Mutual Fund performance – A bootstrap analysis
Are US equity mutual funds able to beat the market and Exchange Traded Funds?Roeland de Bruin 10003336
Study: Economie & Bedrijfskunde Track: Financiering & Organisatie Specialization: Finance
Supervisor: dhr. P. Tuijp Date: 21-02-2014
1. Introduction
This research investigates whether US equity mutual funds are able to outperform the market. Lots of research (e.g. Carhart 1997, Daniel et al. 1997, Fama and French 2009) has been done regarding mutual fund performance, mostly on US equity mutual funds until 2006. We investigate the performance of US mutual funds between 2003 and (September) 2013 and compare the mutual fund performance with the performance of passive investments, Exchange Traded Funds (ETFs).
Mutual funds are long existing long-term investment products. According to the
Investment Company Fact Book (2011), the mutual fund industry managed almost 5 trillion
dollars at the end of 2010. ETFs on the other hand, are relative new long-term investment products. The first ETF was created in 1993. ETFs are simply a basket of securities, usually stocks, that is designed to track a market benchmark (Baiden, 2011). In 2010 ETFs hold assets of more than half a trillion dollars (Birdthistle, 2009). The rapid growing ETF industry is a threat for both the mutual fund industry and the hedge fund industry. Chan, Chen and Lakonishok (2002), Cuthbertson, Nitzsche and O’ Sullivan (2006), Fama and French (2009) and many others found that active mutual funds generally charge higher fees than ETFs. The question rises whether mutual funds are able to beat the market and thereby ETFs, despite of the higher fees. This leads to the research question of this research: Are US equity mutual funds able to beat the market and Exchange Traded Funds?
The results of the earlier research on mutual fund performance are contradictory. Chan, Chen and Lakonishok (2002) and Fama and French (2009) found that, on average, mutual funds underperform the market by about the amount of expenses they charge to investors. On the other hand, Kacperczyk, Sialm, and Zheng (2008) and Cremers and Petajisto (2009) document evidence that at least some subset of mutual fund managers may have security selection skills, and thus are able to gain an abnormal return for mutual funds. Thereby, Kosowski, Timmermann, Wermers and White (2006) find not only that a sizable subgroup of mutual fund managers exhibits stock- picking skills, but also that the superior alphas of these managers persist.
We investigate whether US equity mutual funds can beat the market and passive investments for the period 2003-2013. When we wrote this research, there was only data available till October 2013, so we mainly investigate the mutual fund performance between 2003 and September 2013. We consider this an interesting period due to the mortgage crisis in the US in 2007 and the following Euro crisis in 2008. We investigate a sample of 4474 funds. This sample represents all equity US mutual funds from CRSP that have data for the entire
period. To be able to compare mutual fund performance with the performance of ETFs, we run a Carhart Four-Factor regression to estimate the alpha for both the mutual fund sample and the ETF. To check for robustness, we run a residual bootstrap for this regression. Kosowski et al. (2004) explained several reasons why this bootstrap procedure is necessary. We will give a brief explanation of the main reason in the empirical method. The bootstrap mutual fund alpha will indicate whether mutual funds are able to get a higher return than the market (a significant positive alpha). Besides, with the alphas we can compare the performance of mutual funds with the performance of ETFs by a two-sample mean comparison t-test. We choose the Vanguard Total Stock Market ETF as representative ETF, because it seeks to track the CRSP US Total Stock Market Index, which represents about 99.5% of all US listed equity. For both mutual funds and the benchmark returns we use monthly data. Furthermore we use the same benchmark that Fama and French use to compute their monthly Fama/French factors. The methodology will be further explained later on in the empirical method.
We continue this thesis with a brief summary of the most important literature and the hypotheses in the literature review. Next we describe our data sources and the descriptive statistics. Next we explain the empirical method and the bootstrap methodology. Lastly, we explain and interpret the result of the regressions and the bootstrap and formulate a conclusion. Regression tables can be found at the end of the thesis.
2. Literature review
In the literature review we summarize the literature that is most important for our research. When we have summarized and discussed the literature, we will be able to formulate the hypotheses based on the existing literature. The most important literature that we use in our research is the empirical research from Cuthbertson, Nitzsche and O’ Sullivan (2005) regarding mutual fund performance, the empirical research of Kosowski et al. (2006) regarding the bootstrap analysis of mutual fund performance and the article of Baiden (2011) regarding information on ETFs and the advantages and disadvantages of ETFs.
Cuthbertson, Nitzsche and O’ Sullivan (2005) analyse the performance of UK equity mutual funds between 1975-2005. They use 935 funds to run a Carhart four-factor regression. With the estimations of the Carhart four-factor model they run a residual bootstrap analysis to distinguish luck from skill in individual mutual fund performance. They found that there are a few top performing mutual funds that generate an abnormal return from skill instead of luck. More specifically, they found stock picking ability for somewhere between 5 and 10% of top
performing UK equity mutual funds. The rest of the top performing funds performed better than the market mainly due to luck. Furthermore they reject the hypotheses that bad performing mutual funds are just unlucky. Most of these mutual funds demonstrate bad skill.
Kosowski et al. (2006) examine the performance of 2118 US open-end, domestic-equity mutual funds between 1975 and 2002. They run a residual bootstrap analysis on the OLS estimates of the Carhart (1997) four-factor model and the Ferson and Schadt (1996) model to check for robustness. For their bootstrap procedure they use two test statistics, α and tα. They found that the performance of best and worst managers is not only due to luck. Furthermore they conclude a bootstrap procedure is necessary in future rankings of mutual fund performance. We used this research to determine our bootstrap methodology.
Cuthbertson, Nitzsche and O’ Sullivan (2006) evaluate the academic research on mutual fund performance in the US and the UK, concentrating particularly on the literature published between 1985 and 2005. They conclude that academic work demonstrates that there are relatively few mutual funds that have genuinely positive alphas and picking ex-ante winners (security selection) is very difficult. They found little evidence of successful market timing. The advice that Cuthbertson, Nitzsche and O’ Sullivan (2006) give to most investors is to hold low cost index funds and thereby avoid holding past ‘active’ losers.
Fama and French (2009) examine whether US mutual funds are able to outperform the market and they try to distinguish luck from skill in the cross section of mutual fund returns. They conclude that for 1984 to 2006, mutual funds (in aggregate) underperform the CAPM, three-factor and four-factor benchmarks by the amount of expenses they charge to investors. If there are mutual fund managers with enough skill to generate an abnormal return that covers the costs, these skills are hidden in the average result, by the performance of managers with insufficient skill that underperform the market. To distinguish luck from skill, they compare the distribution of t(α) estimates from actual fund returns with the distribution from bootstrap simulations in which all funds have zero true α. They found strong evidence of both negative and positive manager skill. We will mainly focus on the average results instead of individual performance.
Baiden (2011) examines the advantages and disadvantages of ETFs. He states that ETFs are relative new long-term investment products, which have rapidly grown since its introduction in 1993. Till 2010 ETFs have grown to well over 600 different ETFs, attracting more than half a trillion dollar in investments. David Haywood of the financial research corporation predict that ‘the market of ETFs will grow at 29% clip over the next 5 years out pacing all other investment products’ (Baiden, 2011). He concludes that it is not likely that
ETFs will have more assets under management than mutual funds in the near future, but that ETFs are likely increase their share of total investments at the expense of mutual funds and hedge funds.
Based on the literature it seems that mutual funds, on average, are not able to outperform their benchmarks. Key drivers for this underperformance can be load fees, expenses and turnover. Thereby we expect that mutual funds, on average, underperform ETFs, because ETFs generally have a lower expense ratio than their mutual fund counterparts, mostly because ETF’s are not actively managed, and thereby investors don’t have to pay high management fees (Baiden, 2011). The results of the literature are however contradictory, so it is difficult to determine an expectation.
3. Data
We downloaded the returns of all mutual funds from CRSP. First we excluded all mutual fund with an investment objective other than general equity. We haven’t distinguished different styles of equity mutual funds, such as growth or sector funds, because we evaluate mutual fund performance for all equity funds. From the list of all equity US mutual funds we selected the funds that have data of returns for the entire period, 2003-2013. This resulted in a sample of 4474 US equity mutual funds. Our sample is free of survivorship bias, because all 4474 funds are followed from 2003 to the end of 2013 (i.e. all funds have data available for the entire period).
Data on the returns of the mutual funds will be generated from the CRSP mutual fund database. These are net returns, i.e. after fees, expenses, brokerage commissions but before any front-end or back-end load (Cremers and Petajisto, 2009). Data on the returns of the ETF will be obtained from the Yahoo Finance database. For both the mutual funds and the ETF we use monthly returns. The data for other variables of the Carhart four-factor regression model will be generated from the Kenneth French website and the Fama-French portfolio and factors database.
Table 1 presents the descriptive statistics of variables that we use in both Carhart four-factor regression models. The descriptive statistics of the Fama French portfolio four-factors are the equal in both regressions. The average monthly return of the mutual funds is 0.86%, with a minimum of -55.68% and a maximum of 55.16%. The average return of the ETF is 0.48%, with a minimum of -17.88% and a maximum of 10.96%. The market excess return (MKT) has the highest average monthly return of the Fama French factors, 0.71%. The SMB and HML
factors also have positive average monthly returns, 0.37% and 0.15% respectively. The momentum factor (MOM) has a negative average monthly return of -0.11%.
4. Empirical method
To measure the performance of mutual funds and ETFs we need a representative period. A realistic period should include both a bear and a bull market period. This is important because there are two ways a mutual fund can beat the market. During a bull market, it might be possible that mutual funds are able to outperform the market. But on the other hand, in a bear market, mutual funds might be able to perform less bad than the market. Taking this into consideration, we choose the period between 2003-2013. The given period includes the rise is stock prices during 2003-2007 and 2010-2013, but also the recession between 2007-2008. We chose this period because we wanted to evaluate mutual fund performance for the last decade, including the crisis of 2007-2008.
The performance of the mutual funds has to be compared with a benchmark. We use the same benchmark as Fama and French use to compute their portfolio factors and they use in their research of 2009. They use the value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX of NASDAQ.
4.1 Regression model
To measure the average performance of mutual fund and to be able to compare this mutual fund performance with the performance of ETFs, we need to estimate the alpha for the mutual funds and for the Vanguard Total Stock Market by a risk-adjusting model. To estimate the alphas we will follow the empirical methods of Fama and French (2009) and Carhart (2007). Both researches analyse mutual fund performance with a CAPM, three-factor and four-factor model. Carhart (2007) states that his four-factor model substantially improves on the pricing errors of the CAPM and the Fama French (1993) three-factor model. That is why we only use the Carhart four-factor model, which is basically the Fama French three-factor model with one added variable, MOM. We use Newey-West standard errors to generate results that are robust to heteroskedasticity and autocorrelation.
Ri,t = αi + β1,i MKTt + β2,i SMBt + β3,i HMLt + β4,i MOMt + εi,t. (1)
The variable MKTt means market excess return, which is the return of the market minus the risk-free rate (1-month T-Bill). For the risk-free rate, we follow Carhart (2007) and Fama
French (2009), they both use the 1-month Treasury-Bill. Furthermore, SMBt stands for small minus big and HMLt stands for high minus low. The construction of SMBt and HMLt follows Fama and French (1993). The variable MOM is defined as the momentum factor, and is used to capture the one-year momentum anomaly of the Fama French (1993) model.
The data for both the risk-free rate and the variables MKT, SMB, HML and MOM will be taken from the Kenneth French website. Data mutual fund returns will be obtained from CRSP and data of the return of the ETF will be obtained from the Yahoo Finance database.
4.2 Bootstrap Methodology
Most literature analyses mutual fund performance by ‘conventional’ statistical models (CAPM, three- or four-factor models) to find an alpha. This alpha indicates whether the mutual funds used in the sample are, on average, able to outperform the market. However, estimation result of the Carhart four-factor model may not be robust. To check for robustness, we run a residual bootstrap on the standard errors for this regression. Kosowski et al. (2006) explain several reasons why a bootstrap procedure on mutual fund performance is necessary. Because Kosowski et al (2006) explain these reasons in detail, we only will give a brief explanation of the main reason.
4.2.1 Individual mutual fund alphas
Following Kosowski et al. (2006), we consider the possibility that a significant part of the mutual funds in our sample have alphas that are drawn from a distinctly non-normal distribution. The first reason Kosowski et al. (2006) give is that individual stocks within the mutual fund portfolio have returns with non-negligible higher moments. Although the central limit theorem implies that an equally weighted portfolio of such non-normally distributed stocks will approach normality, this normality may be a poor approximation in practise due to heterogeneous risk-taking of the mutual fund managers. Heterogeneous risk-taking of managers means that they often hold relatively few stocks of industries in their portfolios. This implies that the mutual funds often take higher risks than the market and risk levels differ between mutual funds. Thereby, mutual funds managers often use dynamic strategies, which change the level of risk taking over time. In addition, Kosowski et al. (2006) suggest that market benchmarks may also have non-normalities.
4.2.2 Bootstrap procedure
We use the residual bootstrap for standard errors. This method is explained by Efron and Tibshirani (1986) and (1993). Because these researches thorough analyse the bootstrap procedure, we only provide a brief explanation of the bootstrap standard error procedure. We take the following steps:
1. First we draw a random sample with replacement from the original dataset, creating a bootstrap sample.
2. Next we estimate the coefficients and their standard errors and save these results. 3. We repeat this 1000 times, so we can form a distribution for the bootstrapped alpha. 4. The bootstrap standard error is the standard deviation of the distribution of the
estimated coefficient.
Because we use a large sample, the bootstrap estimates will converge to the true parameters as the number of replications increases. That is why we chose 1000 replications.
4.3 Comparison with passive investments
In the last part of the research we investigate whether mutual funds can beat ETFs. We will use a two-sample mean comparison t-test to compare the alpha of the mutual funds with the alpha of our representative ETF. We expect that the alpha of this ETF will be slightly below zero, because the ETF simply tracks an index (alpha is zero) and bears some costs. However, we assume that the ETF has a tracking error, so it is necessary to estimate the alpha of the ETF with a risk-adjusting regression model. Despite the fact that we expect that the alpha of the ETF will be slight below zero, buying an ETF is the cheapest way to invest in a complete index. Buying all the stocks from an index will generate a lower return than just buying an ETF due to the transaction costs. These transaction costs will be higher than the costs to buy an ETF.
We choose the Vanguard Total Stock market as our representative ETF, because it seeks to track the performance of the CRSP US Total Stock Market Index. This is the same as the benchmark we use in the regression models and thereby Yahoo Finance and Vanguard state that this ETF represents 99.5% of all US listed equity. Besides, it has a lower Total Expense Ratio (TER) than 95% of its alternatives, 0.05%. The results are therefore somewhat conservative. This implies that when mutual funds in our sample are on average able to beat this ETF, they should be able to beat at least 95% of the other ETFs. On the other hand, if
mutual funds underperform our representative ETF, it doesn’t necessarily mean that the mutual funds in our sample underperform all the ETFs.
5. Results
In this section we present the results of our Carhart Four-Factor regressions. The results for the mutual funds are presented in table 2. Panel A presents the results for the mutual funds and panel B represents the results for the ETF, the Vanguard Total Stock Market. For the mutual fund regression (panel A) we mainly obtained small but significant coefficients. The constant and the variables MKT, SMB and HML are significant at 5% significance level, but only the variable MOM is insignificant at a 5% significance level. Most of the variables are significant because the relatively low (robust) standard errors. We obtain a significant positive alpha of 0.0011, which implies an abnormal return of 0.11%. This indicates that the mutual funds in our sample outperformed the market by 0.11%, using the result of the Carhart four-factor model. For the ETF regression (panel B), we mainly observe insignificant estimates. We obtained an insignificant alpha of 0.0043, so we haven’t found evidence of any outperformance of ETFs
However, we explained in our methodology that the results of the Newey-West standard errors on the Carhart four-factor model might not be robust. To check for robustness, we ran a residual bootstrap on the regression results. The results of the residual bootstrap are presented next.
5.1 Bootstrap results
In this section we present the main findings from the residual bootstrap procedure. The results are presented in table 3. Figure 1 and figure 2 show the distribution of the bootstrapped alpha for both the mutual funds and the ETF respectively. In both panels of table 3 we see that the bootstrap standard errors hardly differ from the robust standard errors of Newey-West standard error method on the Carhart four-factor model. This indicates that the estimates of our regression model are robust. Furthermore we can see in panel A that the mutual fund alpha (constant) is still 0.0011 and is remains significant at a 5% significance level. This indicates that we can confirm the results of Newey-West regression and thus we find that the mutual funds in our sample are, on average, able to beat the market during our period. The alpha of the ETF (panel B) remains 0.0043, but is insignificant at a 5% significance level.
To compare the alpha of the mutual funds with the alpha of the Vanguard ETF, we used a two-sample mean comparison t-test. However, we are not able to find evidence of any
outperformance between the mutual funds and our representative ETF, due to the insignificant alpha of the ETF.
6. Conclusion
Using a sample of 4474 US equity mutual funds, we investigated the mutual fund performance between 2003 and (September) 2013. We compared the mutual fund performance with the market and with a passive investment, an ETF. We used the Carhart four-factor model to obtain the alpha for both the mutual funds and the ETF. To correct for heteroskedasticity and autocorrelation we ran a Newey-West procedure instead Ordinary Least Squares (OLS). Furthermore we ran a residual bootstrap analysis for this regression, to check for robustness. In out methodology we explained the two main reasons why this bootstrap analysis is necessary. The expectation was that mutual funds are, on average, not able to beat the market and ETFs.
With the Newey-West standard error procedure we obtained estimates for the coefficients of the Carhart four-factor model. To check whether these estimates are robust, we ran a residual bootstrap on the standard errors. The bootstrap standards errors hardly differed from the robust standard errors obtained by the Newey-West regression. This means that the estimates of the Newey-West regression are robust. We obtained a significant mutual fund alpha of 0.0011, which implies an abnormal return of 0.11%. This means that we can conclude that the mutual funds in our sample on average outperformed the market between 2003-2013.
Furthermore we observed an ETF alpha of 0.0043, which is insignificant at a 5% significance level. We compared this ETF alpha with the alpha of the mutual fund sample by a two-sample mean comparison t-test. We find no evidence of any outperformance between the mutual fund sample and the ETF, because the insignificant alpha of the Vanguard Total Stock Market ETF. This confirms the contradictory in the existing literature. It seems difficult to compare the performance of mutual funds with the performance of ETFs.
7. Discussion
The results and conclusions are not in line with our expectation. Based on the literature, we expected that mutual funds were not able to beat the market and passive investments. However, the results of the existing literature are contradictory. We read several articles (e.g. Kacperczyk, Sialm, and Zheng (2008), Cremers and Petajisto (2009)) that documented evidence of managers’ skill for security selection. The contradictory in mutual funds
performance might stem from the different samples and periods that researchers use. The insignificant alpha of the ETF implies that we are not able to conclude whether mutual funds are able to outperform ETFs or vice versa. We consider this in line with the discussion whether investors are better off buying an ETF than a mutual fund. It appears to be difficult to find evidence of any significant outperformance.
As we described in the introduction, lots of research has been done regarding US (equity) mutual funds. We think it would be interesting to investigate the performance of global mutual fund, both equity and bond funds. We were not able to do this because the data was unavailable.
Reference list
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Table 1 – Summary statistics for the variables of the Carhart Four-Factor model
This table presents the summary statistics for both the dependent variable and the independent variables of the Carhart Four-Factor model. We included the mutual fund return and the return of the ETF. The Fama French factors have the same descriptive statistics in both regressions. The variable MKT is the market excess return, the return of the market (Rm) minus the risk-free rate (rf). Rm is the value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX of NASDAQ and rf is the one-month Treasure bill rate. The construction of SMB and HML follows Fama and French (1993). MOM is defined as the momentum factor.
Min. Average Returns Max. Standard Deviation Skewness Kurtosis Mutual Fund R -0.5568 0,008686 0.5516 0.05211 -0.6423 6.7104 ETF R -0.1788 0.004810 0.1096 0.04363 -0.8049 5.0467 MKT -0.1723 0.007125 0.1134 0.04318 -0.7266 4.8974 SMB -0.0422 0.003667 0.0579 0.02258 0.1993 2.6414 HML -0.0986 0.001539 0.0759 0.0231 -0.4473 5.8777 MOM -0.3472 -0.001136 0.1253 0.04869 -3.0122 21.8274
Table 2 – Result of Carhart Four-Factor estimations
This table reports the estimation result of the regression model described in the empirical method. Panel A presents the estimation results for the mutual funds and panel B presents the estimates for the Vanguard Total Stock Market ETF. We used the Newey-West standard errors to correct for heteroskedasticity of the standard errors. In panel A we used a sample of 4474 mutual funds, representing all CRSP US equity funds with data for the entire period. This results in 577146 observations.
Panel A -‐ Mutual Fund estimates
Coefficients p-value (Robust std. error) Constant 0.001082 0.00 (0.00003780) MKT 1.0073 0.00 (0.001411) SMB 0.1460 0.00 (0.002056) HML -0.05450 0.00 (0.002015) MOM -0.002302 0.087 (0.001345) Funds 4474 Observations 577146 R2 0.7330 Root MSE 0.02693
Panel B - Vanguard Total Stock Market ETF estimates
Coefficients p-value (Robust std. error) Constant 0.004309 0.286 (0.004042) MKT 0.3071 0.038 (0.1480) SMB -0.4025 0.026 (0.1804) HML -0.2019 0.457 (0.2715) MOM -0.08660 0.293 (0.08239) Observations 129 R2 0.0928 Root MSE 0.04139
Table 3 – Results from the residual bootstrap procedure
This table represents the results of the residual bootstrap procedure. We used 1000 bootstrap replications, because the bootstrap estimates converge to the real estimates as the number of replications increases. The coefficients are the same as the coefficients presented in table 2, only the bootstrap standard error differ from the robust standard errors presented in table 2.
Panel A - Mutual Fund estimates
Coefficients p-value (Bootstrap std. error) Constant 0.001082 0.00 (0.00003850) MKT 1.0073 0.00 (0.001410) SMB 0.1460 0.00 (0.002093) HML -0.05450 0.00 (0.002000) MOM -0.002302 0.102 (0.001407) Funds 4474 Observations 577146 Replications 1000
Panel B - Vanguard Total Stock Market ETF estimates
Coefficients p-value (Bootstrap std. error) Constant 0.004309 0.295 (0.004118) MKT 0.3071 0.042 (0.1514) SMB -0.4025 0.029 (0.1840) HML -0.2019 0.456 (0.2708) MOM -0.08660 0.393 (0.1013) Observations 129 Replications 1000
