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Domestic Factors dominate the Fama and French Three-Factor
Model in the EMU
Ruben W. van de Biezen1 ABSTRACT
In an Economic and Monetary Union of the European Union (EMU) context, I test domestic, international, and EMU versions of the Fama and French (1993) three-factor model (3FM). The tests are performed on portfolios of German and French stocks in the period 08/1993 till 07/2011. The results indicate that in the application of the 3FM in an EMU context, domestic factors dominate the 3FM. Furthermore, the findings show that the integration of the stock markets in the EMU is an ongoing process.
This paper investigates whether the time-series variation in stock returns in the Economic and Monetary Union of the European Union (EMU) is described best by domestic, international or EMU versions of Fama and French’s (1993) three-factor model (3FM). The three factors proposed by Fama and French’s (1993) to explain expected returns are (i) the market return in excess of the risk-free rate, (ii) the difference between the returns of portfolios with small- and big-stocks, and (iii) the difference between the returns on high and low book-to-market equity portfolios. In my domestic version of the 3FM the factors are constructed using domestic stock returns. For the EMU version of the 3FM, EMU stock returns are used to construct the factors. In the international version of the 3FM, foreign factors, constructed using non-domestic EMU returns, and domestic factors are used.
Traditionally, the 3FM is applied in domestic contexts, following Fama and French (1993), whom test the 3FM in the US. However, stock markets around the globe are integrating more and more over time, (e.g., Goetzmann, Li and Rouwenhorst, 2005; Volosovych, 2011; Berger and Pozzi, 2013) and in an efficient and integrated capital market, there should be only one set of factors for the 3FM that describe the returns in such a market. To see whether global capital market integration leads to one set of factors for the 3FM, Griffin (2002) compares three versions of the 3FM, with either domestic, international or global factors. Griffin (2002) finds that the domestic 3FM explains time-series variation in returns better and has lower
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pricing errors than the global 3FM. Furthermore, Griffin (2002) reports that the international model, which incorporates domestic and foreign factors, leads to less accurate pricing and only incremental increases in adjusted R2s compared to the domestic 3FM. Griffin (2002) and others that followed, such as Fama and French (2012) and Hou, Karolyi and Kho (2011), show that there is not one set of global factors for the 3FM that describe the returns in global market, despite the global integration of capital markets.
Hardouvelis, Malliaropulos and Priestley (2006) find that the stock market integration of EMU members goes beyond the observed world integration. Therefore, it is interesting to apply Griffin’s (2002) methodology in an EMU context, to see whether assets are priced best by domestic, international or EMU factors, which is done by Moerman (2005) and Alves and Ferreira (2008). Moerman (2005) and Alves and Ferreira (2008) find that also in an EMU context, domestic factors dominate the 3FM. However, data used by Moerman (2005) and Alves and Ferreira (2008) does not go beyond 2003. Since Fratzscher (2002) and Mylonidis and Kollias (2010) find that the integration of EMU stock markets is an ongoing process, it is interesting to look at more recent data.
To sum up, in this paper I test domestic, international and EMU versions of the 3FM on portfolios of German and French stocks in the period 08/1993 till 07/2011 and three equally sized sub-periods. Tests are performed on the three versions of the 3FM using excess returns on book-to-market equity-sorted, size-sorted and size and book-to-market equity-sorted portfolios. In line with Moerman (2005) and Alves and Ferreira (2008), I find that a domestic version of the 3FM better explains the excess returns of stock portfolios than does the EMU version of the 3FM. Furthermore, I show that there are only negligible economic gains when adding foreign factors to the domestic version of the 3FM. The findings also indicate that the integration of the stock markets in the EMU is an ongoing process, which is in line with Fratzscher (2002) and Mylonidis and Kollias (2010).
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The structure of the remainder of this paper is as follows. In Section I, the literature on the financial integration of the EMU and the literature that uses the 3FM to answer the question whether assets are priced in a domestic, international or global/EMU context, are reviewed. I explain the methodology of this paper in Section II. In Section III the data and descriptive statistics are presented and in Section IV the regression results are discussed. I discuss in Section V and conclude in Section VI.
I. Literature Review
A. Financial Integration of the EMU
The signing of the Treaty of Maastricht in 1992 (European Communities, 1992), can be regarded as the birth of the European Union and led to the creation of the Euro as a single European currency. Countries that in addition to being a member of the European Union want to adopt the Euro and therewith become a member of the EMU, have to go through three stages. Going through the three stages leads to the elimination of exchange rate risk between EMU members, completing monetary integration. In 1999 the initial members of the EMU introduce the Euro and follow a single monetary policy under the authority of the European Central Bank.
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Priestley (2006) come to the conclusion that the integration due to EMU membership is robust with respect to the observed world integration. Contrary, Berben and Jansen (2006), and Bekaert, Hodrick and Zhang (2009) report that global factors play an important role in the stock market integration among members of the EMU and European Union, respectively.
Altogether, there are clear signs of financial integration in the EMU, although the magnitude and sources of integration are under debate. Furthermore, it seems that the stock market integration in the EMU is an ongoing process. This ongoing process makes it possible that recent data will reveal EMU factors to dominate the 3FM instead of the domestic factors, which were found by Moerman (2005) and Alves and Ferreira (2008) to dominate for earlier periods.
B. Domestic, International or EMU Factors?
Griffin (2002) was the first to compare three versions of 3FM, with either domestic, international or global factors. Using monthly data from the US, Japan, the UK and Canada, in the period 01/1981 till 12/1995, Griffin (2002), performs regressions on book-to-market equity-sorted and book-to-market equity and size-sorted portfolios, as well as on individual stocks. Griffin (2002) finds that the domestic 3FM explains time-series variation in returns better and has lower pricing errors than the global 3FM. Furthermore, Griffin (2002) reports that the international model leads to less accurate pricing and only incremental increases in adjusted R2s compared to the domestic 3FM.
In line with Griffin (2002), Hou, Karolyi and Kho (2011) and Fama and French (2012) test the 3FM in a global context. Hou, Karolyi and Kho (2011) test models with domestic, international or global factors. Hou, Karolyi and Kho (2011) find that the domestic and international asset pricing models outperform the global model. Focusing on Hou, Karolyi and Kho’s (2011) results of the 3FM on returns of developed countries only2, the addition of foreign factors to the domestic model give the same trivial economic gains as Griffin (2002) finds. Fama and French (2012) divide 23 countries into four regions (North America, Europe3, Japan and Asia Pacific) and test the 3FM with either global or regional factors. Fama and French (2012) find that a European 3FM performs better than a global 3FM. Furthermore, Fama and French (2012) perform robustness checks using an international model and find
2 Hou, Karolyi and Kho (2011) make a difference between emerging and developed markets. 22 countries are
categorized as being developed of which 13 belong to the European Union.
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support for Griffin’s (2002) conclusion that there are only trivial gains with the addition of foreign factors to a regional model.
The results of Griffin (2002), Hou, Karolyi and Kho (2011) and Fama and French (2012) show that despite the global integration of capital markets (e.g., Goetzmann, Li and Rouwenhorst, 2005; Volosovych, 2011; Berger and Pozzi, 2013), it are still domestic factors that dominate the 3FM. However, Griffin (2002) and Hou, Karolyi and Kho (2011) do not specifically test the 3FM in the EMU, which is found to be more integrated than the global market, see for example Hardouvelis, Malliaropulos and Priestley (2006). Fama and French (2012) who do perform tests on European countries do not look at country specific 3FMs and include non-EMU and non-European Union members in their European region tests.
Motivated by findings presented in Section I.A on the financial integration of the EMU, Moerman (2005) and Alves and Ferreira (2008) apply the methodology of Griffin (2002) in an EMU context. Both Moerman (2005) and Alves and Ferreira (2008) find that the EMU models always underperform the domestic and international models, on both explanatory power and pricing errors. Furthermore, both papers report that the addition of foreign factors to the domestic model only yields incremental improvements of the explanatory power of the model, which is in line with the findings of Griffin (2002). The studies of Moerman (2005) and Alves and Ferreira (2008) show that even in a presumed integrated market, domestic factors dominate the 3FM. However, their test-periods do not go beyond the year 2003, only four years after the Euro was introduced. Since then, more countries have entered the EMU and it is likely that the EMU stock markets have integrated more since 2003, see Fratzscher (2002) and Mylonidis and Kollias (2010). It is therefore interesting to look whether in the period after 2003 the integration of the EMU continues and EMU factors, instead of domestic factors, dominate the 3FM.
II. Methodology
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A. Fama and French’s Three-Factor Model
Fama and French (1993) propose a 3FM to explain average stock returns. The three factors in the 3FM are the market return in excess of the risk-free rate (MRF), the difference between the returns of portfolios with small- and big-stock (SMB), and the difference between the returns on high and low book-to-market equity portfolios (HML). The 3FM regression model describes the return on asset i, , in excess of the risk-free rate, , as follows:
( ) ( ) ( ) (1)
where , , and are the unconditional sensitivities of the ith asset to the factors.
B. Griffin’s Empirical Models
In an efficient and integrated capital market, there should be only one set of factors for the 3FM that describe the expected returns in such a market. Griffin (2002) adapts Fama and French’s 3FM into three models; a domestic factor model, an international factor model and a global model. Griffin (2002) tests these models to see whether global or country-specific factors explain time-series variation in US, Japanese, UK and Canadian stock returns, which are presumed to be an integrated market. In this research, Griffin’s three models are tested for the EMU.
For clarity, Griffin’s (2002) global factor model is renamed in this paper the EMU model. The EMU model regression describes the euro-denominated return on domestic asset i, , in excess of the euro-denominated domestic risk-free rate, , as follows:
( ) ( ) ( ) (2)
where , , and are the unconditional sensitivities of the ith asset to the factors, EMRF is the euro-denominated weighted-average of the excess market return in the EMU, ESMB is the excess return for size portfolios in the EMU and EHML is the excess return for book-to-market equity portfolios in the EMU.
Allowing for both domestic and foreign factors results in Griffin’s (2002) international factor model:
( ) ( ) ( )
( ) ( ) ( ) (3)
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capitalization of the countries in the sample that contribute to the domestic and foreign market, respectively.
Allowing only for domestic factors to drive returns leads to the following domestic factor model regression:
( ) ( ) ( ) (4) C. Independent Variables
C.1 Construction of SMB and HML Portfolios
To construct the risk factors in the model regressions, the following procedure is used. Depending on whether the regression is performed with the EMU, international or domestic regression model, respectively, the EMU, foreign and domestic, or domestic stocks from the data set are used to form the SMB and HML portfolios.
The stocks are ranked on size in each month using the value of month t-1, this in contrast to Griffin (2002) and Fama and French (1993), which apply annual sorting. The set is then split using the median size into a small (S) and a big (B) portfolio.
Independently, the stocks are also ranked monthly on their book-to-market equity, though being calculated only once a year because book equity is commonly only established once a year. Book-to-market equity is calculated as the book common equity for the fiscal year ending in year t-1, divided by the market equity at the 1st of January of year t4. This
book-to-market equity is used from the 1st of August in year t till the 1st of July in year t+15.The bottom 30% are classified as low book-to-market equity stocks (L), the middle 40% as middle (M), and the top 30% as high (H).
Using sorts on size and market-to-book value, six portfolios are constructed as the intersections of the two size and the three book-to-market equity portfolios: SL, SM, SH, BL, BM, BH. Monthly value-weighted compounded6 returns are calculated for these 6 portfolios from the 1st of August in year t till the 1st of July in year t+1.
The SMB portfolio is constructed by the simple average of all small-stock portfolio returns minus all big portfolios returns for each month (SMB = [SL+SM+SH–BL–BM–BH]/3). The HML portfolio is the simple average of both high book-to-market equity value portfolio
4 Negative book-to-market values are not used.
5 Fama and French (1993) motivate this procedure to make sure that the book equity of year t-1 is known for the
period the returns are calculated.
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returns minus both low book-to-market equity value portfolio returns for each month (HML = [SH+BH-SL-BL]/2).
Griffin (2002) uses in his equivalent of the EMU factor model, weighted averages of the
country specific factors in the EMU portfolio as EMU factors,
+ . Since Fama and French (1993) construct the factors
in the 3FM in a particular way, a value-weighted average of multiple factors is different than a factor that is constructed using all data underlying the multiple factors. Add to this typical construction of factors the logic behind the EMU factor model, suggesting there is only one set of factors, I calculate the EMU and foreign factors directly, instead of using value-weighted factors. Additionally, by calculating the EMU factors directly, the chance of a sample bias is reduced, since the EMU includes multiple countries with only a few stocks in the data set, see also Table I. For example, the FSMB factor is calculated with all foreign SL, SM, SH, BL, BM and BH using all non-domestic EMU data.
I choose to use monthly sorting above Fama and French’s (1993) yearly sorting because monthly information on market values is easily accessible, allowing stocks with increasing or decreasing size to be included in different portfolios within a year.
C.2 Construction of the Excess Market Return
The domestic, foreign and EMU excess market return is calculated monthly by subtracting a risk-free rate from the value-weighted monthly returns, including negative book-to-market equity stocks, which were excluded from the construction of SMB and HML portfolios.
D. Dependent Variables
In line with Griffin (2002), I use domestic excess monthly returns of portfolios formed on both size and book-to-market equity, as dependent variables in the time-series regressions. In addition, I use domestic excess monthly returns on big and small size portfolios and excess monthly returns on high and low book-to-market equity portfolios which enable me to make comparisons with Moerman (2005) and Alves and Ferreira (2008).
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the 1st of January of year t. Book-to-market equity is calculated as the book common equity for the fiscal year ending in year t-1, divided by the market equity at the 1st of January of year
t. Both the size and book-to-market equity ranked stocks are split in three tertiles. The 9
portfolios are formed as the intersections of the size tertiles and the book-to-market equity tertiles. For these 9 portfolios the value-weighted compounded monthly returns are calculated from the 1st of Augustus of year t till the 1st of July of year t+1, using the book-to-market equity calculated at the 1st of January of year t.
The big and small size portfolios are constructed similar to the SMB portfolios discussed earlier. The domestic stocks are ranked on size in each month in the period from 08/1993 till 07/2011, using the value of month t-1. The size ranked stocks are split in tertiles. The big size portfolio is formed by the tertile with the biggest size and the small size portfolio is formed by the tertile with the smallest size. For the big and small size portfolios the value-weighted compounded monthly returns are calculated from the 1st of Augustus of year t till the 1st of July of year t+1.
The high and low book-to-market equity portfolios are constructed similar to the HML portfolios discussed earlier. The domestic stocks are ranked on book-to-market equity in each month in the period from 08/1993 till 07/2011. Book-to-market equity is constructed yearly on the 1st of January of year t. Book-to-market equity is calculated as the book common equity for the fiscal year ending in year t-1, divided by the market equity at the 1st of January of year t. The book-to-market equity ranked stocks are split in tertiles. The low market-to-book equity portfolio is formed by the tertile with the lowest market-to-book-to-market equity and the high market-to-book equity portfolio is formed by the tertile with the highest book-to-market equity. For the high and low book-to-market equity portfolios the value-weighted compounded monthly returns are calculated from the 1st of Augustus of year t till the 1st of July of year t+1, using the book-to-market equity calculated at the 1st of January of year t.
E. Time-Series Tests Using Size-Sorted, Market Equity-Sorted and Book-to-Market Equity and Size-Sorted Portfolios
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values, to test for autocorrelation up to the third order. In the presence of heteroskedasticity, I use White’s (1980) heteroskedasticity consistent covariance estimates and Newey and West’s (1987) heteroskedasticity and autocorrelation consistent covariance estimates in the presence of autocorrelation, and possibly also heteroskedasticity, to prevent the coefficient estimates to become inefficient.
The prediction from asset pricing models is, and thus also from the three models tested in this paper, that the regressions intercepts are statistically indistinguishable from zero. I test whether intercepts are statistically indistinguishable from zero using the F-statistic of Gibbons, Ross and Shanken (1989), hereafter the GRS F-statistic. The null hypothesis of the GRS F-statistic is that the regression intercepts are jointly equal to zero for all specifications of the model regression. I also use the absolute and simple average absolute regression intercepts to evaluate the pricing errors of the models. Lower absolute intercepts indicate a lower pricing error and therefore, models with a lower absolute intercept are more effective in pricing the assets. Additionally for the book-to-market equity and size-sorted portfolios, the value-weighted absolute regression intercepts and the difference in regression intersects between the smallest size and highest book-to-market equity portfolio and the largest size and lowest book-to-market equity portfolio, hereafter extreme portfolios, are evaluated. The use of value-weighted intercepts to evaluate asset pricing models is advocated by Kan and Zhang (1995) and used by Ferson and Harvey (1994) and Griffin (2002). The difference in regressions intersects between the two extreme portfolios is used by Griffin (2002) to evaluate the three models because in his data set there is substantial cross-sectional variation between average returns in the extreme portfolios.
Contrary to the regression intercepts, asset pricing models make no predictions on the explanatory power; however, a model with high explanatory power indicates that the model has useful factors. I use adjusted R2s, which correct for the addition of extra factors in a regression model, to evaluate the explanatory power of the models.
The models are evaluated on the significance of the factor coefficients, at a 5% significance level. I use the t-statistics of the factor coefficients to see whether the coefficients are significantly distinguishable from zero. Evaluating the factor coefficients helps to see whether the variables in the models help to explain the variation in excess monthly returns.
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explanatory power and fit of the three model regressions changes over time. Because of the continuing financial integration of the EMU, it is expected that the explanatory powers of the EMU factor model regression increase and the pricing errors will decrease overtime. Second, both Equation (3) and (4) are also considered as un-weighted models, setting both and
to one.
III. Data and Descriptive Statistics
A. Data
The data set includes stocks in the period from the 1st of August 1993 till the 1st of July 2011. The data set comprises data from two separate eras, one before the introduction of the Euro and the other after the introduction of the euro. The era before the introduction of the Euro ranges from the 1st of August 1993 till the 1st of July 1999, 1993 being the year the Treaty of Maastricht came effective (European Communities, 1992). This pre-Euro era includes stocks from the countries that have reached the third stage of the EMU on the 1st of January 1999. The era after the introduction of the Euro ranges from the 1st of August 1999 till the 1st of July 2011, and includes stock from the countries of the European Union that have reached the third stage of the EMU. Countries that have reached the third stage of the EMU during the tested period are included from the year the third stage is reached. The periods 08/1993 till 07/1999, 08/1999 till 07/2005 and 08/2005 till 07/2011, are referred to as the first, second and third sub-period, respectively.
A.1 Variable Proxies
Compounded returns are calculated using the return index (RI7), where the compounded return in month t is the natural logarithm of RIt/RIt-1. RI, shows a theoretical growth in value
of a shareholding over a specified period, assuming that dividends are re-invested to purchase additional units of an equity or unit trust at the closing price applicable on the ex-dividend date. As a measure of stock size Datastream’s market value (MV) is used, which is the share price multiplied by the number of ordinary shares in issue. Additionally, book-to-market equity ratios are calculated using common equity, representing common shareholders' investment in a company (WC03501), plus deferred taxes (WC03263), divided by market value (MV).
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As a proxy for the risk-free rate of Germany and France, the harmonized monthly yield on 10-year government bonds of respectively Germany and France, is used. The harmonized monthly yield on 10-year German government bonds is also used as a proxy of the risk-free rate for EMU and foreign MRF factors. The Euro Interbank Offered Rate is not chosen because this rate is not available before 1999.
A.2 Screening Procedure
I construct the data set using constituents list of Thomson Reuters’ Datastream. Stocks that are listed in the EMU Total Market list (TOTMKEM). To control for survivorship bias, the available Dead lists of the EMU countries8 are taken up in the data set as well. The Total Market lists of Datastream incorporate derivatives, as do the Dead lists, which additionally include intra-country and intra-country multiple quotes, funds, trusts, investment companies and financial stocks. To clean the obtained lists from these contaminations, the procedure described by De Moor (2005) is followed, and therewith assuming that stock characteristics are constant over time. The procedure is described below.
I obtain a static list of stocks with information on their name (NAME), ISIN code (ISIN) and Industry Classification Benchmark (ICBIC). If stocks in the list have an ISIN code and it resembles an EMU country code of the ISO 3166-1 alpha-2 standard, the stocks are kept in the data set. The ISIN code is also used to assign a stock to a particular country. Furthermore, stocks which have an ICBIC and which are not categorized as financials are kept in the data set. A similar procedure is followed by Griffin (2002), even though some find that financial and non-financial firms show similar relations between size book-to-market equity (e.g., Barber and Lyon, 1997). Additionally, the names of the stocks are screened manually using the elimination triggers of De Moor (2005), presented in Appendix A. Some of the elimination triggers are internationally valid, while most are country specific. Elimination triggers are grouped in three categories: exchange, equivalent and derivative abbreviations. The names of stocks in Datastream include an exchange abbreviation when a stock is listed on multiple exchanges and the exchange is not the core exchange. Stocks with an exchange abbreviation are removed from the data set. The names of stocks include a derivative abbreviation when the stock is a derivative of common stock. Derivatives are removed from the data set. The names of stocks that include equivalent abbreviations correspond to common
8 Dead lists are available for Austria (DEADOE), Belgium (DEADBG), Finland (DEADFN), France
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stock equivalents, such as options, warrants and preferred stock, and are removed from the data set. In case there is any doubt whether a stock should be removed, it is kept in the data set.
For the stocks that survive the static list screening, time-series data is obtained. Stocks are only kept in the data set when fulfilling the minimum requirement of having at least (i) one month in time with jointly two consecutive return index data points, for month t-1 and t, (ii) a market value in month t-1 and in January of year t, and (iii) common equity and deferred taxes for the fiscal year ending in year t-1.
Finally, there are three more screens applied to the dataset. Stocks with a market value lower than one million euro, are removed from the data set because small stocks are sensitive to errors, have limited liquidity and can be subject to price manipulation (De Moor, 2005). Additionally this screen helps to overcome the inequality between the number of stocks included in the TOTMK and DEAD lists in Datastream, since the TOTMK lists only include the biggest shares and the DEAD lists all the shares9. Stocks with high book-to-market equity ratios are likely to be distressed and therefore stocks with book-to-market equity ratios greater than 10 are removed from the data set (e.g., Fama and French, 1995; Griffin and Lemmon, 2002)10. A problem with the DEAD lists in Datastream is that as soon as a stock is dead, the last available data is kept being presented for all future data points. This problem is overcome by removing all equal consecutive return index data points from the data set. Moreover, this screen removes illiquid stocks from the data set.
After the data set is completed, the obtained data set is once more checked on double listings, by keeping only one stock in the data set in case stocks have the same name or ISIN code and overlapping data points.
A.3 Dependent Variables
Griffin’s (2002) three empirical models are tested for Germany and France, being the two largest economies in the EMU and having the largest number of stocks in the data set, see also Table I. Additionally, Germany and France are chosen because both countries are founding members of the forerunners of the EMU, the European Coal and Steel Community and the European Economic Community.
9 1.23% of the stocks in the TOTMKEM included in data set have at least one data point with a market value
lower than €1,000,000.
14 Table I
Average Monthly Market Capitalization Weights and Number of Stocks for the EMU and Member Countries: 08/1993 – 07/2011. 18 Years
The tables shows the countries that are included in the complete data set, the date these countries entered the third stage of the EMU and the average monthly market capitalization weights in the EMU (Avg. Weight) and number of stocks for the different EMU member countries (Avg. Stocks) for the complete period of 18 years and the three sub-periods of each 6 years. Additionally, the values are also provided for the EMU as a whole. Countries that have reached the third stage of the EMU during the tested period are included from the year the third stage is reached.
08/1993-07/2011 08/1993-07/1999 08/1999-07/2005 08/2005-07/2011 Country Third EMU Stage Avg. Weight (%) Avg. Stocks Avg. Weight (%) Avg. Stocks Avg. Weight (%) Avg. Stocks Avg. Weight (%) Avg. Stocks Austria 1/1/1999 1.21 20.88 1.08 9.78 0.88 23.93 1.66 28.92 Belgium 1/1/1999 3.81 42.08 5.18 30.63 2.80 45.67 3.44 49.94 Finland 1/1/1999 3.98 25.67 1.31 12.57 6.82 32.50 3.80 31.94 France 1/1/1999 33.72 175.37 35.03 147.19 32.31 190.67 33.82 188.24 Germany 1/1/1999 23.37 126.68 21.83 50.06 23.58 150.10 24.71 179.88 Ireland 1/1/1999 0.57 16.69 0.64 16.11 0.42 18.61 0.66 15.33 Italy 1/1/1999 11.26 83.28 10.50 50.54 13.21 83.53 10.07 115.78 Luxembourg 1/1/1999 0.91 2.99 0.13 0.63 0.41 1.92 2.19 6.42 Netherlands 1/1/1999 10.18 78.10 15.28 81.25 8.98 78.53 6.27 74.51 Portugal 1/1/1999 1.07 15.70 0.55 4.63 1.16 18.10 1.50 24.38 Spain 1/1/1999 9.14 41.90 8.46 18.53 8.65 33.64 10.30 73.54 Greece 1/1/2001 1.29 28.23 NA NA 1.15 12.56 1.39 38.67 Slovenia 1/1/2007 0.25 13.27 NA NA NA NA 0.25 13.27 Cyprus 1/1/2008 0.02 14.36 NA NA NA NA 0.02 14.36 Malta 1/1/2008 0.02 1.89 NA NA NA NA 0.02 1.89 Slovakia 1/1/2009 0.00 0.00 NA NA NA NA 0.00 0.00 EMU 1/1/1999 1.00 650.66 1.00 421.90 1.00 685.56 1.00 844.51 B. Descriptive Statistics
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The average number of stocks included in the data set is 650.66. The average number of stocks increases over the three sub-periods from 421.90 in the first period to 844.51 in the last period. This increase cannot be attributed to the expansion of the EMU alone, which is only responsible for an increase in stock count of 68.19, but is realized to a large extent by the increase in the number of stocks for countries that already have been a member of the EMU since the 1st of January 1999.
It is worth mentioning here that it is difficult to compare my data set with those of Moerman (2005) and Alves and Ferreira (2008), because both papers do not clearly mention when a certain stock is included in their data set, e.g., it is unclear in their papers what happens with double listings or foreign stocks on a domestic stock market. I find for instance a relatively small number of German stocks that is included in the first sub-period compared to their papers, although the German market capitalization in my dataset is still large in size. It would be interesting to examine this difference more closely.
B.1 Independent Variables
Table II shows the correlations of the factors and descriptive statistics on mean, standard deviation, the ratio of the mean on its standard deviation, median, minimum and maximum for the 08/1993 till 07/2011 data period. In Appendix B, the same information is also displayed for the three sub-periods (1993 – 1999, 1999 – 2005, and 2005 – 2011).
16 Table II
Descriptive Statistics and Correlations of the Monthly Independent Variables: 08/1993 – 07/2011, 18 Years
Below, the euro-denominated weighted-average compounded returns are expressed in % per month for the period 08/1993 till 07/2011. The table shows the correlations of the factors and descriptive statistics on mean, standard deviation (Std. Dev.), the ratio of the mean on its standard deviation median (t-Mean), minimum and maximum. The 10%, 5% and 1% critical values of t-Mean are 1.65, 1.97, and 2.60, respectively.
EMRF is the EMU return in excess of the harmonized euro-denominated yield on 10 year German government bonds. GMRF and FMRF are the German and French returns in excess of their respective home market euro-denominated risk-free rates. NGMRF and NFMRF are the Non-German and Non-French returns in the EMU in excess of the harmonized euro-denominated yield on 10 year German government bonds.
SMB and HML are the excess returns for the size and book-to-market equity portfolios. The SMB and HML portfolios are constructed by ranking stocks on size and market-to-book equity, forming six portfolios: SL, SM, SH, BL, BM, BH. Monthly value-weighted compounded returns are calculated for these 6 portfolios from the 1st of August in year t till the 1st of July in year t+1. The SMB portfolio is constructed by the simple average of all small-stock portfolio returns minus all big portfolios returns for each month (SMB = [SL+SM+SH–BL–BM–BH]/3). The HML portfolio is the simple average of both high book-to-market value portfolios minus both low book-to-market value portfolios for each month (HML = [SH+BH-SL-BL]/2). Details on the formation of the SL, SM, SH, BL, BM and BH portfolio is provided in Section II.
EMU Factors German Factors French Factors Non-German Factors Non-French Factors
EMRF ESMB EHML GMRF GSMB GHML FMRF FSMB FHML NGMRF NGSMB NGHML NFMRF NFSMB NFHML
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It is noteworthy that all SMB portfolios show negative excess returns for the period 08/1993 till 07/2011, although this is not the case for all sub-periods. This finding matches the reports of Griffin (2002) and Fama and French (2012), who finds both positive and negative excess returns for the SMB portfolios. Contrary are the reports of Alves and Ferreira (2008) and Fama and French (1993), who find positive excess returns on the SMB portfolios. Furthermore, the SMB premium is only significant at a 10% level for Germany in the 08/1993 till 07/2011 period and similar t-values are found in the three sub-periods. The non-significant SMB premium is in line with Fama and French (2012), who find a non-significant SMB premium for their European region, and Artmann, Fitner and Kempf (2012) who do not find a SMB premium in a German context. This finding contributes to the question, reviewed by Van Dijk (2011), whether there is still a size premium in stock returns in the period after the 1980s. On the contrary, the returns on the HML portfolios are all positive and significant, which is in line with findings of Fama and French (1998; 2012), Griffin (2002), Alves and Ferreira (2008).
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an integrated market as the EMU, where size and book-to-market equity risk are expected to have the same magnitude.
The correlations between the SMB and HML portfolios are low, with values of -0.03, -.026 and 0.06 for respectively the EMU, Germany and France, indicating there is little to no size effect in the HML portfolios and vice versa no book-to-market equity effect in the SMB portfolios. Fama and French (1993) and Griffin (2002) find correlations between the SMB and HML portfolios of similar magnitudes.
B.2 Dependent Variables
Table III shows the descriptive statistics on the 9 book-to-market equity and size-sorted portfolios for the period 08/1993 till 07/2011 for Germany and France. The descriptive statistics are calculated monthly and are averaged across the whole period. The Table shows means, standard deviations, medians, minima, maxima, skewness, kurtosis and autocorrelations with 1 month lag for the excess returns in the 9 portfolios. Additionally, the Table shows the average monthly stocks size, book-to-market equity values, % of total market value and number of stocks in the 9 portfolios. In Appendix B, the same information is also displayed for the three sub-periods (1993 – 1999, 1999 – 2005, and 2005 – 2011). Additionally, descriptive statistics for the size-sorted and book-to-market equity-sorted portfolios are presented in Appendix B.
The 9 German portfolios have a range of average excess returns from -1.23% to 0.61% for the period 08/1993 till 07/2011 and the 9 French portfolios produce a smaller range of average excess returns from -0.70% to 0.65%. Looking at the whole test period, the excess returns show a positive relation with size, although this is not as apparent for the different sub-periods. The observed positive relation with size is contrary to what Fama and French (1993) find. However, a positive relation between market-to-book equity values and excess returns is observed in the data set, as do Fama and French (1993).
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The German and French portfolios both show the highest average monthly returns in the first sub-period. Since the late 90’s were characterized with high growth, it is not surprising that the highest returns are observed in this period. The German portfolios clearly perform worst in the period 08/1999 till 07/2005, as in both the previous as the subsequent period, 8 out of 9 portfolios outperform their counterparts in this period. For the French portfolios it is less apparent which the worst performing period is because only 5 out of 9 portfolios in the sub-period 08/2005 till 07/2011 outperform their complements in the previous sub-period.
Table III
Descriptive Statistics for 9 German and French Stock Portfolios formed on Size and Book-to-Market Equity using Monthly Data: 08/1993 – 07/2011. 18 Years
The 9 size and book-to-market equity portfolios are formed as follows. The stocks are ranked on size in each month in the period 08/1993 till 07/2011, using the value of month t-1, and independently, also on book-to-market equity which is constructed yearly on the 1st of January of year t. Book-to-market equity is calculated as the book common equity for the fiscal year ending in year t-1, divided by the market equity at the 1st of January of year t. Both the size and book-to-market equity ranked stocks are split in tertiles. The 9 portfolios are formed as the intersections of the size tertiles and the book-to-market equity tertiles. For these 9 portfolios the value-weighted compounded monthly returns are calculated from the 1st of Augustus of year t till the 1st of July of year
t+1, using the book-to-market equity calculated at the 1st of January of year t.
The descriptive statistics are calculated monthly for the period 08/1993 till 07/2011 and are averaged across the whole period. The table shows means, standard deviations, medians, minima, maxima, skewness, kurtosis and autocorrelations with 1 lag for the excess returns in the 9 portfolios. Additionally, the table shows the average monthly stocks size, book-to-market equity values, % of total market value and number of stocks in the 9 portfolios.
Panel A shows the descriptive statistics for Germany and Panel B for France. Panel A: Germany
Size Book-to-Market Equity
tertiles Low 2 High Low 2 High
Mean (%) Standard Deviation (%)
Small -1.23 -0.45 -0.40 8.70 8.01 7.15 2 -0.89 0.20 0.45 8.19 6.07 6.71 Big 0.02 0.11 0.61 7.14 6.26 6.50 Median (%) Minimum (%) Small -0.33 0.21 0.13 -36.20 -33.82 -38.66 2 0.34 0.67 1.44 -43.45 -16.21 -29.53 Big 1.14 0.84 1.27 -22.43 -22.25 -27.13 Maximum (%) Skewness Small 25.91 29.24 20.52 -0.99 -0.53 -1.10 2 18.92 19.10 20.86 -1.58 -0.29 -1.12 Big 19.43 16.51 14.86 -0.65 -0.64 -0.86
Kurtosis Autocorrelation (lag 1)
Small 3.07 2.31 4.17 0.05 0.27 0.16
2 5.14 0.62 3.05 0.21 0.08 0.12
Big 1.25 0.78 2.03 0.08 0.02 -0.05
Average of Monthly Stock Size (million €) Average of Monthly Book-to-Market Values
Small 112.35 126.54 78.13 0.26 0.56 1.42
2 645.87 549.38 543.91 0.28 0.55 1.15
Big 8994.72 11703.24 8849.16 0.26 0.55 1.04
Average of Monthly Percent of Total Market Value (%) Average of Monthly Number of Stocks
Small 0.28 0.28 0.35 11.00 12.21 19.04
2 2.38 1.82 1.45 14.73 14.11 13.06
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Panel B: France
Size Book-to-Market Equity
tertiles Low 2 High Low 2 High
Mean (%) Standard Deviation (%)
Small -0.70 0.16 0.38 8.17 6.09 5.71 2 -0.38 0.31 0.65 7.27 5.16 6.19 Big -0.08 0.41 0.36 5.84 5.24 6.93 Median (%) Minimum (%) Small -0.21 0.63 0.55 -34.44 -24.65 -21.47 2 0.30 0.75 0.72 -35.37 -22.70 -28.23 Big 0.53 0.59 1.02 -25.03 -17.92 -21.97 Maximum (%) Skewness Small 23.55 19.12 17.62 -0.77 -0.87 -0.49 2 20.32 11.12 14.47 -1.14 -0.98 -0.92 Big 15.06 14.46 19.17 -0.67 -0.36 -0.53
Kurtosis Autocorrelation (lag 1)
Small 2.92 3.15 1.69 0.25 0.29 0.23
2 3.77 2.41 2.62 0.24 0.23 0.22
Big 1.64 0.43 0.96 0.04 0.02 0.05
Average of Monthly Stock Size (million €) Average of Monthly Book-to-Market Values
Small 82.83 87.75 69.87 0.30 0.61 1.37
2 481.13 480.70 468.00 0.31 0.61 1.25
Big 12264.92 10239.15 6011.46 0.29 0.60 1.17
Average of Monthly Percent of Total Market Value (%) Average of Monthly Number of Stocks
Small 0.20 0.27 0.32 14.07 17.46 26.93
2 1.64 1.75 1.51 19.40 20.38 18.36
Big 48.39 32.25 13.68 24.98 20.30 13.49
For the period 08/1993 till 07/2011, the German portfolios show the highest excess return standard deviations, which is also true for all sub-periods. There is a negative relation between the excess return standard deviations and book-to-market equity. A relation between the size and the standard deviation is not observed.
For the whole period, 5 French portfolios outperform their German counterparts, with the German biggest size portfolios outperforming the French biggest size portfolios. In the first sub-period, 4 out of 9 French portfolios outperform the equivalent German portfolios. In the last two sub-periods the differences are more explicit, with only 1 German portfolio outperforming the corresponding French portfolio and in the last sub-period, 6 German portfolios showing higher excess returns than their French complements.
The portfolios show low autocorrelation with 1 month lag, the highest value being 0.29 for Germany and 0.27 for France and absolute values in the biggest size portfolios being all below 0.08.
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biggest size portfolios. This difference might be caused by the fact that in my data set stocks with a market value lower than one million Euro are excluded.
The average stock size of the 9 portfolios also differs from the descriptive statistics presented by Fama and French (1993). Although there is a clear increase of average stock size with increasing size portfolios, smallest and the biggest size portfolios show higher average stock size than Fama and French (1993). The higher average stock size for the smallest size portfolios might be explained by the exclusion of stocks with a market value lower than one million Euro from the data set.
Although the division of the number of stocks over the 9 portfolios is more evenly in my data set than in Fama and French (1993), the average % of total market value in each portfolio does not differ much from their results. The average % of total market value in the smallest size portfolios is a little lower and the average % of total market value in the biggest size portfolios is somewhat higher, especially for the higher book-to-market equity ratio portfolios. The average book-to-market equity ratios for the 9 portfolios are similar to the ratios presented by Fama and French (1993). Just as in Fama and French (1993) descriptive statistics, the book-to-market ratios decrease with increasing size and more explicitly for the highest book-to-market equity portfolios.
IV. Results
The results of the domestic, international and EMU model regressions of the size and book-to-market equity-sorted portfolios are presented first. Thereafter, I assess the results of the book-to-market equity-sorted portfolios and the size-sorted portfolios.
A. Size and Book-to-Market Equity-Sorted Portfolios
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average absolute returns, the absolute value-weighted returns and the differences in returns between the extreme portfolios, and the p-value of the difference between these two extreme portfolios. In Appendix C, the regressions results are presented individually in more detail for each model, test-period and country in tables similar to ones used by Fama and French (1993). For the period 08/1993 till 07/2011, all models show simple average absolute intercepts in the range from 0.14% to 0.24% and value-weighted intercepts from 0.08% to 0.18%. Across the three sub-periods, higher simple and value-weighted average absolute intercepts are observed, ranging from 0.14% to 1.17% and from 0.06% to 0.51%, respectively.
Table IV
Regressions of Book-to-Market Equity and Size-Sorted German and French Monthly Excess Portfolio Returns on Griffin’s Empirical Models: 08/1993 – 07/2011. 18 Years
The table shows descriptive statistics and regression results for the domestic un-weighted (Dom.) and weighted (W. Dom.), international un-weighted (Int.) and weighted (W. Int.) and EMU models for Germany and France using 9 size and book-to-market equity-sorted portfolios. The 9 portfolios are formed as the intersections of three equally-sized and independent sorts on both size and book-to-market equity. The exact construction of the portfolios is described in Section II.
Descriptive statistics on the excess portfolio returns are presented in the table, showing the average absolute return (Avg. |ret.|), the absolute value-weighted return (Avg.VW |ret.|) and the difference in return between two extreme portfolios (H-L ret.), calculated as the difference in average return between the smallest size and highest book-to-market equity portfolio and the largest size and lowest book-to-market equity portfolio, and the p-value of the H-L ret.
The monthly excess returns on the portfolios are used to estimate by ordinary least squares the time-series model regressions presented below:
Domestic Model: ( ) ( ) ( )
International Model: ( ) ( ) ( )
( ) ( ) ( )
EMU Model: ( ) ( ) ( )
The construction of the factors is discussed in Section II. In the un-weighted models both and are
equal to one. As regression results, the table shows the simple (Avg. |α|) and value weighted (Avg.VW |α|) average absolute regression intersects, the difference in intersects between the two extreme portfolios (H-L α) and its p-value, the Gibbons, Ross, and Shanken (1989) F-statistic (GRS F-Statistic) and its p-value, and the average adjusted R2 (Adj. R²).
Panel A shows the regression results for the period 08/1993 till 07/2011, Panel B for the period 08/1993 till 07/1999, Panel C for the period 08/1999 till 07/2005 and Panel D for the period 08/2005 till 07/2011. All returns are in % per month.
Panel A: 08/1993 – 07/2011
Excess Portfolio Returns Germany France
Avg. |ret.| 0.18 0.12
Avg.VW |ret.| 0.16 0.15
H-L ret. -0.43 0.46
p-value (0.35) (0.28)
Germany France
Factor Regressions Dom. W. Dom. Intl. W. Intl. EMU Dom. W. Dom. Intl. W. Intl. EMU
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Panel B: 08/1993 – 07/1999
Excess Portfolio Returns Germany France
Avg. |ret.| 0.49 0.56
Avg.VW |ret.| 1.12 0.93
H-L ret. -1.56 -0.54
p-value (0.03) (0.49)
Germany France
Factor Regressions Dom. W. Dom. Intl. W. Intl. EMU Dom. W. Dom. Intl. W. Intl. EMU
Avg. |α| 0.49 0.48 0.49 0.49 0.44 0.28 0.29 0.28 0.29 0.32 Avg.VW |α| 0.29 0.28 0.29 0.26 0.29 0.19 0.20 0.21 0.20 0.25 H-L α -0.70 -0.70 -0.68 -0.70 -1.09 -0.36 -0.43 -0.36 -0.41 0.34 H-L p-value (0.19) (0.19) (0.19) (0.19) (0.09) (0.29) (0.21) (0.27) (0.22) (0.45) GRS F-statistic 1.44 1.25 1.46 1.31 1.46 2.35 1.85 2.07 1.47 1.26 GRS p-value (0.19) (0.28) (0.19) (0.25) (0.18) (0.02) (0.08) (0.05) (0.18) (0.28) Adj. R² 0.517 0.508 0.545 0.539 0.460 0.798 0.794 0.802 0.800 0.700 Panel C: 08/1999 – 07/2005
Excess Portfolio Returns Germany France
Avg. |ret.| 1.19 0.04
Avg.VW |ret.| 0.68 0.19
H-L ret. -1.56 -0.54
p-value (0.59) (0.31)
Germany France
Factor Regressions Dom. W. Dom. Intl. W. Intl. EMU Dom. W. Dom. Intl. W. Intl. EMU
Avg. |α| 0.86 0.87 0.83 0.82 1.17 0.47 0.47 0.50 0.50 0.55 Avg.VW |α| 0.51 0.50 0.51 0.51 0.51 0.14 0.14 0.14 0.15 0.39 H-L α -1.41 -1.43 -1.55 -1.63 -1.96 -0.15 -0.15 -0.45 -0.43 -0.87 H-L p-value (0.01) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.04) (0.00) (0.17) GRS F-statistic 2.45 2.50 2.24 2.35 2.89 2.41 2.25 1.89 1.77 1.83 GRS p-value (0.02) (0.02) (0.03) (0.02) (0.01) (0.02) (0.03) (0.07) (0.09) (0.08) Adj. R² 0.757 0.759 0.763 0.764 0.676 0.785 0.780 0.796 0.793 0.708 Panel D: 08/2005 – 07/2011
Excess Portfolio Returns Germany France
Avg. |ret.| 0.46 0.17
Avg.VW |ret.| 0.28 0.09
H-L ret. -1.56 -0.54
p-value (0.17) (0.03)
Germany France
Factor Regressions Dom. W. Dom. Intl. W. Intl. EMU Dom. W. Dom. Intl. W. Intl. EMU
Avg. |α| 0.14 0.14 0.24 0.24 0.51 0.20 0.19 0.19 0.19 0.18 Avg.VW |α| 0.11 0.13 0.16 0.16 0.28 0.12 0.12 0.06 0.07 0.07 H-L α -0.12 -0.12 -0.11 -0.13 0.36 0.58 0.60 0.56 0.57 0.42 H-L p-value (0.72) (0.71) (0.73) (0.70) (0.49) (0.01) (0.01) (0.01) (0.01) (0.14) GRS F-statistic 1.56 1.55 1.52 1.73 1.66 1.56 1.58 1.37 1.42 0.78 GRS p-value (0.15) (0.15) (0.16) (0.10) (0.12) (0.15) (0.14) (0.22) (0.20) (0.64) Adj. R² 0.856 0.855 0.869 0.868 0.766 0.889 0.889 0.893 0.894 0.842
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errors can be observed for either absolute simple or value-weighted regression intercepts for the EMU model.
Across all four test-periods and both simple and value-weighted absolute regression intercepts, the weighted models’ regression absolute regression intercepts are 10 out of 32 times lower, 13 out of 32 times equal and 9 out of 32 times higher than their un-weighted counterparts. Additionally, the absolute differences between weighted and un-weighted simple and value-weighted absolute regression intercepts are not bigger than 0.03%. These results indicate that the weighted models do not provide an improvement in pricing errors compared to the un-weighted models.
Using the GRS F-statistic, the null hypothesis that the intercepts are jointly equal to zero can only be rejected 5 out of 30 times over all periods, excluding the period 08/1999 till 07/2005 in which all nulls are rejected at a 10% significance level. Figure 1 helps to visualize how it is possible that the null hypothesis of the GRS test is only rejected a few times, even though the simple and value-weighted absolute averages both show high pricing errors relative to the excess portfolio returns. Figure 1 plots the realized versus the predicted monthly excess portfolio returns of the 9 German and French book-to-market equity and size-sorted portfolios for the un-weighted domestic and international models and the EMU model for the period 08/1993 till 07/2011. The realized monthly excess returns are the time-series averages of the monthly excess portfolio returns. The predicted monthly excess returns are calculated by the regression estimates and the average factor values. The realized excess monthly return is presented on the vertical axis and the predicted monthly excess return is presented on the horizontal axis. In addition, Figure 1 highlights the smallest size and highest book-to-market equity portfolio () and the largest size and lowest book-to-market equity portfolio (). The horizontal or vertical distance to the diagonal represents the pricing error. Although in the period 08/1993 till 07/2011 the average absolute monthly excess portfolio returns of the French domestic model are lower than for the German domestic model, the GRS p-value of the French domestic model is 0.02 and GRS p-value of the German domestic model is 0.61. Figure 1 shows that the German realized versus predicted portfolio average monthly excess returns are more evenly distanced from and divided across both sides of the diagonal. The equal division across both sides of the diagonal makes it possible that the GRS
F-statistic cannot distinguish the joint regression intercepts from zero. It is also worth
25 Figure I
Realized versus Predicted Monthly Excess Returns for 9 German and French Book-to-Market Equity and Size-Sorted Portfolios for Un-Weighted Domestic and International
Models and the EMU Model: 08/1993 – 07/2011. 18 Years
The figure plots realized versus predicted monthly excess returns of 9 German and French book-to-market equity and size-sorted portfolios for un-weighted domestic and international models and the EMU model in the period 08/1993 till 07/2011. The 9 portfolios are formed as the intersections of three equally-sized and independent sorts on both size and book-to-market equity. The exact construction of the portfolios is described in Section II. The predicted excess monthly returns on the portfolios are calculated using the equations presented below:
Un-Weighted Domestic Model: ̂ ( ̅̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅̅)
Un-Weighted International Model: ̂ ( ̅̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅)
̂ ( ̅̅̅̅̅̅̅̅) ̂ ( ̅̅̅̅̅̅̅̅)
EMU Model: ̂( ̅̅̅̅̅̅̅̅) ̂( ̅̅̅̅̅̅̅̅) ̂( ̅̅̅̅̅̅̅̅)
26
Across all four test-periods and both simple and value-weighted absolute regression intercepts, the international model regression absolute regression intercepts are 7 out of 16 times lower, 5 out of 16 times equal and 4 out of 16 times higher than their domestic counterparts. These results indicate that there is no clear improvement in pricing errors when adding foreign factors to the domestic model. For individual portfolio pricing errors the trivial importance of foreign factors is also visualized in Figure 1, which shows that there is hardly any observable difference between the un-weighted domestic models versus the un-weighted international models in the period 08/1993 till 07/2011.
In the periods 08/1993 till 07/2011 and 08/1999 till 07/2005, respectively, 8 out of 10 and 9 out of 10 differences in the regression intercepts of the extreme portfolios are significantly different from zero at a 10% significance level. These results which show the inability of all models, the EMU model aside, to explain differences in average returns for the extreme portfolios. The inability to explain differences in average returns for the extreme portfolios is further supported by the little evidence of cross sectional variation in excess portfolio returns between the extreme portfolios. I only find significant differences in 2 out of 8 times, at a 10% significance level, of which none are significant in the period in which significant differences in the regression intercepts are observed. On the contrary, Figure 1 helps to loosen these findings regarding the French domestic and international models in the period 08/1993 till 07/2011. In Figure 1 the significant difference in extreme portfolio intercepts for the German models are clearly observed. However, the significant differences in extreme portfolio intercepts for the French domestic and international model are much lower than their German counterparts. Additionally, the significant differences in extreme portfolio intercepts for the French domestic and international model do not differ much from the insignificant French EMU model difference in extreme portfolio intercepts.
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factor. On the contrary, the evidence of a size effect is more ambiguous, with 206 out of 360 factor loadings that are significant at a 5% level. Across all four periods and both countries, the foreign factor loadings of the un-weighted and the weighted international models are only 86 out of 432 times different from zero at a 5% significance level. These results indicate that the foreign factors add little to the explanatory power of international model. Furthermore, there are no clear signs that any of the factor loadings is more often significantly different from zero for a specific model. Though, the factor loadings for the French SMB and HML factors are more often significant than for all German models.
In the period 08/1993 till 07/2011 the average adjusted R2s range from 60.8% to 81.1%. In the sub-periods 08/1993 till 07/2011, 08/1993 till 07/2011 and 08/1993 till 07/2011, the average adjusted R2s range from 46.0% to 80.2%, from 67.6% to 79.6% and from 76.6% to 89.3%, respectively. In all four test-periods for both Germany and France, the lowest adjusted
R2s are clearly observed for the EMU models. Across the three sub-periods the adjusted R2s of the EMU model show an increase over time, starting with 46.0% for Germany and 70.0% for France in the first sub-period and ending with 76.6% and 84.2% in the last sub-period, respectively. Likewise, the adjusted R2s of all other German models show similar incremental values for subsequent sub-periods. Increases in adjusted R2s are also observed for the French models, although the increase in explanatory power is less pronounced.
The adjusted R2s of the weighted and the un-weighted versions of the domestic and international models show similar values in each of the four test-periods. Looking more closely at the adjusted R2s of the un-weighted models compared to their weighted counterparts, the explanatory power of the un-weighted models is 12 out of 16 times higher or equal to their weighted counterparts. In those cases that the adjusted R2s of the weighted models are higher, the additional explanatory power compared to the un-weighted models, across all periods, is 0.2% or less. These findings indicate that the weighted models do not contribute much to the explanatory power compared to the un-weighted models.
Comparing the adjusted R2s of the un-weighted domestic and international models, no large differences between explanatory powers can be observed. Although the explanatory power of the international model is always higher than that of the domestic model, the difference is no more than a few ‰. However, there is one exception for the German models in the period from 08/1993 till 07/1999, where the difference is 2.8%.
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the German models show substantial lower explanatory power than the French models. In the subsequent sub-periods the difference is however negligible. The difference in explanatory power between the German and French models might be caused by the fact that far less German stocks are taken up in the data set for the first sub-period than French stocks. The limit number of German stocks in the first period cause that on average less than 6 stocks are taken up in each of the 9 portfolios. This limited number of stocks per portfolio might cause these portfolios to be less diversified and more exposed to idiosyncratic risk. An argument for this assumption can be found in the regression results with book-to-market equity-sorted and size-sorted portfolios, see Section IV.B and IV.C. The regression results in Section IV.B and IV.C also show less explanatory power for the German models in the first sub-period compared to the French models, but the difference is far less apparent. In both the German book-to-market equity- and the size-sorted portfolios the average number of stocks is higher than 16. The higher number of stocks per portfolio makes these portfolios more diversified and therefore less likely to be influenced by idiosyncratic risk than the book-to-market equity and size-sorted portfolios.
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B. Book-to-Market Equity-Sorted Portfolios
Table V presents the results of the domestic, international and EMU model regressions for high and low book-to-market equity-sorted portfolios. The Table shows the absolute intercepts, the adjusted R2s and the GRS F-statistics for France and Germany independently.
For the period 08/1993 till 07/2011, all models show average absolute intercepts in the range from 0.04% and 0.20%. Across the three sub-periods (1993 – 1999, 1999 – 2005, and 2005 – 2011), higher average absolute intercepts are observed, ranging from 0.03% to 0.60%. Generally, the average absolute intercepts are higher for Germany across all models than for France. The highest observed absolute average intercepts, except for Germany in the period 08/1993 till 07/2011, are those of the EMU model. The average pricing errors of the weighted models are in all four test-periods higher than, or equal to their un-weighted counterparts, which is a sign of misspecification of the weighted models. The difference between the average absolute intercepts of the un-weighted domestic and international models in the period 08/1993 till 07/2011 and the period 08/1993 till 07/1999 is lower than 0.02%. In the period from 08/1999 till 07/2005 the domestic model shows the lowest pricing errors. The differences between the average absolute intercepts of the un-weighted domestic and international model in the period from 08/1999 till 07/2005 are 0.13% and 0.09% for, respectively Germany and France. In the last sub-period, the German domestic model outperforms the international model with 0.07% and the French international model outperforms the domestic model with 0.04%. These results show that the un-weighted domestic model provides more accurate or equal pricing compared to its international counterpart.
Although the F-statistics of all model regressions are found to be highly significant, it is interesting to look more closely at the significance of the factor loadings11. Looking at the significance of individual factor loadings helps to see whether all factors contribute to the explanatory power of the different models. The regression intercepts across all models and both countries are only 2 out of 80 times significantly different from zero at a 5% level, which is an indication that none of the models show significant pricing errors. It is worth mentioning that the factor loading of the domestic and the EMU excess market return is always significant at a 5% level. I also find strong signs of a book-to-market equity effect, with 70 out of 80 significant factor loadings for the HML factor. The EMU model shows the worst book-to-market equity effect, with only 10 out of 16 significant factor loadings at a 5% level. On the
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contrary, the evidence of a size effect is less convincing, with only 28 out of 80 factor loadings that are significant at a 5% level, of which only 6 for the German models. Across all four periods and both countries, the foreign factor loadings of the un-weighted and the weighted international models are only 13 out of 96 times different from zero at a 5% significance level. These results indicate that the foreign factors add little to the explanatory power of international model. Additionally, there are no clear signs that any of the factor loadings is more often significantly different from zero for a specific model, except for a less profound book-to-market effect for the EMU model compared to the other models.
Using the GRS F-statistics, I cannot reject the null hypothesis that all intercepts are jointly equal to zero at a 10% significance level for all models and both countries for the period from 08/1993 till 07/2011 and the period 08/2005 till 07/2011. In the period from 08/1993 till 07/1999, both the French weighted and un-weighted international model intercepts are not jointly equal to zero at a 10% significance level. Furthermore, from 08/1993 till 07/1999 the German EMU model intercepts are not jointly equal to zero at a significance level of 1%. In the period from 08/1999 till 07/2005 all German GRS F-statistics are significant at a 5% level or lower. For France only the EMU model intercepts are jointly not equal to zero at a 1% significance level. Overall, the domestic models’ intercepts are jointly only 1 out of 8 times significantly different from zero, the international models’ intercepts are jointly 2 out of 8 times significantly different from zero and the EMU model’s intercepts are jointly 3 out of 8 times significantly different from zero. Generally, the GRS F-statistics show that the null that the intercepts jointly are equal to zero, cannot be rejected at a 10% significance level
In the period 08/1993 till 07/2011 the average adjusted R2s range from 66.8% to 91.2%. In the sub-periods 08/1993 till 07/2011, 08/1993 till 07/2011 and 08/1993 till 07/2011, the average adjusted R2s range from 68.9% to 91.9%, from 76.2% to 91.0% and from 72.8% to 94.6%, respectively. In all four periods and across Germany and France, the lowest adjusted
R2s are clearly observed for the EMU models. Across the three sub-periods the adjusted R2s of the French EMU model show a clear increase over time, starting with 78.3% in the first sub-period and ending with 90.8% in the last sub-sub-period. A pattern in the adjusted R2s of the German EMU model across the three sub-periods cannot be observed. Contrary, the adjusted
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values in each of the four test-periods. Looking at the adjusted R2 of the un-weighted models compared to their weighted counterparts more closely, the explanatory power of the un-weighted models is 9 out of 16 times higher. In those cases that the adjusted R2s of the weighted models are higher, the additional explanatory power compared to the un-weighted models, across all periods, is 0.4% or less. These findings indicate that the weighted models do not contribute much to the explanatory power compared to the un-weighted models.
Comparing the adjusted R2s of the un-weighted domestic and international models, no large differences between explanatory powers can be observed. Although the explanatory power of the international model is always higher than that of the domestic model, the difference is, except for the German portfolios in the second sub-period, no more than a few ‰.
In sum, the weighted models do not positively contribute to the pricing or the explanatory power of the models, compared to the un-weighted models. Furthermore, the un-weighted domestic model provides more accurate or equal pricing compared to its international counterpart and clearly has lower pricing errors than the EMU model. Across all models, the GRS F-statistics show that generally the null that the intercepts jointly are equal to zero, cannot be rejected at a 10% significance level. Additionally, the explanatory power of the un-weighted domestic model is much higher than that of the EMU model. Furthermore, the addition of foreign factors to the international models only yield small increases in adjusted
