The performance of mutual funds during the financial crisis

The performance of mutual funds during the financial crisis Abstract The performance of mutual funds has been an interesting topic of research in the last few decades. The most common measurements for the performance are Jensen s alpha and the ratio s of Sharpe en Treynor. This thesis investigates the differences in performance of mutual funds in two periods, namely the period before the current financial crisis, dated from January 2003 until Augustus 2008, and the period during the financial crisis, dated from September 2008 until December 2011. I concluded that mutual funds during the financial crisis were able to beat the market, but with less amount than before the crisis. Name: Anouk van Spanje ANR: s417428 Bachelor Student Business Economics Type: Empirical study Supervisor: Y. Zhou Date: 18-may-2012

Chapter 1: Introduction and problem formulation Mutual funds appear to be first established by a Dutch merchant in 1744 (Rouwenhorst, 2004). They were introduced in the United States in 1890 (Fink, 2008), but nowadays mutual funds are very popular. A mutual fund is more or less a package of multiple stocks and/or bonds. To choose in which one you want to invest, you can look at the risks and returns related to that, because the amount of risk aversion is very personal. By investing in mutual funds you can make money by getting dividends on stocks, interest on bonds and selling your mutual fund when the price increases. But investing in mutual funds also brings costs, like the fees you have to pay such as management expenses, operational expenses and load fees. The performance of mutual fund can be measured in various ways. Over the last decades multiple researchers have investigated which methodology is best. A well-known measurement is Jensen s alpha by Jensen (1968) which is constructed using the Capital Asset Pricing Model by Sharpe (1964), Lintner (1965) and Treynor (1962). A positive alpha means that the fund has performed better than the market and vice versa. This method could also be used by using other asset pricing methods, such as Fama-French (1993) or Carhart (1997) which are extensions of the CAPM. Other well-known measurements for the performance of a mutual fund are the Sharpe-ratio (1964) and the Treynor-ratio (1962) where (R i R f ) are respectively divided by the standard deviation of the portfolio and the β i of the portfolio. There has already been a lot of research on the performance of a mutual fund. There are some studies in which this performance is linked to a financial crisis. Since we have all been confronted with the current financial crisis, I would like to find out what kind of impact this has on the performance of mutual funds. As we all know, in a crisis the price of funds will fall down. What I would like to investigate is whether mutual funds will defeat the market or vice versa by looking at Jensen s alpha and to see whether there is a different outcome for a period before the crisis and the period during the current crisis. The current financial crisis has started in 2008. For many the fall of the Lehman brothers was the big start of the crisis. This happened on 15 September 2008. In this thesis I also took this event as the start of the crisis. In order to find out how mutual funds perform during the current crisis I have composed the following research question: Is there a difference between the performance of mutual funds during the current financial crisis and before this period? In order to answer this question I have composed some sub questions: 1.) What are Jensen s alphas in the period before the crisis and the period during the current financial crisis? 2.) Is there a different outcome when using different performance measurements?

This thesis consist of a literature study with empirical findings. To simplify the method, the research is limited to the United States of America. To measure the performance Jensen s alpha is used. This alpha is derived by using the CAPM model. The necessary data are obtained from Datastream and from CRSP. To work with this data, the program STATA 11 is used. After taking a look at the alphas which came out of the regressions, I conclude that mutual funds performed better than the market. However the funds performed better in the period before the crisis than in the period during the crisis. This is also the case according to the Treynor-ratio. However according to the Sharpe-ratio, the mutual funds performed better during the crisis than before. The thesis will be allocated in chapters. In chapter 2 I will discuss the performance measurements and the current literature. In chapter 3 the empirical findings will be shown which leads to chapter 4 where I will give a summary of the thesis, give some points of discussion and recommendations and finally the conclusion will be found. Chapter 2: Literature survey There has been a lot of discussion about the question how to measure performance of mutual funds and different methods have been followed. The most common methods are the Sharperatio, Treynor-ratio and Jensen s alpha. There are some issues on how to implement these models. One of the questions is how to handle the expenses which are made in issuing a mutual fund, such as the fees. Should performance be measured before or after deducting these expenses? Another issue is which benchmark to use. There has been a lot of research on the performance of mutual funds and the outcomes are very different. 2.1 Performance measurements Many researchers based their studies on using the classical Capital Asset Pricing Model (CAPM). This one-factor model was first introduced by Sharpe (1964) and Lintner (1965). The formula of this model is as follows: R it = R f + β i (R mt R f ) + ε it (1) In this equation R it is the return of the i-th asset at time t, R f is the return of the riskless asset, β i is the systematic risk of asset i, R mt is the return of the market portfolio at time t and ε it is the residual.

Sharpe (1966) didn t just contribute by introducing the CAPM; he also introduced the rewardto-variablity-ratio, which is now known as the Sharpe-ratio. This ratio was based on the ratio that Treynor (1962) first introduced, the reward-to-volatility-ratio. These ratios tell whether a portfolio s returns are caused by investment decisions or if they are a result of excess risk. The higher the ratio, the better the risk-adjusted performance has been. The difference between the Treynor-ratio and the Sharpe ratio is that in the first the average annual return minus the pure interest rate are divided by the beta of the portfolio, while the second ratio is divided by the volatility. These ratios can be used as a measurement for the performance of mutual funds. By estimating the outcomes of the ratios, the mutual funds can be shown in a ranking list. The higher the ratios are, the better the fund performed. Jensen (1986) came with a whole new approach to measure performance. The outcome of the ratios of Sharpe and Treynor were listed and ranked. These were relative approaches, since the funds were compared to each other. Jensen (1986) found a way to compute an absolute approach. He wanted to measure the performance to certain standard. Jensen (1986) pointed out that performance exists of two dimensions. The first one is about the ability to predict future prices and the second one is about minimizing the insurable risk. His method only takes the first dimension into account. His method was based upon the CAPM model. By rewriting formula (1) the following formula is shown: R it - R f = β i (R mt R f ) + ε it (2) This formula can be seen as a regression formula, where β 0 is equal to zero. Jensen stated that this β 0 could be seen as a measurement of the performance from the fund. Since then the β 0 was known as Jensen s alpha (α J ). The formula is as follows: α J = R it [ R f + β i * (R Mt R f ) + ε it ] (3) A positive alpha indicates that the fund has performed better than the market and vice versa. This method could also be used by using other asset pricing methods, such as Fama-French (1993) or Carhart (1997), which are extensions of the CAPM. The Fama-French 3-factor model extended the CAPM by adding size and value factors. One factor they added was small-minus-big. This factor was composed by looking at the market value of equity and accounts for the size of firms. Another factor they added was high-minus-low. This factor is calculated by using the book-to-market ratios. By including these factors, the model adjusts for the consideration that value and small cap stocks outperform markets regularly.

Carhart (1997) extended this model by adding a momentum factor. This factor is constructed by the monthly return difference between the returns on the high and low prior return portfolios. This way the cross-sectional return patterns are captured. In the use of the CAPM and Jensen s alpha some assumptions are made. One of those assumptions is that all investors are risk averse. Another assumption is that all investors have homogeneous expectations of the investment opportunities. The investors choose their portfolio only by their expected returns and their variance on the returns. Another assumption is that there are no transactions costs and taxes en finally all assets should be infinitely divisible. 2.2 Current findings performance mutual funds As mentioned, there has already been a lot of research on the performance of mutual funds. On the question whether mutual funds can outperform the market different methods have been used and different conclusion have been drawn. The most important issues are whether which benchmark to use and how to deal with the expenses made. The current research can be divided into two important groups. The first group is about the efficient market hypothesis. According to this hypothesis stock prices incorporate all public information and the returns of stocks are unpredictable, so no one could profit by trading, stock picking or market timing. The second group states the opposite by saying mutual funds are able to make abnormal returns by the amount of the expenses. The risk of a portfolio can be divided in two kinds of risk. There is a systematic risk, as used in the CAPM model, which is a fixed amount of risk which cannot be avoided. On the other hand there is an unsystematic risk, which is possible to eliminate. According to the second group mutual fund s managers could be able to decrease this unsystematic risk. Hereby an overview of the findings on the current research. As Sharpe (1966) introduced the Sharpe-ratio, he implemented this ratio on a sample of 34 mutual funds. He compared this sample to the Dow Jones index in the same period. The result was that the ratio of the mutual funds laid 0.4% lower. Treynor and Mazuy (1966) used a non linear CAPM and studied 57 mutual funds. They found that fund managers are seen unable to anticipate on swings in the market. Then of course Jensen (1968) was the first who used Jensen s alpha. He found that before expenses mutual funds scatter around the market line, so he concluded that managers do not have useful information to beat the market. He found an average alpha of -1,1%. Friend et al. (1970) made a difference between a value-weighted NYSE index and an equally-weighted NYSE index as benchmark. They estimated Jensen s alpha at respectively

+217 basis points and +22 basis points. Then MacDonald (1974) used the equally-weighted NYSE index where his alpha was on average +62 basis points. Mains (1977) then commented on Jensen saying that it might be better to use monthly data instead of annual data, because he thinks that will improve the estimate of the beta and reduce the impact of expenses. The annual data result in an average alpha of -62 basis points, while the result of the monthly data was +9 basis points. Kon and Jen (1979) did a research in which they used the same data as Treynor and Mazuy (1966). When using an equally-weighted index as benchmark, they concluded that on average that mutual fund managers do have the predictive ability to outperform the market. Then Alexander and Strove (1980) also used a non-linear CAPM, but used a value-weighted index benchmark. Their average alpha was estimated at +120 basis points. Veit and Cheney (1982) used the S&P500 as a benchmark, which resulted in an alpha of 103 basis points. While Shawky (1982) using an equally-weighted market portfolio concluded that the returns of mutual funds are in line with the NYSE returns, Henriksson (1984) and Chang and Lewellen (1984) concluded that the returns before load fees lie along the security market line, which implies that managers do have enough information to offset their expenses. Berkowitz et al. (1988) used the S&P500 as benchmark and estimated an alpha of +68 basis points. Grinblatt and Titman (1989) came to an average alpha of +60 basis points. Ippolito (1989) used the methods and data from Jensen (1968). Before expenses he came to an alpha of +81 basis points. After expenses 88,8% of the alpha s were insignificant different from zero, 8,4% were significant positive and 2,8% were significant below zero. Lee and Rahman (1990) used a value-weighted index benchmark and estimated an alpha of -60 basis points. However, when using a non-linear CAPM the average alpha was +72 basis points. Malkiel (1995) put Jensen s alpha against two different benchmarks; the Wildshire 5000 which includes small companies and the S&P500 which includes large companies. He also calculated the alpha s before and after deducting expenses. As logical, the alpha s after expenses were lower than before expanses. Remarkable is that the alpha s comparing tot the Wildshire 5000 were significant higher than the alpha s of the S&P500. Chevalier and Ellison (1996) studied whether mutual fund performance is related to characteristics of fund managers that may indicate ability, knowledge, or effort. They estimated an average alpha of -50.2 basis points. Carhart (1997) concluded that after expenses the average active fund cannot beat its benchmarks. He also concluded that funds prefer smaller stocks and growth stocks.

Chen et al. (1999) have taken a look at stock picking skills, by using stock trades data. Using raw returns, they found that stocks purchased by funds are performing better than stocks which are sold by funds over the next year. This concludes that active funds have the ability to pick stocks before expenses and trading costs. Kjetsaa (2004) studied mutual funds from Morningstar. He concluded that the performance of actively managed funds before expenses is equal to the average market return. Also he concluded that the performance after expenses is less than the market by about the investment expenses. Fama and French (2008) also estimated the alphas before fees and expenses close to zero and the alpha s after expenses were negative by about the amount of fees and expenses. Karoui and Meier (2008) have taken a look at 828 newly launched mutual funds. These funds started by earning higher returns and positive abnormal returns. Ferreira et al. (2009) studied 16316 open-ended actively managed funds from 27 different countries. They concluded that after fees and expenses the funds underperformed the market. Azar and Al Hourani (2010) compared the mutual funds against four different benchmarks; the S&P500, the Dow Jones Industrial Average, The Russell indexes and the NASDAQ stock market index. They also made a difference before and after deducting expenses. They found evidence that S&P500 is the best benchmark and following the outcomes of the S&P500 they concluded that mutual funds outperform before expenses while their returns after expenses are marginally significant. The outperformance is between the 70.3 and 268.4 basis points. Chapter 3: Empirical findings 3.1 Method As seen in the previous chapter, different methods and different types of data are used. I will explain which method and type of data I have chosen to use in this thesis. As seen in the different studies the choice of benchmark is a very important issue which affects the outcome of the study. Also differences between the equally-weighted method and the value-weighted method have been found. In this thesis I have chosen to use the S&P 500 Composite index as a benchmark, which is a value-weighted index. In the current literature this index has been recommended and in comparison to other benchmark this one came out as the best.

Furthermore I have chosen to use monthly data instead of annual data. Mains (1977) also used monthly data, because he thought that it would improve the estimate of the beta and it would reduce the impact of expenses. His results showed that there was indeed a difference when using monthly data instead of annual data. This monthly data are annualized though. When taking a look on the issue whether to use the rate of return before or after deducting expenses, I have chosen to take the rate of return after deducting all management expenses and 12b-fees, which are operational expenses. In this return the front and rear load fees are excluded. 3.2 Data In order to measure the performance of mutual funds during the crisis, certain data is required. In this paragraph I will explain which data I used and where I got this data from. The returns of mutual funds are obtained from Center for Research in Security Prices (CRSP). For 10610 open-ended mutual funds the return per share was available for the entire period. This return is defined as the change in Net Asset Value including reinvested dividend from one period to the next. The Net Asset Values are net of all management expenses and 12b-fees. Front and rear load fees are excluded. Also the extensions to the CAPM from Fama and French (1993) and Carhart (1997) are obtained from CRSP. These factors are also composed monthly. As a benchmark the S&P 500 Composite index is used. The returns on this index are obtained from Datastream for the period January 2003 until December 2011. This index is a value-weighted index and provides an overview of the overall U.S. equity market. Companies are selected based upon their market size, liquidity and industry grouping. The index emphasizes on the mid-cap and large corporations. The S&P 500 index is considered as one of the best benchmarks to compare the overall U.S. market performance. For the risk-free rate the U.S. Treasury Bill rate is used. This monthly rate is obtained from Datastream for the period January 2003 until December 2011. Often the three-month U.S. Treasury Bill is used as the risk-free rate, but since the S&P 500 Composite as well as the returns of the mutual funds are monthly data, I have chosen to also use a monthly rate for the risk-free rate. Another concern by using this data as the risk-free rate is that the rate which is shown is on the 15 th of the month, while the other data are shown from the last day of the month. Since a lot can happen in two weeks, there might be some inconsistency due to this time difference.

After retrieving the data as described I merged these data together in Stata 11 by using the date as key indicator. After that I sorted the data on the number of the mutual fund as provided by CRSP, so the mutual funds with their associated returns per time are listed. The risk-free rate and the S&P 500 Composite returns are also accompanied to the relative date per mutual fund. This way it was possible to generate the variables individual risk premium and market risk premium. These are respectively composed by deducting the risk-free rate from the return of the mutual funds and deducting the risk-free rate from the S&P 500 Composite returns. To define the current financial crisis, a dummy variable is used. A value for this dummy of one indicates the crisis. In table I an overview of all the variables and their definition is given. Table I Definition of variables In this table the abbreviations which are used are defined. Variable mret sprt rf rirf rmrf D smb hml umd Definition Annualized monthly return of the mutual funds Annualized monthly return of the S&P 500 Composite index Risk-free rate (annualized one-month U.S. Treasury Bill) Individual Risk Premium Market Risk Premium Dummy variable; 0 = before crisis, 1 = during crisis Small minus Big, factor of Fama-French High minus Low, factor of Fama-French Momentum factor, factor of Carhart 3.3 Empirical findings In this paragraph the empirical outcomes can be found. First the summary statistics will be discussed. Then the outcomes of the regressions of the one-factor CAPM, the Fama-French three-factor CAPM and the Carhart 4-factor CAPM will be shown and an comparison between the two periods will be made. Also the outcomes of the Sharpe- and Treynor-ratio will be discussed and finally a Chow-test for proving a structural break between the two periods has been done.

3.3.1 Summary statistics In Table II the summary statistics of the relevant variables are shown. We can see that the mean return of the mutual funds is higher than the mean returns of the S&P Composite index. This indicates that the funds performed better than the market. However the rang between the minimum and maximum of the mutual funds is much bigger than the range of the S&P500 Composite index. A graph of the risk-free rate and the returns on the S&P 500 Composite index can be found in the Appendix. Table II Summary statistics This table presents the number of observations, the mean, the standard deviation, the minimum value and the maximum value for the variables mret, sprt, rf, rirf, rmrf, D, smb, hml and umd. Variable Observations Mean Std. Dev. Min Max mret 1145880 0.0057108 0.0427686-0.7997263 0.5515504 sprt 1145880 0.0042875 0.0436812-0.1694245 0.107723 rf 1145880 0.001502 0.0014399 0.00001 0.0040901 rirf 1145880 0.0042088 0.0427969-1.0232 0.5514088 rmrf 1145880 0.0027855 0.0437124-0.1701218 0.1077063 D 1145880 0.3703704 0.4829041 0 1 smb 1145880 0.0037898 0.0236841-0.0428 0.0589 hml 1145880 0.0012204 0.0242224-0.0993 0.0768 umd 1145880-0.0018185 0.0514578-0.3475 0.1252 In table III the mean of the relevant variables are given for the period before the crisis, denoted by D=0 and the period during the crisis, denoted by D=1. We can see that the returns from both the market and the mutual funds are lower during the crisis than before the crisis, which is in consistency with the theory that the market will fall down in times of crisis. Also noticeable is the fact that the risk-free rate has dropped in the period during the crisis. Since the market is very risky in times of crisis, it seems plausible that also the offered risk-free will decrease. Also the factors small-minus-big, high-minus-low and the momentumfactor all decrease in times of crises. Although the change in small-minus-big is not very big, the factor high-minus-low and the momentum factor both change from positive to negative.

Table III Summary statistics This table presents the mean of the variables mret, sprt, rf, rirf, rmrf, D, smb, hml and umd from the period before the crisis and the period during the crisis. Variable Mean D=0 Mean D=1 mret 0.0071431 0.0032759 sprt 0.0059564 0.0014504 rf 0.0023017 0.0001426 rirf 0.0048414 0.0031334 rmrf smb hml umd 0.0036548 0.0038853 0.003975 0.0029985 0.0013078 0.0036275-0.0034625-0.0100075 3.3.2 Regressions In Table IV the outcomes of the regression on the one-factor CAPM are shown. We could see that Jensen s alpha is positive, both in the period before the crisis as well as in the period during the crisis. Therefore we can conclude that mutual funds were able to beat the market. Noticeable is that the alpha was a little bit higher before the crisis than during the crisis, whit a certainty of at least 95 percent. As logical, the beta is in the period during the crisis higher. Table IV Regression coefficients using the one-factor CAPM This table presents Jensen s alpha, the portfolio s beta, their standard errors, their t-statistics and the 95%-confidence interval for the period before the crisis and the period during the crisis. D=0 Coefficient Std.Err. T 95% min 95% max α 0.002454 0.0000291 84.25 0.0023969 0.0025111 β 0.6532293 0.0010262 636.54 0.6512179 0.6552406 D=1 Coefficient Std.Err. T 95% min 95% max α 0.0022387 0.0000607 36.88 0.0021197 0.0023577 β 0.6840651 0.0009833 695.65 0.6821378 0.6859924

Table V shows the outcomes of the regression on the Fama-French 3-factor CAPM. Recognicable from the regression on the one-factor CAPM, Jensen s alpha is in both periods greater than zero. Also in this scenario Jensen s alpha is decreased and the beta has increased in comparison with the period before the crisis. It seems that all coefficients are lower than the coefficients in the one-factor CAPM, except for the beta during the crisis. Possibly the higher the risk, the lower the alpha. When taking a look at the coefficients of smb and hml, we see that as well before as during the crisis smb was positive. This indicates that small cap firms have higher expected returns than big cap firms. Hml however had a positive effect before the crisis, but during the crisis this effect was negative. So before the crisis value stocks performaned better than growth stocks and vice versa. Table V Regression coefficients using the Fama-French 3-factor CAPM This table presents Jensen s alpha, the portfolio s beta, the coefficients of smb and hml, their standard errors, their t-statistics and their 95%-confidence interval for the period before the crisis and the period during the crisis. D=0 Coefficient Std.Err. T 95% min 95% max α 0.0020245 0.0000301 67.19 0.0019655 0.0020836 β 0.6194082 0.0010761 575.59 0.617299 0.6215173 smb 0.1354997 0.0013673 99.10 0.1328198 0.1381796 hml 0.0067004 0.0017795 3.77 0.0032126 0.0020836 D=1 Coefficient Std.Err. T 95% min 95% max α 0.001241 0.0000616 20.14 0.0011202 0.0013618 β 0.6888011 0.0012567 548.12 0.6863381 0.6912641 smb 0.152622 0.0026726 57.11 0.14733839 0.1578601 hml -0.1264733 0.0021606-58.54-0.130708-0.1222385 The coefficients of the regression on the Carhart 4-factor CAPM are shown in Table VI. Again in both periods Jensen s alpha is positive, so also in this 4-factor model the mutual funds were able to beat the market. However this coefficents are lower than the coefficients of the two other models. Again, during the crisis the alpha was lower and the beta higher compared to the period before the crisis. Also compared to the other models, both alpha s and the beta before the crisis are lower in this model. Remarkable is that the beta from the period

during the crisis is not certainly different from the beta in the 3-factor model. When taking a look at smb and hml we see the same effects as in the Fama-French-model. Looking at the umd we see that in times of crisis this coefficient has turnend from positive to negative. Table VI Regression coefficients using the Carhart 4-factor CAPM This table presents Jensen s alpha, the portfolio s beta, the coefficients of smb, hml and umd, their standard errors, their t-statistics and their 95%-confidence interval for the period before the crisis and the period during the crisis. D=0 Coefficient Std.Err. T 95% min 95% max α 0.0017635 0.0000304 58.06 0.0017039 0.001823 β 0.6409813 0.0011327 565.91 0.6387613 0.6432013 smb 0.1227278 0.0013806 88.89 0.1200218 0.1254338 hml 0.266047 0.0018062 14.73 0.0230646 0.0301447 umd 0.0509316 0.000853 59.71 0.0492596 0.0526035 D=1 Coefficient Std.Err. T 95% min 95% max α 0.0003864 0.0000625 6.19 0.000264 0.0005088 β 0.6683771 0.0012877 521.06 0.665863 0.6708912 smb 0.1603427 0.0026594 60.29 0.1551304 0.165555 hml -0.1724259 0.002454-76.79-0.1768267-0.1680251 umd -0.0693659 0.0009865 70.32-0.0712994-0.0674324 3.3.3 Sharpe- and Treynor-ratio In the previous subsection the method of Jensen s alpha is used. Other performance measurements for mutual fund are the ratios of Sharpe and Treynor. The outcomes of these ratios are shown in Table VII. According to this results the Sharpe-ratio tells us that mutual funds performed better during thecrisis than befer, which is in contradiction to the models where Jensen s alpha is used. However the results of the Treynor-ratio are in line with the results of the regressions; mutual funds performed better before the crisis than during the crisis.

Table VII Sharpe-ratio and Treynor-ratio during the different time intervals This table presents the Sharpe-ratio and the Treynor-ratio in the two different time intervals. D Sharpe-ratio Treynor-ratio 0 0.0158186737 0.0074114863 1 0.0542429803 0.0045805582 3.3.4 Chow-test In order to proof that there is a difference between the period before the crisis and the period during the crisis a Chow-test is used. This way we can test for structural breaks. The formula to compute the Chow test is as follows: ((SSEc SSE1 SSE2)/k)/(SSE1 + SSE2)/(N1 + N2 2k) (4) In this formula SSEc is the sum of squared errors of the pooled data, SSE1 the sum of squared errors of the period before the crisis and SSE2 the sum of squared errors of the period during the crisis. N1 and N2 are the number of observations of respectively the period before and during the crisis and k is the number of variables. The formula approximately equals F(k,N1+N2-2k). When this two are significantly equal, there is a structural break. In Table VIII the results of the Chow-test on the 1-factor CAPM, Fama-French 3-factor model and the Carhart 4-factor model are given. All three tests show a significance equality, so there is indeed a structural break between the period before the crisis and the period during the crisis. Table VII Chow-test This table presents the Chow-test for the one-, three- and four-factor CAPM. # factors Chow Prob > F 1 F(2,1145876) = 211.6473307 0.00000 3 F(4,114572) = 978.7124639 0.00000 4 F(5,114570) = 2553.049995 0.00000

Chapter 4: Summary and conclusions 4.1 Summary The popularity of mutual funds kept increasing in the last decades. Therefore it is necessary to understand how to measure the performance of the mutual funds. There has been a lot of research in the last decades. The most common method to measure the performance of mutual funds is Jensen s alpha. A positive alpha means that the mutual fund has outperformed the market and vice versa. This CAPM can be extended by the factors of Fama and French (1993) and Carhart (1997). Other well-known measurements are the Sharpe-ratio and the Treynorratio. How higher the ratio, the better the fund s performance. In this thesis the performance of mutual funds during the current financial crisis are measured and compared to the performance before the crisis. 4.2 Discussion and recommendations During this research some difficulties have come up. These might have had an influence on the results. One issue is the fact that the risk-free rate has been represented by the one-month U.S. Treasury Bill, which is monthly dated at the 15 th of the month. This is an issue since the returns of the market and of the funds are dated at the last day of the month. Mostly during the crisis, the risk-free rate can vary daily, so it is possible that the difference of about two weeks between the risk-free rate and the other rates of return could have a huge impact on the outcome of the regressions. Another issue to take into account is that for the rate of return of the mutual funds I used the returns per share. This should not be very different than the total rate of return, but it might have a little impact though. In further research on this subject, it might be interesting to be looking at some mutual funds separately, instead of using the entire dataset as a whole. This way it is possible to find out which mutual funds really did better during the crisis than before the crisis. The performance of mutual funds can be ranked as in Jensen (1968) before and during the crisis to get a clear picture of the differences between these two periods and to see whether the ranking list before the crisis relates to the ranking list during the crisis.

4.3 Conclusions In the last few decades a lot of research has already been done on the performance of mutual funds. Especially the performance measurement of Jensen (1968), better known as Jensen s alpha has been used. Some concluded a positive Jensen s alpha, which means that the mutual funds had outperformed the market, while others came to the conclusion of a negative alpha. During this investigation I have taken a look between the difference of a period before the current financial crisis and the period during the current financial crisis. My sub-research questions were as follows: 1.) What are Jensen s alphas in the period before the crisis and the period during the current financial crisis? 2.) Is there a different outcome when using different performance measurements? After doing the regressions, I can answer the first subquestion. In the period before the crisis, Jensen s alpha is 25 basispoints in the one-factor CAPM. In the Fama-French 3-factor model the alpha has dropped to 20 basis points. When using Carhart s 4-factor model Jensen s alpha was 2 basis points. In the period during the crisis Jensen s alpha in the one-factor CAPM is estimated at 22 basis points. Using the 3-factor model this alpha is 12 basis points and when doing the regression on Carhart s 4-factor model an alpha of 4 basis points is estimated. After taking a look at the results, subquestion two can be answered. Using the method of Jensen s alpha, the different models show different outcomes. The more factors extended to the CAPM, the less Jensen s alpha. This is the case both in the period before the crisis as in the period during the crisis. When taking a look at Jensen s alpha, mutual funds were able to beat the market as well in the period before the crisis as during the crisis. However the funds performed better before the crisis than during the crisis. Using the Treynor-ratio I came to the same conclusion. However the Sharpe-ratio had a contrary conclusion. So when answering the research question of Is there a difference between the performance of mutual funds during the current financial crisis and before this period? by taking a look at the answers of the sub-questions, I can conclude that there is indeed a difference between these two periods. Except for the Sharpe-ratio, mutual funds are performing better before the crisis than during the crisis.

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Appendix Graph 1: Graph of the risk-free rate over the entire period. Graph 2: Graph of the returns on the S&P 500 Composite index for the entire period.