The influence of the recent financial crisis on
the risk-return relationship in Germany
Joris Koning
10250905
Bachelor Thesis
1 Abstract
This study looks at the effect that the recent financial crisis has had on the risk-return relationship in the German stock market. A dummy variable indicating pre/post crisis and an interaction variable between this dummy variable and the idiosyncratic risk variable are added to a Fama-Macbeth regression to examine the effect of the recent financial crisis on the relationship between idiosyncratic risk and return. Evidence is found for a change in the idiosyncratic risk-return relationship from an insignificant relationship before the recent financial crisis to a significant negative relationship after the beginning of the recent financial crisis.
2
Table of Contents:
I. Introduction ... 3
II.
Literature review ... 5
III. Theoretical framework ... 7
IV. Methodology ... 8
V. Data ... 11
VI.
Results ... 14
VII.
Conclusion ... 18
VIII.
References ... 189
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3
Introduction
A well-known and logical economic principle is that risk in an investment has to be
compensated with a higher return. Research on different kinds of securities demonstrated a clear positive relationship between the riskiness of a security and the return of the security (Baker and Wurgler, 2013). That is why stocks generally earn higher returns than less risky corporate bonds, and corporate bonds earn higher returns than the less risky treasury bonds. So theory expects stocks with a higher volatility to provide a higher return. However, empirical research shows that this positive relationship does not always hold between different securities in the stock market. Several papers found a negative relationship between the risk of stocks and their returns. (See, e.g., Haugen and Heins (1975); Ang, Hodrick, Xing, and Zhang (2006); Ang, Hodrick, Xing, Zhang (2009) and Baker and Haugen (2012). The phenomenon of a reverse risk-return relationship in the stock market is called the ‘Low Risk Anomaly’.
The risk-return relationship is a widely discussed subject in the field of finance and research on this topic is not unambiguous. Different papers examine the risk-return relationship with the use of different methods that display different results. Goyal and Santa-Clara(2003) find a significant positive relationship between the lagged equally-weighted stock variance and the value weighted average return on the market. Fu(2009) uses the exponential EGARCH method which makes use of conditional variances and finds a significant positive relationship between risk and return.
However, contrary results are found by Glosten, Jagannathan and Runkle(1993) and Ang, Hodrick, Xing, Zhang(2009) (AHXZ hereafter). The latter used the three-factor model of Fama and French(1993) and a two stage Fama-Macbeth(1973) regression to research the relationship between expected return and past idiosyncratic volatility of stocks around the world. Their results show a significant negative relationship and they conclude that this is a worldwide phenomenon.
Despite the extensive research on the risk-return relationship, the effect of periods with financial turmoil on the risk-return relationship has received little attention in the debate. In the last three months of 2008, the stock market in Germany experienced a major stock market crash with a drop in value of the DAX-index of 32% in three months. This stock market crash was the result of the 2007-2009 financial crisis caused by the house market
4 bubble in the U.S. (Duca, Muellbauer & Murphy, 2010). There are several reasons to assume that the financial crisis did change the risk-return relationship on the stock market. First, Yu & Yuan(2011) showed that investor’s sentiment can influence the mean-variance tradeoff on the stock market. It is obvious that a stock market crash like the one in the end of 2008 changed the investor sentiment. Secondly, Prospect theory, as introduced by Kahneman and Tversky (1979), states that people that experience losses tend to take more risk in an attempt to earn back their lost money. These are only two possible reasons for a change in the risk-return relationship on the stock market during the financial crisis. This makes it interesting to examine the effect of the financial crisis on the risk-return relationship. This is the first paper that examines the effect of the financial crisis on the relationship between risk and return using the three-factor model of Fama and French(1993).
The main question conveyed in this paper is: Has the relationship between idiosyncratic risk and expected return changed since the start of the financial crisis? To answer this question, idiosyncratic risk is defined relative to the three factor model of Fama and French(1993). To analyze the effect of the financial crisis on the risk-return relationship, a dummy variable indicating pre/post crisis and the interaction variable between the dummy variable and the idiosyncratic volatility variable will be added to a Fama-MacBeth (1973) regression. Data from the German stock market will be used. However, the German stock market is one of the largest stock markets in Europe and an effect of the financial crisis on the risk-return relationship that is found for the German stock market will provide informative implications for other stock markets in Europe as well.
This section introduces the subject of the risk-return relationship and the research question that this paper aims to answer. The rest of this paper is organized as follows. In the second section an overview is given on the literature about the risk-return relationship in the stock market and about the effect of the recent financial crisis on the risk-return
relationship. In section three the theoretical framework for the research in this paper is given. In section four the method that is used in this paper to answer the research question will be explained. Section five will introduce the data that is used in this paper. In section six the results are presented and in section seven the results will be discussed and a conclusion will be drawn from the results.
5
Literature review
The risk-return relationship.
The capital asset pricing model of Sharpe (1964) and Lintner (1965), which was built on the framework of Markowitz (1952) assumes that idiosyncratic risk does not play a role in the pricing of assets because investors are able to hold a portfolio of stocks to diversify away all the idiosyncratic risk. This implies that investors only care about systematic risk. Assuming that the CAPM is right there would be no relation between the idiosyncratic risk of a stock and its return. However, Merton (1987) has showed that in a situation where investors do not have access to all the information within a market, they cannot fully diversify away all the firm specific risk which implies that investors require a higher return for stocks with more idiosyncratic risk. Malkiel and Xu(2002) tested idiosyncratic volatility under the framework of Fama and Macbeth(1973) and the framework of Fama and French(1992). They have found that idiosyncratic volatility is useful in explaining cross sectional expected returns under both frameworks and conclude that idiosyncratic volatility is more powerful in
explaining the cross-section of returns than the CAPM beta or size measures. This result supports Merton his finding that investors do require a risk premium for idiosyncratic risk. More empirical evidence for a positive relationship between idiosyncratic risk and return is given by Fu(2009), who has used exponential EGARCH models to estimate expected idiosyncratic volatility. He has found a significantly positive relationship between the by the EGARCH models estimated conditional idiosyncratic volatility and expected returns. In contrast to these results, there is also evidence in the finance literature for a negative relationship between risk and return. Glosten, Jagannathan and Runkle(1993) have used 7 different GARCH-M specifications to examine the role of model specifications when estimating the risk-return relationship. They have found that the standard GARCH-M model, which gave a positive but insignificant relationship in their research is not correctly specified. Therefore, they have modified the standard GARCH-M so that positive and negative
unanticipated returns are allowed to have different effects on conditional variance. With the use of this modified model they have found a negative relationship between the conditional mean and the conditional variance of the excess return on stocks, which becomes even stronger and significant when conditional variance is allowed to depend on seasonal
6 influences and the interest rate. More recently, Ang, Hodrick, Xing, and Zhang (2006) used the three-factor model of Fama and French(1993) to analyze the risk-return relationship in the cross-section of U.S. stocks. They have found that stocks in the U.S with more
idiosyncratic volatility tend to have lower returns than stocks with less idiosyncratic volatility. In their paper, stocks are divided in five portfolios sorted on the idiosyncratic volatility of the stocks. They find a 1.06% higher average return for the quintile portfolio with the lowest idiosyncratic volatility stocks than for the quintile portfolio with the highest idiosyncratic volatility stocks. A higher return for stocks with less idiosyncratic volatility implies a negative relationship between idiosyncratic volatility and return. To ensure that this finding cannot be a result of only a small sample or data snooping, AHXZ have examined the same relationship for the seven largest equity markets around the world and concluded that the negative relationship between idiosyncratic volatility and return is a worldwide phenomenon. Concluding, it is clear that idiosyncratic risk plays a role in the determination of stock returns. However, financial literature is not unambiguous about whether the relationship between idiosyncratic risk and return is positive or negative.
The effect of periods with financial turmoil on the risk-return relationship
Aragó and Salvador(2010) is the only paper that examines the effect of the recent financial crisis that started in 2007 on the risk-return relationship. They have made use of the GARCH-M approach and define three different specifications for the conditional variances: a standard GARCH model, a regime switching RS-GARCH model and a MIDAS specification. With use of the RS-GARCH model they have found a significant positive relation between risk and return. They also found the interesting result that investors are less risk averse during the period from 2007-2009, which is the period of the financial crisis, than in the period before 2007. To find this result they have introduced a dummy variable in the RS-GARCH specification, which has a significant negative coefficient. The possible explanation for the lower risk aversion during financial turmoil periods they give is that investors have a different risk perception depending on the market turmoil. The same investment is perceived riskier in periods of calm than in periods of financial turmoil where any investment involves risk (Aragó and Salvador, 2010).
7
Theoretical framework
The three-factor model
In this paper the standard three-factor model of Fama and French (1993) (three-factor model hereafter) is used to define the idiosyncratic risk of stocks and to estimate the risk factor loadings. The three-factor model is used a lot in the analysis of financial data in the United States and recently also “around the world” (Brückner, Lehmann, Schmidt & Stehle ,2014). The three-factor model provides an alternative to CAPM for the expected return estimation. The model adds two additional factors to the original CAPM to explain the influence of the size and the book-to-market ratio of a firm on its expected return. Similar to the CAPM, the three-factor model makes use of the conventional market factor which contains the excess return of the market to estimate expected return. However, the three-factor model expands the CAPM by taking into account the difference in return between small and big firms and the difference in return between firms with a high and low book-to-market ratio to determine the excess return of an asset. The three-factor model is described by equation 1:
Ri− Rf= α + βMKT[Rmkt− Rf] + βSMBSMB + βHMLHML (1) Where Ri stand for the asset’s return, Rf stand for the risk free rate and the Rmkt variable stands for the market portfolio return. The SMB factor stands for the return of small firms minus the return of big firms and the HML factor stands for the return of firms with a high book-to-market-ratio minus the return of firms with a low book-to-market ratio.
Fama and French(1995) proved that the size and the book-to-market factor do have an effect on the long term profitability of firms. They found small firms tend to be less profitable than large firms and that firms with a high book-to-market value tend to be persistently distressed while a low book-to-market ratio is associated with sustained strong profitability.
The Fama-Macbeth(1973) regression
Fama and Macbeth (1973) provided an approach to asset pricing that is widely used in the finance literature. The Fama-Macbeth (1973) regression estimates the premium that is
8 rewarded for an asset’s risk factor exposure by the market in two steps. First, a time-series regression is performed where an asset’s excess return is regressed against the factors that are assumed to drive the assets returns. The regression equation is shown in equation 2. 𝑟𝑟𝑖𝑖,𝑡𝑡= α𝑖𝑖+ β1𝐹𝐹1,𝑡𝑡+ β2𝐹𝐹2,𝑡𝑡+ ⋯ + 𝐵𝐵𝑛𝑛𝐹𝐹𝑛𝑛,𝑡𝑡+ ε𝑖𝑖,𝑡𝑡 (2) Where 𝑟𝑟 is the asset’s excess return and 𝐹𝐹 stands for the factor that is considered to drive the asset’s returns. The regression coefficients of this regression show the extent to which the asset is exposed to the factors. The regression coefficients are called the risk factor loadings. Second, a cross-sectional regression is performed where an asset’s excess return is regressed on the risk factor loadings that are estimated by the first stage time-series regression. The second stage regression is shown in equation 3.
𝑟𝑟𝑖𝑖= α𝑖𝑖+ γ1𝛽𝛽̂1,𝑡𝑡+ γ2𝛽𝛽̂2,𝑡𝑡+ ⋯ + γ𝑛𝑛𝛽𝛽̂𝑛𝑛,𝑡𝑡+ ε𝑖𝑖,𝑡𝑡 (3) Where 𝑟𝑟 is the asset’s excess return and 𝛽𝛽̂ is the estimated risk factor loading from the first stage regression. The regression coefficient of this second stage regression indicates the premium that is rewarded for the exposure to the risk factors.
Methodology
As it is described in the introduction, the aim of this paper is to answer the question whether the financial crisis has had an effect on the risk-return relationship in the stock market of Germany. In this section the method to answer this question is described and the regression model is given.
Measuring idiosyncratic volatility
First, it is necessary to estimate the idiosyncratic volatility as a measure of risk. Similar to AHXZ, the three-factor model is used to define the idiosyncratic volatility. The excess return is regressed on the three factors (MKT, SMB, and HML) for each stock separately on a daily basis. The regressions take the form of equation 4:
9 rti = αi+ βMKTi MKTt+ βiSMBSMBt+ βHMLi HMLt+ εti (4) Where r is the asset’s excess return and MKT, SMB and HML are the Fama and French(1993) factors from daily data. These regressions produce an error term for each stock, which can be used to create a new variable: idiosyncratic risk. To measure the idiosyncratic risk of stocks per month the standard deviation of the error term in regression 4 is calculated with use of equation 5.
𝜎𝜎
𝑖𝑖= �
∑ (𝜀𝜀𝑡𝑡 𝑖𝑖−𝐸𝐸(𝜀𝜀 𝑡𝑡 𝑖𝑖))2 𝑛𝑛 𝑡𝑡=1 𝑛𝑛(5)
Where 𝜎𝜎 is the standard deviation of the stock’s residuals per month, 𝜀𝜀 is the stock’s residual from regression 4 and n is the number of stock return observations in the specific month. This calculation has to be performed for each month separately. The idiosyncratic risk of the stocks per month will be used as an independent variable in the second stage of the two stage Fama-Macbeth(1973) regression that is described below.
Examining the effect of the financial crisis on the risk-return relationship
In the first stage of the Fama-Macbeth(1973) regression, the three-factor model of Fama and French is used to measure the risk factor loadings per firm on the three Fama and French factors (MKT, SMB and HML). The regressions take the form of equation 6:
rti= αi+ βMKTi MKTt+ βiSMBSMBt+ βHMLi HMLt+ εti (6) Where r is the asset’s excess return and MKT, SMB & HML are the Fama and French(1993) factors from monthly data. This regression is similar to equation 4 but in this case the excess return and the three factors are regressed on a monthly basis. The monthly excess returns of the stocks that are listed at the DAX-index are used as the dependent variable and the monthly values for the three factors are used as the independent variables. The three betas that are found with this regression function measure to what extent each asset’s excess return is affected by each factor. The higher the beta on a factor, the more sensitive an asset is for changes in this factor. However, the regression coefficients of this regression do not measure the premium that is rewarded for the exposure of the asset to the risk factor. In the
10 second stage of the two stage Fama-Macbeth(1973) regression, the values of beta that are obtained with the use of the first stage regression can be used to find the premium that is rewarded for the risk exposure of the assets.
The second and final stage of the Fama-Macbeth(1973) regression is a cross sectional regression. In this regression the created idiosyncratic risk variable, the three risk factor loadings that are found with the use of equation 3, the excess return per month and two newly introduced variables are used. To control for the effect of the financial crisis on the stock market, a dummy variable is introduced in this regression, which is zero before the beginning of the financial crisis and one after the beginning of the financial crisis. This variable is called the DUMMYFC variable. The point in time where the financial crisis that started in 2007 begins to have an effect on the stock market in Germany is chosen on the basis of the course of the DAX-index. The total return index of the DAX is shown in graph 1. On the horizontal axis the date is shown and on the vertical index the total return index of the DAX-index starting at 3000. From October 2008 the DAX-index decreases from 5806.33 to 4394.79 index points in December 2008. This decrease in value of more than 24% can be seen as a major stock market crash. That is why this paper uses October 2008 as the beginning of the financial crisis on the stock market in Germany. This implies that the DUMMYFC variable will be one from the beginning of October 2008.
Graph 1- The beginning of the financial crisis on the German stock market
Source: Datastream 3000 4000 5000 6000 7000 8000 9000 01 -2 007 02 -2 007 03 -2 007 04 -2 007 05 -2 007 06 -2 007 07 -2 007 08 -2 007 09 -2 007 10 -2 007 11 -2 007 12 -2 007 01 -2 008 02 -2 008 03 -2 008 04 -2 008 05 -2 008 06 -2 008 07 -2 008 08 -2 008 09 -2 008 10 -2 008 11 -2 008 12 -2 008 01 -2 009 02 -2 009 03 -2 009 04 -2 009 05 -2 009 06 -2 009
11 To control for the interaction between the financial crisis effect and the idiosyncratic volatility, an interaction variable is generated by multiplying the DUMMYFC variable by the idiosyncratic volatility variable. This interaction term is called: IV*DUMMYFC. Finally, with the excess return as dependent variable and the idiosyncratic volatility, the three risk factor loadings, the DUMMYFC and the IV*DUMMYFC as independent variables, the regression takes the form of equation 7.
ri(t, t + 1) = c + γ1σi(t − 1, t) + γ2βMKTi+ γ3βSMBi+ γ4βHMLi
+γ5DUMMYFCi(t, t + 1) + γ6σi(t − 1, t) ∗ DUMMYFCi(t, t + 1) + εi(t, t + 1) (7)
Where 𝑟𝑟𝑖𝑖 is stock i’s excess return from month t to t + 1. The term 𝜎𝜎𝑖𝑖(𝑡𝑡 − 1, 𝑡𝑡) is stock i’s idiosyncratic volatility computed using daily data over the previous month from t – 1 to 1. βMKTi, βSMBi and βHMLi are the risk factor loadings on the three factors as found with regression function 6. The time lag of these variables is irrelevant because they are constant over time. The term 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐹𝐹𝐷𝐷𝑖𝑖(𝑡𝑡, 𝑡𝑡 + 1) is the variable that indicates whether the excess return from month t to t + 1 is realized before or after the beginning of the financial crisis. The interaction variable is given by the term σi(t − 1, t) ∗ DUMMYFCi(t, t + 1). This variable consists of 2 different time lags. The timing of the variables in the regression is important because this paper assumes that the idiosyncratic volatility over the period from month t-1 to t influences the excess return of the period from month t to t+1. Together these
independent variables are assumed to explain for the excess return of the stocks.
Data
The daily stock return data of all DAX listed stocks are obtained from Datastream. The data type that is used is the daily percentage change of the total return index. For the monthly stock data, exactly the same data is used but now on a monthly base. The time period used is from the 1st of January 2000 until the 30th of June 2014. Graph 2 shows the returns of the DAX-index per year during the time period that is used in this research.
The data on the three factors of Fama and French is obtained from the database of Brückner, Lehmann, Schmidt and Stehle (2014). For both the daily and the monthly data, the top stock market segment without tax credit data is used. The reason why the top stock
12 -50 -40 -30 -20 -10 0 10 20 30 40 50
Dax-index return
Dax-return (%) market segment data is used and not the all stock market segment data is because, as noticed in Brückner et al. (2014) the data of the top market segment is less likely to be affected by small and tiny firms from the lower market segments and because empirical results for the top market segment is less likely subject to IPO effects.Graph 2 - The historical returns of the DAX-index
Source: Datastream
The precise way in which Brückner et al. (2014) defined the data in their database is as follows: the MKT factor is calculated as the return of the market portfolio minus the return on risk free assets, where they use their own data sample to define the market portfolio return. For the risk free rate they use the 1-month money market rate of Europe (EURIBOR). The SMB factor is calculated as the difference between the rates of returns on the MSCI Germany SMID Cap (small and mid caps) and the MSCI Germany Large Cap. For the HML factor, they use the MSCI Germany Value and MSCI Germany Growth indices. Table 1 presents summary statistics for the stock returns of the companies listed on the DAX-Index. The number of days included in the dataset is equal to the number of trading days on the stock market in Germany for most of the companies. The reason why there are fewer days of data available for four companies is that these companies were not registered at the stock market at the 1st of January 2000.
13
Table 1 - summary statistics of DAX-listed stocks. Company
Name Number of days volatility (%) Total volatility (%) Idiosyncratic excess return (%) Average
Adidas Allianz 3687 3687 31 37 25 23 12 -2 BASF 3687 29 19 10 BMW 3687 34 24 11 Bayer 3687 33 25 9 Beiersdorf 3687 28 26 10 Commerzbank 3687 48 36 -11 Continental 3687 42 35 22 Daimler 3687 35 21 3 Deutsche Bank 3687 40 26 -1 Deutsche Boerse 3409 34 28 13 Deutsche Post 3461 30 23 4 Deutsche Telekom 3687 34 25 -8 EON 3687 30 23 2
Fresenius Medical Care 3687 28 26 5
Fresenius 3687 32 30 13 Heidelbergcement 3687 40 35 6 Henkel 3687 26 22 10 Infineon Technologies 3637 61 51 7 K + S 3687 37 32 18 Lanxess 2396 41 30 19 Linde 3687 27 21 9 Deutsche Lufthansa 3687 34 26 1 Merck KGAA 3687 32 29 13 Muenchener ruck 3687 33 23 0 RWE 3687 29 23 0
14
SAP 3687 39 30 8
SIEMENS 3687 35 21 5
Thyssenkrupp 3687 38 27 2
Volkswagen 3687 39 31 18
Note: the 3th and the 4th column report average volatility of the stocks, The values are annualized by multiplying by √254.
The last column reports average return. These values are annualized by multiplying by 254.
The data on volatility in table 1 is all annualized data by multiplying by √254. The first measure is total volatility, which is measured as the standard deviation of the raw daily stock return. The second measure is the idiosyncratic volatility, computed with respect to the three-factor model as described in equation 4. The average annual total volatility is 35% where Infineon technologies has the highest total volatility of 61% and Henkel the lowest total volatility of 26%. The average annual idiosyncratic volatility is 27%, Infineon also has the highest idiosyncratic volatility with a value of 51%, BASF has the lowest idiosyncratic volatility with 19%. Total volatility and idiosyncratic volatility are highly correlated with each other with a correlation of 86%. The last columns contains the average excess returns in percent of the 30 companies, this data is annualized by multiplying by 254.
Results
This section discusses the results of the regression model that was introduced in section three. First, the effect of the financial crisis on the risk-return relationship will be shown and discussed. Next, the relationship between idiosyncratic risk and return before the start of the financial crisis will be shown and compared to previous research. Finally, the regression coefficients on the control variables will be shown.
Table 3 shows the results of the second stage Fama-Macbeth(1973) regression in equation 7. The two regression coefficients on the DUMMYFC and the IV*DUMMYFC variables are used to examine whether the financial crisis has had an effect on the relationship between idiosyncratic risk and return. Both regression coefficients are significant at the one percent level, which indicates that the financial crisis has had an effect on the risk-return relationship. However, the sign of the two regression
15 coefficients are contradictory. The regression coefficient on the dummy variable
indicating pre/post crisis is positive with a value of 2.61 while the regression coefficient on the interaction variable between idiosyncratic volatility and the financial crisis dummy variable is negative with a value of -1.67. First, the implications of the negative regression coefficient on the interaction variable will be given and thereafter the implications of the positive regression coefficient on the dummy variable will be given. Table 3 – The effect of the financial crisis on the risk-return relationship
Variable Regression
Coefficient 95% Confidence interval
Constant .3813374 (0.75) -.6148184 1.377493 IV .10318 (0.42) -.3815232 .5878832 β(MKT) -1.499336 (-1.18) -3.987978 .9893072 β(SMB) 1.356323 (1.21) -.8481915 3.560838 β(HML) -.3517774 (-0.41) -2.017304 1.313749 DUMMYFC 2.61446*** (4.63) 1.508038 3.720882 IV*DUMMYFC -1.667099*** (-4.99) -2.32241 -1.011788 R-squared Adjusted R-squared 0.0099 0.0088 F-value: 8.51
Note: Table reports Fama-Macbeth(1973) regression in equation (6), *** Means significant at the 1% level, t-statistic is shown in the brackets underneath each coefficient
16 To determine the implications of the regression coefficient on the interaction term it is useful to take a look at the regression coefficient on the idiosyncratic risk variable. This regression coefficient indicates that the relationship between the idiosyncratic risk and return was slightly positive with a value of 0.10 before the start of the financial crisis. However, this regression coefficient is not significant. The negative regression coefficient on the interaction term indicates that when the financial crisis started the positive but
insignificant relationship between idiosyncratic risk and return changed to a strongly significant negative relationship. This change in the relationship between idiosyncratic risk and return proves that the financial crisis has had an effect on the risk-return relationship. This negative change in the risk-return relationship indicates that investors require a lower return for investments with the same amount of idiosyncratic risk since the financial crisis. Furthermore, the negative regression coefficient on the interaction term indicates that investors became risk seeking during the financial crisis. The negative regression coefficient shows that investors require less return when a stock carries more idiosyncratic risk. A possible explanation why investors became risk seeking during the financial crisis is given by prospect theory as described by Kahneman and Tversky (1979). This theory states that people can become risk seeking when they made a loss in an attempt to make their investment behavior profitable again.
In contrast to the negative regression coefficient on the interaction variable, the regression coefficient on the DUMMYFC variable is positive. This positive coefficient shows a strong positive relationship between the financial crisis dummy variable and the excess return. The significant positive coefficient implies that the excess return is 2.61% higher in the period after the start of the crisis than in the period before the start of the crisis, assuming that the other variables stay constant. Investors thus require an extra return of 2.61% for investments with the same amount of risk, indicating that investors became more risk averse since the start of the financial crisis. This result is remarkable and not logical according to the regression coefficient on the interaction variable, which states that
investors became risk seeking since the start of the financial crisis. A possible explanation for the positive coefficient on the dummy variable can be found in the data. To explain the contradictory result on the dummy variable regression coefficient the DAX-index return as shown in graph 2 is used to compare the index returns before and after the start of the
17 financial crisis. It is notable that the return of the DAX-index is negative in the first three years of the time period that is used in this research. The negative returns in the beginning of the 21st century are caused by the burst in the dot-com bubble (Ofek & Richardson, 2003). Furthermore, the DAX-index drops down heavily during the financial crisis in 2008, but the index restored fast and in 2009 the return is positive again. Combining the index drop in the beginning of the data sample and the quick restore of the index after the financial crisis, the positive regression coefficient on the DUMMYFC variable could be influenced by another factor than the financial crisis. If the three factor model has not correctly priced the stocks during the first three year of our data sample, which is not improbable because of the burst of the dot-com bubble, the negative returns of the first three years are captured by the regression coefficient on the DUMMYFC variable. This implies that the regression coefficient on the DUMMYFC variable is biased and does not correctly describes the effect of the financial crisis on the risk-return relationship.
In contrast to the regression coefficients on the financial crisis dummy variable and the interaction variable, the regression coefficients on the idiosyncratic volatility and the three factor loadings are not significant. As mentioned before, the regression coefficient on the idiosyncratic volatility variable shows the effect of the stocks idiosyncratic volatility on its return before the start of the financial crisis is slightly positive with a value of 0.10. This result implies that the significant negative relationship between idiosyncratic risk and return that AHXZ found for the U.S and for many countries in Europe including Germany has disappeared. However, the idiosyncratic volatility coefficient is not significant and a negative value is not excluded in the 95% confidence interval. This means that the negative
relationship between risk and return that AHXZ found cannot be rejected on the basis of this result. A possible reason for the deviation of this study from AHXZ is that they controlled for three firm characteristics (size, book-to-market and lagged return) in their regression, which are not used in this regression. Another explanation for the difference between the results in this paper and the results from AHXZ could be that they used a different time period in their dataset. The time period over which they found a significant negative relation is from 1980 until 2003 while the results in this thesis indicate an insignificant relation from 2000 until October 2008.
18 the SMB factor is positive with 1.36 and the coefficient on the HML factor is slightly negative with -0.35. However, none of the 3 coefficients on the risk factor loadings is significant.
Conclusion
This paper has examined the effect of the financial crisis on the risk-return relationship for the stock market in Germany using data from the beginning of 2000 until June 2014. The empirical literature is not unambiguous about the risk-return relationship. Some papers find a positive relationship between risk and return while others find a negative relation between risk and return. This paper finds evidence for a change in the relation between idiosyncratic risk and return during the recent financial crisis. The results of this paper show an
insignificant relationship between idiosyncratic risk and return before the financial crisis and a significant negative relationship between idiosyncratic risk and return after the beginning of the recent financial crisis. A negative relationship between risk and return implies that investors became risk averse during the financial crisis, which can be explained by the prospect theory of Kahneman and Tversky (1979). Moreover, this finding indicates that the relation between risk and return is not consistent over time, which could be an explanation of the contradictory results in the previous literature.
One limitation of this research comes from the fact that it explains the effect of the financial crisis with the use of a dummy variable that splits the data sample in two groups with the financial crisis as splitting point. To be a precise indicator of the effect of the financial crisis on the risk-return relationship, the effect of the financial crisis should be the only difference between the period before and after the financial crisis. Further research could make use of different time periods to examine whether there are more changes in the risk-return relationship. Another idea for further research is to extend this research for other countries to find evidence that the effect of the financial crisis on the risk-return relationship does not only exist in Germany but is a global phenomenon.
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