University of Amsterdam
Amsterdam Business School, Faculty for Economics and Business July 2014
Bachelor Thesis Business Economics
Ex post cost of equity: the choice between EMU or domestic CAPM for the Dutch equity market.
Bozidar Vujanovic Student number: 10189815
Thesis instructor: Dhr. Dr. K.B.T. Boe Thio
Abstract
This paper used the CAPM and the 3 factor model to see which market proxy, domestic or EMU had the best fit with the monthly ex post return of the 64 publicly traded companies in the Netherlands from 2000 till end 2009. For the domestic market benchmark, the MSCI Netherlands was used and for the EMU market benchmark the MSCI EMU was used. The reason for selecting the MSCI indexes was because they are made according to the same methodology, which would give a more representative comparison. This empirical research is limited to the EMU and not for the whole Euro area because in this case the purchasing power parity does not have to be taken into account due to a single currency. The results showed that the MSCI EMU had a better fit for the mid and small cap of the Dutch equity market. For the large cap there was a better fit with the MSCI Netherland. The reason that the MSCI Netherlands had a better fit with the large cap of the Dutch equity market is because 71.5 percent of the MSCI Netherlands index consist out of: Unilever, ING, Philips, ASML, Akzo Nobel, Ahold, Aegon, Heineken, Reed elsevier and KPN. Due to the large weight of large cap firms in the MSCI Netherlands, once regressed these firms have a positive bias toward the domestic market proxy.
1 Introduction
Berg and Demarzo (2011) described the capital asset pricing model (CAPM) as a practical way to identify investments with the similar risks. For the CAPM to perform properly, the market portfolio used needs to be a portfolio that only contains systematic risk. The discussion which market portfolio (market proxy) should be used, has been a discussion amongst scholars in the Financial Management Association.
One paper in the Financial Management Association by Robert S. Harris and others (2003) examined which market proxy, Global or Domestic had a better fit with the return of large US companies in the S&P 500. They believed that the extensive integration of the world financial markets would give the conclusion that the Global market proxy should have a better fit with the large US companies. Surprisingly, they concluded that the domestic CAPM had a better fit than the Global CAPM. Robert S. Harris and others (2003) have pointed out that the results are consistent with results obtained by Cooper and Kaplanis (2000) who supported the idea that there is a certain home bias in the global capital markets. Robert S. Harris and others (2003) gave another possible clarification by suggesting that because the domestic market proxies are almost always used by practitioners of the CAPM to estimate the cost of the capital, this could generate a prediction that causes itself to become true. This is also known as a self-fulfilling prophecy.
This paper would like to test the hypothesis that ex post returns of the Dutch companies have a better fit with an European monetary union (EMU) market proxy than a Dutch market proxy. Despite the increasing integration of Dutch equity markets with the EMU there is no research to be found for alternative market proxies for the Dutch equity market. If the EMU market proxy has a better fit compared to the Dutch market proxy, then this would provide a reason for investors to question the market proxy they use when estimating the cost of capital for Dutch stocks. This would also mean that the possibility exists that the systematic risk of the Dutch equity market is better represented by an EMU market proxy than a Dutch market proxy.
Robert S. Harris and others (2003) use the ex-ante estimated returns according to analysts growth forecasts and discount cash flow models provided by IBES1. This paper is restricted to using the ex post returns because of denied access to IBES. In order to get a beta
estimation of the Dutch companies, ordinary least squares method (OLS) will be used to regress the excess return of Dutch companies in the large, mid and small cap against a Dutch market proxy and a EMU market proxy excess returns. The first analysis will do this
according the CAPM and the second analysis will include the size and the value premium in the regression according to the Fama and French 3 factor model (1996). Once these two analyses are done, the estimation which market proxy has the best fit can be seen by the R squared and the significance of the estimators.
1 The Institutional Brokers' Estimate System
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2 Literature review
The market portfolio in CAPM can be described as sufficiently diversified and efficient portfolio that represents the systematic risk in the economy. In the market portfolio the firm specific risk is diversified away. According to CAPM investments have similar risk if they have the same sensitivity to market risk. This sensitivity to the market is measured through the beta. The beta measures the relation of individual assets with the market proxy that is being used. One hypothetical example would be that when Unilever would have a beta of 0,6 it would mean that if the price of the market proxy would go up with 1 percent, the price of Unilever would go up by 0.6 percent. (Berg and Demarzo, 2011).
The CAPM has been criticized for its simplicity and because it could not explain some
anomalies in empirical findings. Fama and French (1993) made an extension of this model by adding two estimators HML(high minus low) and SMB(small minus big). The HML
estimator explains one anomaly in which “value stock” outperforms “growth stocks”. So the estimator in the regression captures the monthly premium “value stocks” get over “growth stocks”. A firm with high book to market ratio is called a “value stock” and firms with low book to market ratio are called “growth stock” (Fama and French, 1993). The second
anomaly is that “small firms” tend to outperform “large firms”. The SMB estimator explains the monthly premium “small sized firms” get over “large sized firms”. Market capitalization is used as a measure to describe if a company is large or small. (Fama and French, 1993)
Stehle (1977) and Stulz (1995a, 1995b, 1999) believe that a domestic market proxy is only appropriate for the CAPM formula, if the asset is traded in an economy in which capital in and outflow is restricted. In contradiction with Robert S. Harris (2003), Stehle (1977) found empirical evidence in support of the global market proxy over the domestic market proxy for US stocks from 1956 to 1975.
Literature on alternative market proxies for the Dutch equity market could not be found. However it would be of interest to point out the study done by Hardouvelis, Malliaropoulos and Priestly (2006) in which they evaluated the effect of the introduction of Euro on capital markets. The conclusion was that since 1995 the level of integration in the capital markets has increased. One reason is that by the inauguration of the Euro the anticipated returns of the EMU countries started to be govern by EMU market risks and less by local risks. The
elimination of exchange rate exposure has led to more uniform valuation of equities in EMU countries. One of the advantages of comparing the Dutch market proxy with the EMU market proxy is that the assumption of Purchasing Power Parity (PPP) over the long term (Gärtner, 2009) is not needed. This parity explains the difference in currency value through the purchasing power, but with an common currency in the EMU the PPP is not necessary anymore.
3 Research method
The two analyses in this paper are cross section regressions on systematic risk. The first according to CAPM and the second one according to the 3 factor model. The first analysis in this paper regresses the monthly ex post risk premium of every stock in the Netherlands(Ri − Rf) with the risk premium of the Dutch market proxy (Rm − Rf)from 2000 until the end of 2009. After that the same is done for the EMU market proxy. This will give the linear approximation of the beta (βi) a constant alpha (α)and the error term (ε).
Formula CAPM:
(Ri − Rf) = α + βi(Rm − Rf) + ε Formula 1(Berg and Demarzo, 2011)
E(Ri) expected stock return
α a constant which is assumed to be zero in CAPM Rf return on risk free asset
E(Rm) expected return if the market proxy
ε error term
The same is done when using the 3 factor model only two additional estimators are added HML and SMB. The CAPM does not take the value and size premium into account, therefore premiums are included into the error term. With the 3 factor model a part of the error term is explained in comparison with the original CAPM. This second analysis is done because in the original CAPM it is not clear whether the market proxy had a better fit because of a better representation of the systematic risk or a better representation of the value and size premium. (Ri − Rf)= α + βi(Rm − Rf) +βs ∗ SMB + βh ∗ HML + ε Formula 2
SMB Monthly premium for small sized firms HML Monthly premium for value stock
When this is done it creates a cross section regression analysis on the systematic risk and it makes it possible to compare the fit of the two market proxies. To analyse which market proxy has the better fit, the significance of the estimators and the R2 are compared. It is important for the estimators to be significant in order to be sure that they are not equal to zero2. TheR2 measures the proportion of variance in the stock return, which can be explained by the market return. The scale ranges between zero and one, with one being the perfect fit. When the R squared is equal to 1 it would mean that there is no error term. As you can see in the formula below this would mean that the sum squared of errors (SSE) would be equal to zero or extremely close to zero.
R
2= 1-
SSESST Formula 3 SSE Sum of squared errors SST Sum of squared total
The accuracy of the R squared found in the regression output is determined by the
significance of the estimators discussed earlier. In this research the criterion is at least one percent significance for the betas. The other estimators will also be accepted at five percent. 2
The estimators are tested with a T-test with Ho:βi=0,βs=0,βH=0 and H1:βi,βs,βh=not equal to zero.
2 Significance at 1%(*), 5% (**), 10%(***) and 20%(****).
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3.1 Research implementation
Berg and Demarzo (2011) show in figure one below how the beta is estimated true OLS.
Figure 1 (Berg and Demarzo, 2011)
The dots in the figure show the excess return of the market on the horizontal axis and on the vertical axis the excess return is shown of the company Cisco at the same point in time. OLS creates a line that minimizes the vertical distance between all the dots and the line. The slope of this line (beta) compares the volatility of the stock with that of the market. To recreate the example above for this research the program STATA is used. The first step is to upload all the monthly excess return of the Dutch companies into STATA. This is also done for the market proxies and the value and size premiums. To calculate the regressions the command REGRESS is used.
See below for an example:
CAPM with Dutch market proxy: Regress Unilever MSCI Netherlands CAPM with EMU market proxy: Regress Unilever MSCI EMU
3 factor model Dutch market proxy: Regress Unilever MSCI Netherlands HML NL SMB NL 3 factor model EMU market proxy: Regress Unilever MSCI EMU HML EU SMB EU
4 Data
The stock prices used in this paper are all provided by DataStream. This includes all the stocks traded in the Dutch equity market and the prices of MSCI Netherlands, MSCI EMU and the German ten year government bond index. One problem with these stock prices is that when a firm pays out dividend, they lose cash to investors. This decreases the market
capitalization of the firm. This dividend return is thus not included in the stock price
anymore. For the stock price to be an accurate representation of the past returns, reinvestment of the dividends is needed to keep all the return information in the stock prices.
This is why DataStream has a RI (return index) function. This function assumes that dividends are reinvested to purchase additional shares at the closing value of that day in which the dividend was distributed. This method adds 1/260th part of the yearly dividend yield, while each part represents a workday.3
3 Holidays are ignored.
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With these prices the return of the market proxies and of the stocks can be calculated. As previously mentioned the prices at the end of each month are given by DataStream, but to calculate the return we use the following formula: r
=
P(t)−P(t−1)P(t−1)
With P(t) being the new price and P(t-1) being the price in the month before that. Once this is done, the return of the German ten year government bond index is subtracted to get the excess return of the indexes and stocks, so the regression can start. The German ten year government bond index is considered as the risk free return (Rf) in this paper.
For the Dutch market proxy the MSCI Netherlands is used and for the EMU market proxy the MSCI EMU is used. The MSCI Netherlands Index is designed to measure the performance of the large, mid and small cap segments of the Dutch equity market and the MSCI EMU Index does the same for the ten Developed Markets in the EMU.4 These two market proxies will give us the best comparison because they are both made according to the MSCI Global Investable Market Indexes (GIMI) Methodology.
Kenneth R. French (2014) has calculated the yearly premiums for the HML and SMB estimators for the whole Euro area. In this paper the assumption is made that the HML and SMB estimators are equal for Europe and the EMU. In the table below the monthly premiums can be found derived from the earlier mentioned yearly premiums (EAR5).
Table 1 (monthly premium in percentages for size and value in Europe)
For the Dutch equity market there is no official estimate of the HML and SMB factors, so the findings of Nick Marnix Suurmond (2010) are used. In his bachelor thesis he tried to find evidence of the size and value premium for the Dutch equity market. Suurmond did not find strong evidence for the value premium in his paper. However, he did find evidence for the size factor after the collapse of the internet bubble where the size premium seems to act as a risk factor. Similar evidence is found in this paper regression output.
Table 2 (monthly premium in percentages for size and value in the Netherlands)
The SMB and HML estimators are calculated in the same way as is found in the paper of Fama and French (1993). First all the stocks in the Netherlands are divided in low, medium and high book to market ratio (L,M,H). Then it is also divided into two parts according to small and big market capitalization (S,M). This creates six different portfolio’s (S/L, S/M, S/H, B/L, B/M, B/H). For example the S/L portfolio consists of stocks that have low market capitalization and high book to market ratio. Formula 4 shows how the SMB estimator is derived and formula 5 shows how the HML estimators is derived.
SMB= (S/L + S/M + S/H)/3 − (B/L + B/M + B/H)/3 Formula 4 4
Austria, Belgium, Finland, France, Germany, Ireland, Italy, the Netherlands, Portugal and Spain.
5
Effective interest rate.
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HML= (S/H + B/H)/2 − (S/L + B/L)/2 Formula 5
As can be seen the SMB formula looks at the average return of small sized firms (S) minus the average return of big sized firms (B). Therefore it does not take the market to book ratio into account to capture the premium small sized firms have over big sized firms. The HML formula is the opposite, so it looks at the average return of firms with high market to book ratio (H) minus the firms with low market to book ratio (L) to capture the premium of value stock of growth stock. This is also done for Europe by Kenneth R. French (2014).
5 Empirical results CAPM:
In table 3 below the results of the regression for the Dutch large cap are shown. The firms that performed better under the MSCI EMU are colored red and the firms that did better under the MSCI Netherlands are colored in black. One difference with Robert S. Harris and others (2003) is that this research has a higher R squared. This is due to the fact that this paper uses ex post returns instead of ex ante expected returns. With ex ante expected returns the R squared is lower because the analysts growth forecasts and discount cash flow models provided by IBES are also tested. For the stocks in the large cap all of the betas are
significant at one percent and the alphas of the regression are close to zero and not significant, except for Unibail Rodamco.
Table 3
For the Dutch large cap, 50 percent of the firms performed better under the EMU market proxy. However there is a negative average difference of the R squared of 1,11 %. This means that on average the MSCI Netherlands had a better fit with the stocks in the large cap. Akzo Nobel had a R squared of 65,41 with the MSCI Netherlands and with the MSCI EMU it had a R squared of 53,2. With a decrease of 12,21 this is the largest decrease of all the large cap firms.
The reason that the MSCI Netherlands had a better fit with the large firms of the Dutch equity market is because 71.5 percent of the MSCI
Netherlands index consists out of: Unilever, ING, Philips, ASML, Akzo Nobel, Ahold, Aegon,
Heineken, Reed elsevier and KPN (see table 4). Due to their large weight in this market index, once regressed these firms have a positive bias toward the domestic market proxy. Surprisingly KPN, ING, ASML and Philips have a better fit with the MSCI EMU even with the positive bias towards the MSCI Netherlands. In the EMU market proxy there are no bias effects because the ten firms with the biggest weights in the index are all non-Dutch firms.
Table 4
In table 5 below the results show that all the betas of the mid cap firms are also significant at one percent. In the mid cap the output shows that there are more significant alphas at five percent in comparison to the large cap. Arcadis and Accelgroup have significance alphas at one percent.
Table 5
For the mid cap the number of firms that had a better fit with the EMU market proxy was 66,67 percent. On average the MSCI Netherlands had an R squared of 31,68 percent and the MSCI EMU had a R squared of 33,46 percent. This is an average increase in the R squared of 1,78 percent which means that on average the EMU market proxy performed better. ASM international and TKH group have the highest increase of their R squared of about 10 percent. In table 6 the regression output for the small cap stocks is shown. The betas are all
significant at one percent, except for Value 8. This means that the return of Value 8 could not be explained by the beta and that CAPM is not valid. Amsterdam commodities show
significance of an alpha at one percent.
Table 6
For the small cap 73,91 percent of the firms perform better under the EMU market proxy. The average R squared difference is 2,38 percent which means that the MSCI EMU has a better fit.
Of all the 64 firms, 41 firms performed better under the MSCI EMU market proxy and on average there is a higher R squared of 1.09 percent for the EMU market proxy. This is no strong evidence for an overall better fit. However if we look at firm specific situations, there is evidence that the MSCI EMU has a better fit for a large part of the Dutch equity market. There is also evidence that as the caps become smaller the home bias decreases. Robert S. Harris and others (2003) also asked for further research on this topic to be done for smaller cap firms since in their study they only use large cap firms. This raises the question if Robert S. Harris and others (2003) already anticipated that the smaller firms would have a better fit with the alternative market proxy. However since there is no research to be found for this matter it is hard to say if this is a general empirical finding.
The simple CAPM does not take the value and the size premium into account. With the next analysis of this paper the two estimators are added to the model.
5.1 Empirical results Fama and French 3 factor model
In table 7 the results of the regressions for the Dutch large cap according to the 3 factor model are shown. All the betas are significant at one percent and there are no changes with the alpha from the original CAPM. When regressed with the MSCI Netherlands the SMB estimator is significant at five percent for Arcelormittal, Corio and Randstad. The regression of the large cap firms with MSCI EMU brings further evidence of the SMB estimator for Arcelormittal, Corio and Randstad. This time it is significant at one percent. There is no strong evidence for the HML estimator. However this is consistent with the findings of Suurmond (2010).
Table 7
Like in the simple CAPM model, 50 percent of the firms performed better under EMU market proxy. There is still a decrease in the average difference in the R squared of 0,83 %. Arcelormittal, Corio and Randstad had a significance of five percent with the SMB
Netherlands and a significance of one percent with the European SMB estimator. The European SMB factor has thus a better fit for these firms.
In table 8 the regressions are shown for the mid cap. All the betas are significant at one percent. The regression with the domestic estimators show evidence of the SMB factor for Bam group and Brunel at a significance of five percent. The regression output show evidence for the HML estimator with a significance of five percent for ASM International. The
regression with the EMU estimators show evidence for the SMB factor at one percent for Brunel.
Table 8
For Brunel, the SMB estimator has a closer fit with SMB Europe than with SMB
Netherlands. The HML estimator for ASM International has better fit with the Dutch HML estimator and the SMB estimator of Bam group also has a better fit with the Domestic estimator. With the 3 factor model 76.2 percent of the firms in the mid cap performed better under the MSCI EMU than the MSCI Netherlands. This is an increase of almost ten percent in comparison with the original CAPM. The average R squared of MSCI Netherlands was 33,02 percent and for the MSCI EMU it was 34,74 percent. This is an increase of 1,72 percent, which is similar to the original CAPM.
Table 9 shows the results of the regressions of the 3 factor model for the small cap. The same results are found for the original CAPM. The betas are all significant at one percent except for Value 8. The regression with the MSCI Netherlands gave evidence for the SMB estimator for Beter Bed and Heijmans with a significance of five percent. There is evidence that the HML estimator is significant at five percent for Ballast Nedam. The regression with MSCI EMU also gave evidence for the SMB factor for Beter Bed at five percent. Brill shows evidence for the HML factor at one percent and for Heijmans and Kas Bank at five percent.
Table 9
With the small cap, 19 out of 23 firms have a higher R squared in comparison with the MSCI Netherlands. The average difference of the R squared is 2,37 percent which means that the MSCI EMU had an overall better fit for the small cap with the 3 factor model. This is also similar to what is found in the original CAPM.
The regressions with the 3 factor model come close to the results of the original CAPM. 45 out of 64 companies performed better under the MSCI EMU. This is four more in comparison with the original CAPM. The average difference of the R squared is 1,156 percent. This is a small increase compared with the original CAPM which had an increase of 1,09 percent. Of the 64 firms 11 firms show evidence of the HML and SMB estimator. This makes the discussion whether there is a value and size premium questionable for the Dutch equity market.
6 Conclusion
The large cap in the Dutch equity market had a better fit with the MSCI Netherlands for the CAPM and the 3 factor model. This could be explained by the fact that the ten biggest firms in the MSCI Netherlands are all in the Dutch large cap, which created a positive bias towards the MSCI Netherlands. KPN, ING, ASML and Philips also had this positive bias but had a
better fit with the MSCI EMU. This is strong evidence that for these four firms the MSCI EMU is a better fit. In the regression output there is evidence of the SMB estimator for Arcelormittal, Corio and Randstad. For the Dutch SMB factor this was significant at five percent and for the European SMB factor this was one percent. For these three firms the European SMB factor had a better fit. There is no evidence found of the HML factor for the large cap.
The regressions in the mid and small cap show that the firms have a better fit with the MSCI EMU. This is found for the CAPM and the 3 factor model. The data seem to show evidence that the home bias decreases as the caps decrease. However, this could also be as a result of the positive bias explained before.
There is evidence that the European SMB estimator is better represented in the mid and small cap than the SMB Netherlands. Despite the lack of evidence for the HML factor for Brill, Heijmans and Kas Bank, there is evidence for the HML Europe.
The 64 companies of the Dutch equity market had an average difference of the R squared of 1,156 percent for the 3 factor model and the original CAPM had in difference of 1,09 percent. Although this could be regarded as lack of strong evidence that the MSCI EMU had a better fit, if we look at companies’ specific situations, a conclusion can be found that there was evidence that the MSCI EMU had a better fit. The best examples are KPN, ING, ASML and Philips who had large weights in the MSCI Netherlands but still had a better fit with MSCI EMU.
Further research on this matter should be expanded to other developed countries of the EMU6 to see if similar results are found. However these researches are limited until there is an official recognized scientific database with publicly accepted estimates of the HML and SMB estimators for the individual countries of the EMU. With proper HML and SMB estimators the EMU area will become an ideal place for empirical research in this area and it would create greater transparency.
6
Austria, Belgium, Finland, France, Germany, Ireland, Italy, Portugal and Spain
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