motivation for the usage of weighted portfolios lies in the fact that value-weighted portfolios better capture the different return trends of small and big stocks and low and high book-to-market stocks that are more realistic in terms of investment opportunities (Fama and French, 1993). All stocks with positive book-to-market ratios on December t-1 and market capitalization on or before March 31st fiscal year-end and market capitalizations as of March 31st are ranked independently according to their size and BE/ME ratio. In the next step, the sample of firms will be classified equally as small market capitalization firms (S for small) and large market capitalization (B for big). The intersection of the two rankings gives six value-weighted portfolios: HB, MB, LB, HS, MS and LS. These six value-value-weighted portfolios allows

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for constructing the two risk factors. The first return variable ‘SMB’ (small minus big) for each country is constructed as follows; (HS+MS+LS-HB-MB-LB)/3. The return variable ‘HML’ (high minus low) for each country is constructed by; (HS+HB-LS-B)/2. These risk factor returns are calculated for each month. Furthermore, the high (H) BE/ME portfolios and low (L) BE/ME portfolios are obtained as H = HS+HB and L = LS+LB. The portfolios are constructed once a year in June. Datastream offers the market-to-book value. Therefore, in order to retrieve the book-to-market ratio, the inverse of the market-to-book ratio is needed for all stocks within the constituent list of the German total equity market index. In order to control for survivorship bias, delisted securities will be incorporated in the sample. Additionally, due to possible systematic differences across firms with book-to-market values, firms without book-to-market values are still included in the analysis but placed in a missing group.

The Euro area three factor model is obtained from Kenneth R. French’s data library. They constructed the risk factors for the European countries. The countries that are taken into account are: Austria, Belgium, Switzerland, Germany, Denmark, Spain, Finland, France, Great Britain, Greece, Ireland, Italy, Netherlands, Norway, Portugal and Sweden. Logically, The Fama and French methodology is applied when constructing the risk factors. Moreover, the market is the return on a region’s total value-weight market portfolio minus the risk free rate. One difference between the Euro area model from French’s website and the Germany model is that the returns of the Euro area model are denominated in Dollars while the returns in the German model area Euro denominated. This discrepancy does affect the performance analysis. Therefore, the US dollar denominated European risk factor returns needs to be converted into Euro denominated returns. The conversion is done by using the spot exchange rate between the Euro and US Dollar. The spot exchange rate is retrieved from Datastream and formulated as the amount of Euro that an investor receives for paying 1 US dollar. The following equation holds for the calculation of the Euro denominated returns8_:

𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸,𝑖𝑖+1€ = ⎝ ⎛� 1 + 𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸,𝑖𝑖+1𝐸𝐸𝑈𝑈$ � ∗ �𝑆𝑆 � € 𝑈𝑈𝑆𝑆$ � � 𝑖𝑖+1 𝑆𝑆 � € 𝑈𝑈𝑆𝑆$� � 𝑖𝑖 � ⎠ ⎞ − 1

𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸,𝑖𝑖+1€ = Return of the size factor for the Euro Area expressed in Euro.

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𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸,𝑖𝑖+1𝐸𝐸𝑈𝑈$ = Return of the size factor for the Euro Area expressed in US Dollar.

𝑆𝑆 � € 𝑈𝑈𝑆𝑆$� �

𝑖𝑖= Spot exchange rate of € per 1 US$.

5. Descriptive Statistics

5.1 Risk factors

In the following subsection are the descriptive statistics of the explanatory variables, the summary statistics concerning the mean return, standard deviation, skewness, kurtosis and the Jarque-Bera value for the complete sample period analysed.

Risk factors average risk premiums

Table 4 gives an overview of the average risk premiums for the common risk factors in stock returns which are the average returns of the independent variables. The average mean excess return of the German market index is negative with a value of -1.73%. That means that per unit of market beta, the average market excess return is negative. This is also statistically significant (t=-5.12). The second remarkable result from the summary statistics is the negative mean return of the German SMB portfolio with a value of -0.12 percent per month. According to the data, the mean returns of small caps firms are on average lower than large-cap firms while a positive average size-related risk premium would be expected in the returns in the SMB portfolio (Fama and French, 1993). Although according to the t-test that gives a value of -0.56, it is not statistically significant different at 5% from zero. The HML portfolio does produce a mean premium return of 1.32 percent with a t-value of 5.51 which is both economically and statistically significant at 1%. In other words, the value-related premium is significantly positive which is in line with the results of Fama and French (1993). They found a premium of 0.40% per month with the corresponding t-value of 2.91. The Euro area average market excess return is also negative and statistically significant different from mean zero (t=-4.86). Both in terms of statistics and economics are the average excess market return of Germany and the Euro area comparable to each other. In contrast to the negative mean return of the German SMB does the European SMB risk factor give a positive average return of 0.15% per month with the corresponding t value of 0.76 and therefore is lacking both economical and statistical significance. The final European risk factor, HML, produces an average return of 0.46% per

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month and is therefore remarkably lower than the country HML. This observed average return is, therefore, both economically and statistically large (t=2.21). The Jarque Bera test takes into account both the skewness and kurtosis to check whether it matches a normal distribution and it is adjusted for the small sample size. In all cases is the null hypothesis of normality rejected at 1% except for the Euro area excess market return. However, this result was expected since asset pricing models are usually biased and skewed (Lewellen et al. 2010)9.

2

48-month rolling average return and standard deviation of the market factors.

Figure 1-3 represent the 48-month rolling average return, standard deviation and correlation coefficient of the German and the Euro Area market factor. Market fluctuations can be more properly detected and analysed in this structure. The sample period incorporates large economic happenings that impacted stock prices such as the dotcom bubble and the housing bubble and the subsequent global financial crisis. These market situations undoubtedly affected the market returns. The dotcom bubble started in 1997 and ended approximately in 2000. This bubble could explain the increased average return of both market factors in this period. Moreover, the standard deviation increased gradually in the same period for both the Germany and the Euro Area market return. During the start of the financial crisis in 2007, all the market portfolios realized negative average returns in combination with increased volatility. The average large drop in stock prices and increase in standard deviation indicates the stock market crash in 2007-2008. Also, the Euro crisis which reached its most critical point in 2011 possibly affected the stock markets. However, in this period of increased sovereign debt risk and political uncertainty, the volatility of the average excess market return of Germany and the Euro area increased, but the mean excess returns became positive from 2011-2012. In the final period, contain the years 2013-2014 and 2015-2017, the returns of both markets remain positive without in combination with a gradual decrease in volatility. All in all, figure 1 and 2 show that the 48-month rolling average return and standard deviation of the German and Euro Area market strongly co-move during the sample period. Only during the years 2009-2015 did the German market experience higher volatility than the Euro Area market. However figure 3 shows a positive correlation between both market returns in the years 1996-2011 and a negative correlation in the last six years which is the period after the Euro crisis.

9_{Lewellen et al. (2010) emphasize the importance of confidence intervals instead of standard errors due to the}

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Correlation matrix

The correlation matrix in Table 5 could give an indication of multicollinearity between variables. In that case, high correlations would be expected. Mason and Lind (1996) indicate that there is no multicollinearity if the Pearson correlations are between -0.70 and 0.70. From the matrix, it can be seen that for the German factors, the highest (negative) correlation is -0.3346 between the market excess return and SMB factor. The second highest correlation is between the HML factor and the SMB factor with a value of -0.1935. As a result, there is not sufficient evidence to assume multicollinearity between the German risk factors. The correlations between the European risk factors are larger than the German factors but remain within the Mason and Lind (1996) bounds. The largest (negative) observed correlation is between the EU SMB and EU market return with a value of 0.5199. In other words, the conclusion of non-multicollinearity between the risk factors does also hold for the European variables. It is interesting to see to what extend the German market index does co-move with the European market index because a high correlation could indicate the level of stock market integration within the Euro area. A correlation of 0.2566 is observed between these indices which is relatively small. Higher correlations would be expected in case of integrated markets such as Germany. The correlations between the SMB factors (-0.0861) and HML factors (0.0856) are also substantial small and thus in line with the excess market return correlation. These results do not agree with previous studies that examined correlations across Euro Area equity returns such as Gjika and Horvath (2013) and Adjaouté and Danthe (2004)10. It can be concluded that the correlations between the Country and Euro Area factors do not necessarily indicate integrated stock markets between the Euro Area and Germany.

5.2 Six Value-weighted portfolios

Table 6 shows the differences in average excess returns between the six value-weighted portfolios over the complete sample period from 1993-2017. First of all, it can be seen that the volatility of the portfolios are quite similar to each other. Based on the CAPM theory, you would expect that fully diversified portfolios would produce the highest Sharpe ratio. In other words, the highest excess return given the amount of systematic risk. When analysing the mean

10_{Both Gjika and Horvath (2013) and Adjaouté and Danthe (2004) find increasing long-term correlation}

between European equity stock markets. However, Adjaouté and Danthe (2004) also point out an unusual low correlation in the years 1996-1999.

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excess returns in combination with the volatility, it becomes clear that portfolios producing the highest mean excess returns do not necessarily have higher volatilities. That could indicate that the portfolios that have lower mean excess returns but higher standard deviations are not adequately diversified regarding idiosyncratic risk.

There is no clear indication of a size effect from the table. When controlling for the value effect, small and low BE/ME firms have on average higher excess returns than large and low BE/ME firms. However, in case of high BE/ME firms, large-cap firms outperform small-cap firms on average. Nevertheless, there is some evidence in favour of the value effect. When controlling for size, small high BE/ME firms outperform small low BE/ME firms. The same conclusion can be drawn for large firms. All in all, the descriptive statistics give insights about the data which can be used for further explanations of the regression results in a later stadium.

6. Results

6.1 Regression results

The following section elaborates on the regression results and the analysis of these results. The criteria to assess the results are similar to the criteria of Griffin (2002) and Moerman (2005). First of all, Jensen’s alpha, which measures the pricing error, will be analysed. On top of that, the adjusted 𝑅𝑅2s will be reviewed. According to the null hypothesis of a perfect fit, the predicted alpha in the estimated equation should have a value equal to zero. Logically, for all the dependent variables consisting of test assets, the mean absolute pricing error and the adjusted 𝑅𝑅2 is given.

Table 7: Sub-period analysis

First of all, a general conclusion can be formulated from the results containing the complete sample period from 1993-2017. The observed alpha, also called the pricing error from the country model is substantially larger compared to the alpha of the Euro Area model. But when looking at the adjusted 𝑅𝑅2, it becomes obvious that the Country model outperforms the Euro Area model with a value of 0.8848 compared to 0.1100. Despite the larger pricing error, the German model does better explain variation in stock returns of German listed stocks than the Euro area model. This result is not striking, since the German risk factors are constructed

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from the same test portfolios. Nevertheless, analysing sub-period performance measures could give insights in the behaviour of both asset pricing models in describing the cross-sectional stock returns of the value-weighted portfolios.

Starting with the first subsample covering the years 1993-1997, the results show that the value-weighted portfolios have an alpha which is on average 2.0684% and an average adj, 𝑅𝑅2 of 0,8609 in case of the Country model. Both measures remain below the complete sample average. The European model produces an average alpha of 0.7182% and adjusted, 𝑅𝑅2 of 0.1453. These numbers indicate that the European model does perform better in describing German cross-sectional stock returns in the first subsample compared to the complete sample. The years 1993-1997 are the first few years after the foundation of the European Monetary Union. Stage two was implemented in this period in which a forerunner of the current European Central Bank was founded with the goal of improving the monetary cooperation between the member countries. Moreover, the Stability and Growth Pact was adopted in order to implement budgetary rules and a new exchange rate mechanism in order to stabilize the currencies of participating countries and the euro which would be introduced in 1999. In other words, an increase in financial integration and possible stock market integration was expected in subsequent years after the first sub sample.

From Panel C in table 7, it can be seen that the Country model produces an average alpha of 2.0223% which is smaller than the period before and an average adj. 𝑅𝑅2 which has also decreased compared to the period before. As a result, it is difficult to point out whether this model does perform better in describing stock returns compared to the period before. This also holds for the European model in which the pricing error increased from 0.7182% to 0.8567% and the adj. 𝑅𝑅2 from 0.1452 to 0.1691. Important developments are the introduction of the euro as a single currency in 1999 and the introduction of a definitive single monetary union. These two occasions are expected to further improve the financial integration within the Euro area. Existing literature provides sufficient evidence for increased stock market integration starting from this period. Therefore, an increase in performance of the Euro Area model was expected but did not occur when analysing the pricing error. Another event to take into account is the dotcom bubble which occurred roughly in 1997-2001. Such a worldwide overpricing in stock market in which prices are unlocked from their fundamentals could decrease the performance of asset pricing models. This might explain the stagnation in performance of both the European as well as the Country model in describing stock returns since the Fama and French risk factors could fail to proxy risks related to business cycle fluctuations.

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of both asset pricing models. First of all. The Euro was implemented and used from 2002. As mentioned before, a single currency excludes exchange rate risk, and increases transparency across stock markets by standardizing prices and results into more common risk for European investors. This could be in favour of the Euro Area model since this model uses European risk factors as explanatory variables. Moreover, the housing prices expanded at a high pace resulting into a bubble and led to the global financial crisis from 2007. As mentioned before, extreme business cycles such as the housing bubble could result into weaker performance of asset pricing models due to its inability to capture the macroeconomic mechanism related to systematic risk11. Panel D shows an increase in the mean pricing error but also an increase in average adj. 𝑅𝑅2 of the Country model. These results again do not give a clear conclusion about the change in performance. More interesting is the performance of the Euro model. The average alpha increases to 2.4051% and the average adj. 𝑅𝑅2 increases from 0.1691 to 0.2409. The higher average adj. 𝑅𝑅2 could be evidence of increased financial and stock market integration despite the higher pricing error. This result can be compared with the conclusion of Moerman (2005) in which an increase in relative performance of the Euro model was observed. Moreover, it is interesting to see a continuation in his findings since the sample in Panel D are the first five years that follows up the complete sample of Moerman (2005).

The global financial crisis started in 2007 and continued in the subsequent years. This could affect the performance of both models. Also the Euro crisis that started in 2009 and reached its most critical point in 2011 could influence the performance of both models. As mentioned before, the Fama and French model is not adjusted for extreme events (e.g. time varying betas) such as crises despite the noticeable impact of these crises on risk levels. On top of that, a sort of event study methodology is difficult to construct in case of crises. Crises could be seen as a series of events that could result into a “domino effect” in the global market without certain start and ending dates. Therefore, instead of assuming a start and ending date, the choice has been made to split the sample in sub periods of five years. The results in Panel E do not indicate a strong decrease in performance. In case of the Country model, with an average value of 3.3387%, a strong increase in the pricing error is observed. Nevertheless, the average adj. 𝑅𝑅2 (0.9308) improved compared to the period before. The opposite is observed for the Euro Area model in which both performance measures decreased (alpha = 2.3821%. adj. 𝑅𝑅2= 0.2179). In other words, the Country model lost some power due to an increase in the average pricing error

11_{Brooks and Del Negro (2004) show that stock market bubbles could stimulate co-movements across national}

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but meanwhile improved in terms of describing power due to an increase in the average adj. 𝑅𝑅2 while the Euro Area produced a lower average pricing error and lower average adjusted 𝑅𝑅2. Conclusively, the short-term effect of the Euro crisis on both asset pricing models is ambiguous.

The final period contains the years 2013-2017 in which the aftermath of the Euro crisis is taken into account. From the Country model point of view, the average pricing error decreased (from 3.3387% to 2.6109%) compared to the period before and approached its average level of the complete sample. In terms of adj. 𝑅𝑅2(from 0.9308 to 0.9106), the model ended worse off with respect to the previous period. Therefore, the net change in performance is ambiguous. More interesting are the performance measures for the European model in which a strong decrease in performance is observed in both the pricing error (from 2.3821% to 3.6806%) as well as the adj. 𝑅𝑅2 (from 0.2179 to 0.0072). An adj. 𝑅𝑅2 close to zero indicates a poor performance of the Euro Area model and the alpha is more than twice as large as the full sample average alpha. These two results could indicate that the Euro crisis indeed negatively affected the performance of the Euro area model on long-term. As mentioned before, an increase in sovereign debt risk and political uncertainty could negatively affect stock market integration. Moreover, bad credit ratings and more volatile inflation also characterized the period during the Euro crisis. These occasions could affect the way how investors estimate risk and stimulate home bias behaviour resulting into segmentation in stock markets.

Figure 4 visualizes the ratio of average alpha from the Country model over the average alpha from the Euro Area model. An increase in ratio means that the average pricing error of the Country model becomes relative larger than the average pricing error of the Euro Area model. The ratio is equal to 2.88 in the period (1993-1997) and decreases to 2.36 and 1.04 in the next two periods which shows that the Country model performs relative better than the Euro Area model in terms of average alpha. Therefore, the hypothesis in which an increase in relative performance of the Euro Area was expected, does not hold for the years 1993-2003. However, the k-ratio becomes larger during the years 2008-2012 which favours the Euro Area model. Finally, the ratio becomes smaller in the final period which is caused by a relative increase of the Euro Area average alpha. This could indicate that the Euro crisis could have affected the performance of the Euro Area three factor model on long-term.

It can be concluded that the hypothesis of increase in relative performance of the Euro model compared to the Local model, under the null hypothesis of European stock market integration is partially observed when looking at the average adjusted 𝑅𝑅2. The Euro model average adjusted 𝑅𝑅2 increased more compared the Country average adjusted 𝑅𝑅2 for the period 1993-2012. However, the mean alphas do not indicate an increase in performance for the

Effect of Euro crisis on the relative performance between the country and Euro area specific Fama and French Three factor model : evidence from Germany

Masters of Finance – Asset management Thesis