The influence of cross-sectional volatility in stock
return on active fund performance
Studentnr: 2584123 Name: Wesley Pilage Study Program: MSc Finance
Supervisor: dr. A. Plantinga
Field keywords: Cross-sectional volatility, Active portfolio management, U.S. mutual fund performance, stock selection.
Abstract
1. Introduction
One of the basic assumptions in modern portfolio theory is that investors are rational and markets are efficient. Active portfolio management does not follow the efficient market hypothesis presented by Fama (1970). The efficient market hypothesis states that current stock prices reflect all available information. Investors who use active strategies try to profit from mispriced securities. Investment companies who manage mutual funds aim to outperform the market and therefore achieve higher returns than passive managed funds. There has been a lot of critics on active portfolio management, because research through history show us that active portfolio management is not able to outperform passive portfolio management, mainly because of the fee charged by these investment companies. Jensen (1968) finds that the alpha (which is representing the active return of mutual funds) is on average negative after charging fees. This alpha, also known as Jensen alpha, is a risk adjusted measure that is able to predict the average return of a portfolio. Also more recent studies of Elton et al. (2003 and 2011) and Fama and French (2010) find a negative alpha for mutual funds return after charging fees and other expenses.
It is also interesting to observe how these mutual funds perform before charging fees. Grinblatt and Titman (1989) discovered that these mutual funds actually outperform passive funds before charging fees. Also follow up research from Grinblatt and Titman (1993) and Daniel et. al (1997) confirm that the returns of mutual funds outperform the returns of passive funds, because they present positive alphas for mutual funds before charging fees.
The focus of the studies from Pastor and Stambaugh (2002) and Kacperczyk et al (2004) is on identifying the best stock picking fund managers who can outperform the passive benchmark. Kacperczyk et al. (2004) observe managers who exhibit the so called “time-varying skill”. These managers are able to successfully pick stocks in economic booms and time the market in recession. They find that managers with this skill outperform the market with 50 to 90 basis points per year. Different economic environments can create profit opportunities for active managers if they have good time-varying skills. Economic booms and recessions mostly go hand in hand with high levels of cross-sectional volatility. Von Reibnitz (2013) examined portfolios of mutual funds in different volatile environments. After making different portfolios, the most active U.S. funds found to be significantly outperforming the benchmark in times of high monthly cross-sectional dispersion in returns.
Cremers and Petajisto (2009) use “active share” as measurement for activeness of a fund manager, active share is the fraction of the portfolio that is different from the benchmark. By using this measurement it is possible to compare the returns of the most active managed funds with less active funds. Cremers and Petajisto (2009) use the four factor model of Carhart (1997) in their research to regress benchmark-adjusted returns of different levels of active share portfolios. One of the conclusions of the research of Cremers and Petajisto (2009) is that funds with the highest active share turn out to have significant positive alphas and therefore outperform their benchmarks both before and after expenses. Funds with the lowest active share underperform after expenses. They use 1990 to 2003 as their sample period.
As discussed in the studies of Von Reibnitz (2013) and Cremers and Petajisto (2009) there seem to be evidence that in some economic environments the most active portfolios can outperform the market. I want to see if I can also find positive alpha return for different portfolios of mutual funds in the period 2008 to 2015, by using and analysing daily return data. I am especially interested in the situation where active managers got the highest potential for profit opportunities, which should be on days when high cross-sectional volatility is present, according to Von Reibnitz (2013). This research differs from most conventional academic papers about this subject, since it is using and analysing daily data instead of monthly data. By using daily returns, it is possible to use a more recent dataset, which contain enough data points to accurately estimate alpha returns.
best circumstances for active management to outperform. It does so by creating five portfolios which are selected on fund activeness. These portfolios are tested in five different volatile environments, ranging from a very high cross-sectional volatile environment to a very stable environment with low cross-sectional volatility.
U.S. mutual funds during 2008 to 2015 is on average underperforming. This under-performance is especially driven by two extreme environments, which are days where stock returns are very dispersed or when there is very low return dispersion. Therefore, no matter the level of activeness, stock returns have to be sufficiently dispersed for active management to be valuable. I find that the least to middle active managers, significantly underperform during days where stocks returns are very dispersed. The mutual funds in my sample period don’t show significant outperformance. A possible explanation is that the mutual funds cannot outperform during the economic crisis of 2008 - 2009 and are affected by the consequence of the crisis in the years following.
2. Literature review
De Silva, Sapra and Thorley (2001) observe the unusually high cross-sectional variation of stock returns in the United States during the 1990’s. They find that this high variation in security returns has led to the wide dispersion in fund returns. They argue that the main reason for the increase in dispersion of fund performance is the natural result of the high cross- sectional variation of stock returns. They find that the influence of changes in the informational efficiency of the market or management skills is small, therefore traditional methodologies that assume constant dispersion should be re-examined.
Ankrim and Ding (2002) find that the spread between successful and unsuccessful active managers has increased extremely during the same period (1990’s). Also, these findings are not just unique for the United States, since they are observable in several international equity markets. Whatever is the cause of highly volatile environments, Ankrim and Ding (2002) find that the active risk in the portfolio of active managers increased, without an explicit increase in the aggressiveness of their “bets”.
shows the (short run) market’s volatility expectations by tracking index options. Investors can analyse the return dispersion and/or the VIX and forecast overall equity alpha dispersion over the next 3 to 12 months. They can use these analyses to adjust their strategies and seek for outperformance opportunities by adding value at the right time. A recent study of Byun (2016) find that return dispersion can be used to indirectly predict market volatility through improving the parameters of a GARCH process for aggregate volatility. By applying Byun’s findings for the mutual fund market, it can help improve the timing of active mangers to be more active.
Above literature suggest that increasing or decreasing the activeness of the portfolio is important and can add value in certain environments. However, a recent study from Cremer and Pareek (2016) find that high frequency trading funds generally underperform, even when they include funds with a high Active Share. They find that funds with a patient investment strategy, which means that the portfolio has a holding period of minimum 2 years, generally outperform their benchmark. Cremer and Pareek also find that institutions that use an active patient strategy in general outperform. This is in contrast with the findings of Gorman, Sapra and Weigand (2010), since they argue that active investors could profit by changing the activeness of their portfolio in the short run.
Active investing is a zero sum game, when not taking into account the cost of active fund management. The goal of an active investors is to “beat” the market, thus by outperforming passive management. When an investor is taking a different position to the market, this investor is by definition trading with other investors. Petajisto (2003) breaks down U.S. fund portfolios in two components: the S&P 500 Index, which is the passive component, and all the deviations from the index, which constitute the active component. The active component is causing the performance of the mutual fund. For every active investor with a long position in the active component should be another active investor with a short position in this active component, which makes it a zero sum game. In practice, where cost of active fund management are present, active investing is worse than a zero sum game.
environment and it effect on different active strategies used by managers. Von Reibnitz (2013) find negative alpha for the average active fund. But when setting up multiple portfolios and testing them in different environments, she find return outperformance in times of high stock return dispersion for the most active funds. This means that in highly cross-sectional volatile months the most active managers outperform the market at the expense of the less active managers. Von Reibnitz (2013) also states that the timing when to invest might be more important than selecting in which fund to invest, since her study only reports significant positive alpha’s in periods of high return dispersion.
Kosowski (2011) observes U.S. funds in two extreme economic environment, in times of regression and times of economic boom. He finds that the fund’s risk-adjusted performance difference between recession and expansion periods is statistically and economically significant. Therefore U.S. funds on average perform better during a recession than during boom periods. This is not in line with Von Reibnitz (2013), who find no outperformance in recessionary months as a whole, since no fund portfolio is able to achieve significant alphas during these months.
3. Research methods
3.1 Determining environments: Cross-sectional volatility
Cross-sectional volatility (CSV) is a measure for the stock picking opportunities of active managers. When there is a high level of CSV on a particular day, the stock returns on that day are very dispersed. CSV at day t is calculated using the following formula:
3.2 Active fund selection
Some mutual funds might be more sensitive to different volatility environments than other funds. Therefore five different fund portfolios are created, varying from most active funds to least active funds. The criteria for selecting funds is the fund’s R-squared. The R-squared is the coefficient of determination, which indicates the proportional amount of the variation of fund i that can be explained by the benchmark. More active funds should have a lower R-squared than less active funds since they should deviate more from the benchmark. The S&P 500 is used as a benchmark. The formula for calculating the R-squared for mutual fund i with benchmark m is:
=
2
(2)
Where ! is the covariance between the returns of fund x with benchmark m. The is representing the standard deviation of the mutual fund multiplied with the standard deviation of the index.
This method differs from the R-squared predictor of Amihud and Goyenko (2013) since the R-squared is not obtained from rolling regressions on a multifactor model. They obtain a lagged R-squared that is more sensitive for values close to the last of the rolling regression observations. The method of Amihud and Goyenko (2013) might give biased results and therefore I am using the single benchmark model to determine the funds R-squared. In contrast, the single factor method that I use to determine R-squared does not take into account the Fama and French factors. By obtaining the R-squared of all mutual funds, five different portfolios are created by sorting the R-squared from high (R5) to low (R1). Where portfolio R5 contains funds with the highest R-squared and thus is the least active portfolio and R1 is classified as the most active portfolio.
3.3 Mutual fund performance
− " = ɑ + $ % &' + ( %) + ℎ +%, + %-% + . (3) Where is the return to active funds i in day t, " is the risk free rate, % &' is the value-weighted return on all NYSE, AMEX, and NASDAQ stocks minus the risk free rate. %) , +%, and %-% are the daily returns to the size, book-to-market and momentum factor
mimicking portfolios of the FFC model, respectively.
I have included 5 dummy variables who represent the different environments like discussed before. The sample is divided in 5 quintiles, every quintile containing 20% of the total sample. So every dummy represents a CSV quintile, ranging from low CSV to high CSV. Regression analysis is used for all five portfolios in every quintile, resulting in 25 combinations to estimate alpha return. By using these dummy variables it is possible to examine and compare the out- or underperformance of each portfolio for every environment. By including a dummy (e.g. high CSV) all observations within this category take the qualitative value 1 and all the observations out of this category take the value 0.
The time series exhibits conditional heteroscedasticity, and therefore the error terms are not independent and identically distributed. In our data, volatility clustering is present, meaning that periods of high variance tend to group up together. The Engle’s (1982) ARCH-LM test is used to assess the significance of ARCH effects. Since the p-value of this test result is significant, there is evidence for ARCH effects. The Gauss-Markov assumptions of the linear regression to be the best linear unbiased estimator does not longer hold. A GARCH (1,1) model is used to help describing the changing volatility in the financial market.
Some alternative measurements to estimate alpha returns are also used in this paper. A robustness test for a alternative measure of fund dispersion is applied. By creating less quintiles with a wider range to see if the original alpha is robust to a alternative measure of dispersion. Also a alternative measure is applied to see if the estimated alpha is not too depended on a certain period of the sample.
returns are least dispersed. Only two quintiles are used because of statistical purpose, since using this monthly approach reduces the dataset by a factor 21. I didn’t use a larger dataset, since comparison with the daily return approach wouldn’t be possible.
4. Data
4.1 Mutual fund data
Fund data is derived from the Thomson Reuters Datastream. Constituent list are used to collect the data of all U.S. mutual funds and after that, the data is filtered. Only active fund (non-index) data is used in the entire performance analysis. The Lipper classification is used to achieve funds that invest in the U.S. equity market. The data is filtered on at least 70% equity of the fund.
Total return data is used, so the fund’s return include reinvested dividends and are net of fees and expenses. When using constituent lists, survivorship bias can be a concern. This is due to the fact that constituent list use funds which are still present and doesn’t include funds which have disappeared. After filtering, 4,528 mutual funds remain present. Five fund portfolios are made by selecting on fund activeness as described in the section research methods.
4.2 Benchmark model
The benchmark model is used to measure fund activeness and alpha. MRKT is the excess market return ( − ") on all NYSE, AMEX, and NASDAQ stocks minus the risk free rate. This risk free rate is the one month treasury bill rate. SMB, HML, MOM are the daily returns on different portfolios which represent the size, book to market and momentum factor.1 4.3 Cross-sectional volatility
The cross-sectional volatility is determined by calculating the cross-sectional standard deviation of all stocks for every day from 2008 to 2015 of the S&P 500. The stock returns are obtained from the Wharton Research Data Services (WRDS) by using the Centre for Research in Security Prices (CRSP). For the whole sample period 2008 to 2015 the mean is 1.83%, the median is 1.50% and the sample’s maximum is 14.12% with a minimum of 0.57%. By sorting CSV into 5 quintiles, the highest CSV quintile consists for the largest part of data from 2008
to 2009. This is also observable in figure 1, which shows higher levels of daily CSV from 2008 to 2009 in comparison with 2010 to 2015.
Figure 1. Time series plot of daily cross-sectional volatility
This figure plots the daily cross-sectional volatility from the constituents of the S&P 500, calculated following equation (1). The daily CSV is calculated from January 2008 to may 2015.
Figure 1 show some high levels of daily CSV during the financial crisis in 2008 - 2009. For the period 2010 to 2015 the figure reports daily CSV that mostly lies between 1% - 2%, which is around the mean and median of the whole sample. The highest quintile of CSV consists for the largest part of data from 2008 to 2009, but also includes the highest cross-sectional volatile days from 2010 to 2015.
Table 1. Descriptive statistics cross-sectional volatility quintiles
All Low CSV 2 3 4 High CSV
Mean 1.83% 1.04% 1.29% 1.51% 1.87% 3.46% .Median 0.00% 1.07% 1.28% 1.50% 1.85% 2.99% Standard Deviation 1.04% 0.12% 0.05% 0.07% 0.14% 1.31% Maximum 14.12% 1.19% 1.38% 1.66% 2.19% 14.12% Minimum 0.57% 0.57% 1.19% 1.38% 1.66% 2.19% Count 1861 373 372 372 372 372
The table reports the descriptive statistics of the daily cross-sectional volatility for the whole sample and the five different quintiles. Every quintile contains 20% of the total sample. The minimum and maximum indicates the range of the quintiles.
5. Results
Table 2 shows the estimated alphas obtained by regressing daily portfolio returns on the daily factor return of the FFC model. R1 is the portfolio which contain the most active funds and portfolio R5 contain the least active funds. The last column reports estimated alphas for all mutual funds in the sample. The bottom row reports estimated alphas without using CSV dummy variables. The estimated annualized alpha for the whole sample without dummy variables is -1.89%, which is a significantly negative return.
Table 2. FFC alphas for all active fund portfolios in different CSV quintiles
R1 R2 R3 R4 R5 All High CSV -6.65% ***-7.02% ***-6.11% ***-5.77% ***-4.34% ***-5.96% (-1.74) (-2.75) (-3.61) (-4.41) (-3.88) (-3.74) Q4 0.63% -0.77% -0.87% *-1.67% ***-2.13% -1.02% (0.24) (-0.44) (-0.85) (-2.18) (-3.49) (-1.04) Q3 0.12% -1.78% -1.52% ***-2.11% ***-1.70% *-1.75% (0.05) (-1.23) (-1.73) (-3.40) (-3.90) (-2.20) Q2 -1.19% -0.66% -0.40% -0.69% -0.57% -0.54% (-0.73) (-0.54) (-0.54) (-1.10) (-1.12) (-0.75) Low CSV **-2.83% ***-3.37% ***-2.64% ***-2.07% ***-1.80% ***-2.69% (-2.46) (-3.91) (-4.93) (-3.89) (-4.42) (-5.14) All *-1.75% ***-2.25% ***-2.01% ***-2.00% ***-1.81% ***-1.89% (-2.12) (-3.90) (-5,35) (-6.50) (-7.66) (-5.43)
The five portfolios underperform in the highest CSV quintile. The portfolios R5 to R2 report significant negative annualized returns between -4.34% and -7.02%. In the highest CSV quintile the estimated alphas are the most negative, with a negative alpha return of -5.96% for the whole sample. The opposite quintile, which got the lowest CSV, report significant negative alpha returns for all the portfolios. In this lowest quintile, the portfolios R5 to R2 are significant at the 1% level and the most active portfolio R1 is significant at the 2.5% level. This most active portfolio, R1, is the only portfolio that reports positive alphas (at Q4 and Q3), but these returns are not significant.
Figure 2 is an overview of the estimated annualized FFC alphas for all portfolios in each quintile. Especially the extreme quintiles of very high CSV or very low CSV are the driving forces of the overall significant negative alpha return.
Figure 2. estimated FFC alphas for portfolios R1 to R5 in all CSV environments
This figure reports the results of table 2. The annualized performance (annualized from daily returns) for each portfolio is shown over each of the 5 dispersion quintiles for the period 2008 to 2015. This figure shows that especially the highest CSV and lowest CSV quintiles are the driving force of the overall underperformance.
Table 3 reports FFC alphas for three different quintiles instead of five. By doing so, the highest quintile is not as overrepresented by high levels of CSV during the economic crisis of 2008 to 2009 anymore. By analysing and comparing table 3 with table 2, the FFC alphas of table 3 are in line with table 2. Table 3 reports only positive alpha return for the middle quintile for the most active portfolio, although this positive alpha is again not significant. The
highest CSV quintile reports significant negative alphas for the least active funds (R2-R5), but again not for the most active portfolio R1. At low levels of daily CSV the table again reports significant negative alpha returns for all portfolios. It seems that changing the range of quintiles doesn’t influence the estimated alphas drastically.
Table 3. FFC daily alphas in three different CSV environments
R1 R2 R3 R4 R5 ALL
High -3.73% **-4.00% **-2.35% ***-3.44% ***-3.03% -3.27%
Mid 0.57% -0.22% -1.04% ***-1.43% ***-1.42% -0.95%
Low **-2.69% ***-2.81% ***-2.44% ***-1.66% ***-1.26% ***-2.04%
All *-1.75% ***-2.25% ***-2.01% ***-2.00% ***-1.81% ***-1.89%
This table reports annualized portfolio alpha. Every day t, funds are sorted into five different portfolios (R1 to R5) based on their R-squared. After that, all days in the sample are sorted into three quintiles based on the level of , calculated following equation (1). For each portfolio the alpha is estimated by regressing the daily portfolio returns on the daily factor returns of the FFC model for each CSV quintile. The regression intercept, alpha, is reported with its z-statistic between brackets. A GARCH (1,1) model is used for this regression analysis to deal with ARCH-effects. ***,**,* denote significance at the 1%, 2.5% and 5% level, respectively
By using three dummy quintiles instead of five, the highest quintile is not overrepresented by data from the economic crisis anymore. However, these data points are still present and might influence the alphas in such a way that it does not report significant positive returns for the most active funds during high cross-sectional volatile environments as found by Von Reibnitz (2013). Therefore table 4 reports estimated FFC alphas for a shortened period. This sample excludes the years 2008 to 2009, since this is the climax of the economic crisis. 2008 and 2009 consist of mostly highly cross-sectional volatile days, therefore it is interesting to see what happens with the portfolios performance in this quintile. Table 4 reports the estimated daily FFC alphas for this sample.
Table 4. Estimated FFC alphas sample excluding 2008-2009
R1 R2 R3 R4 R5 All High -5.63% -5.23% ***-4.72% ***-4.17% ***-3.86% ***-4.17% 4 0.82% -1.80% -2.45% ***-2.15% ***-1.84% -1.72% 3 -2.35% -1.23% -0.70% -0.82% -0.53% -1.11% 2 -2.06% **-3.08% ***-2.16% -1.16% -0.55% *-1.67% Low *-2.95% ***-2.95% ***-2.76% ***-2.30% ***-2.26% ***-2.56% All ***-2.23% ***-2.71% ***-2.19% ***-2.03% ***-1.82% ***-2.06%
R5) based on their R-squared. After that, all days in the sample are sorted into quintiles based on the level of , calculated following equation (1). For each portfolio the alpha is estimated by regressing the daily portfolio returns on the daily factor returns of the FFC model for each CSV quintile. A GARCH (1,1) model is used for this regression analysis to deal with ARCH-effects. ***,**,* denote significance at the 1%, 2.5% and 5% level, respectively.
When analysing the results for this sample, I find similar outcomes in table 4 as in table 2. Again, this sample does not report significant positive alpha returns, but the only (insignificant) positive alpha is again reported for the most active funds (R1) in the fourth quintile. For the highest CSV quintile we again find significant negative alpha returns for the least active funds (R5-R3), with the second most active portfolio (R2) being insignificant negative as only difference with table 2.
The same research methods are applied for monthly data, during the same time period. The estimated annualized alpha returns can be found in table 5 in appendix A. Table 5 report a significant negative alpha at the 5% significant level of -1.23% for the whole sample without dummy variables. It also reports a significant negative alpha of 1.81% for the lowest CSV quintile. Also for monthly data, there are still no significant positive alpha returns reported. For the monthly approach, the regression results are roughly the same for monthly data. Table 6 reports the coefficients of the FFC factors. The market factor reports significant coefficients for all portfolios in all environments. Meaning that the return of all portfolios in combination with different environments can be partly explained by excess market return. The market factor tells us how the funds in the portfolio on average move with the market.
The most active portfolios (R1, R2) report significant positive coefficients for the SMB factor, this signals that portfolio R1 and R2 includes funds which are weighted toward small-cap stocks. The least active portfolios (R4, R5) report significant negative SMB factor coefficients, and therefore these portfolios are weighted toward large-cap stocks. Portfolios R1, R2 and R3 also report significant negative HML factors, which means that these portfolios are weighted toward growth stocks. R4 and R5 report positive significant HML factors, which means that these portfolio are weighted toward value stocks.
following period. Interestingly, the highest CSV quintile only reports a significant MOM coefficient for the least active portfolio (R5). The other more active portfolios (R4-R1) are not (significantly) effected by the momentum factor during high CSV.
Table 6. Coefficients of the FFC factors for all portfolios in different CSV environments
MRKT R1 R2 R3 R4 R5 All High ***0.9999 ***1.0042 ***0.9995 ***09912 ***0.9985 ***1.0016 4 ***1.0312 ***1.0337 ***1.0029 ***0.9889 ***0.9930 ***1.0092 3 ***1.0304 ***1.0279 ***1.0080 ***0.9969 ***0.9988 ***1.0126 2 ***1.0146 ***1.0152 ***0.9962 ***0.9866 ***0.9942 ***1.0015 Low ***0.9942 ***1.0004 ***0.9866 ***0.9894 ***0.9993 ***0.9950 All ***1.0249 ***1.0213 ***0.9989 ***0.9894 ***0.9955 ***1.0056 SMB High ***0.0987 ***0.0512 -0.0012 ***-0.0681 ***-0.0995 **-0.0145 4 ***0.1215 ***0.0505 -0.0088 ***-0.0800 ***-0.1058 -0.0138 3 ***0.0644 0.0207 ***-0.0281 ***-0.0841 ***-0.1054 ***-0.0323 2 ***0.0902 ***0.0380 **-00162 ***-0.0721 ***-0.1058 ***-0.0177 Low ***0.0554 0.0067 ***-0.0368 ***-0.0756 ***-0.1056 ***-0.0335 All ***0.0826 ***0.0300 ***-0.0222 ***-0.0791 ***-0.1062 ***-0.0244 HML High ***-0.1147 ***-0.1019 ***-0.0656 ***0.0199 ***0.0115 ***-0.0416 4 ***-0.1411 ***-0.1083 ***-0.0453 ***0.0593 ***0.0297 ***-0.0351 3 ***-0.1651 ***-0.1285 ***-0.0536 ***0.0587 ***0.0268 ***-0.0479 2 ***-0.1397 ***-0.0921 -0.0143 ***0.0626 ***0.0292 ***-0.0257 Low ***-0.1495 ***-0.0994 -0.0135 ***0.0661 ***0.0293 ***-0.0313 All ***-0.1235 ***-0.0928 ***-0.0348 ***0.0504 ***0.0228 ***-0.0318 MOM High -0.0132 -0.0075 -0.0044 -0.0062 ***0.0081 0.0012 4 ***0.0569 ***0.0377 ***0,0118 **-0.0086 -0.0005 ***0.0171 3 ***0.0556 ***0.0350 -0.0014 ***-0.0164 *-0.0071 **0.0115 2 ***0.0624 ***0.0430 0.0065 ***-0.0153 -0.0058 ***0.0164 Low ***0.0881 ***0.0672 ***0.0206 -0,0129 *-0.0090 ***0.0276 All ***0.0416 ***0.0311 ***0.0104 ***-0.0047 0.0013 ***0.0143
The estimated annualized alpha reported in table 2 belong to the output of this regression analysis. The coefficient of the MRKT corresponds to the excess market return ( − ") on all NYSE, AMEX, and NASDAQ stocks minus the risk free rate. The reported coefficients SMB, HML and MOM correspond to the daily returns on different portfolio’s which represent the size, book to market and momentum factor of the FFC model. Every day t, funds are sorted into five different portfolios (R1 to R5) based on their R-squared. After that, all days in the sample are sorted into quintiles based on the level of , calculated following equation (1). A GARCH (1,1) model is used for this regression analysis to deal with ARCH-effects. ***,**,* denote significance at the 1%, 2.5% and 5% level, respectively.
environments. In general it seems that momentum is not significantly present in highly CSV environments, except for the least active funds in portfolio R5. The returns of the most active to middle active funds cannot be explained by the momentum factor.
6. Conclusions
By sorting 4,528 active U.S. equity funds into five portfolios, I find significant negative returns for all portfolios during days of low cross-sectional volatility. However, I also find significant negative returns for all portfolios except for the most active portfolio in a highly cross-sectional volatile environment. The estimated annualized alpha for the whole sample without dummy variables is -1.89%, which is a significantly negative alpha return. This significant negative alpha return is mainly driven by fund returns during very low or very high cross-sectional volatile environments.
My findings suggests that for all active managers, no matter the level of activeness, stock returns have to be sufficiently dispersed. Since this study finds significant negative returns for all portfolios during an environment of low cross-sectional volatility. Therefore, the costs of actively managed funds in such a environment are too high and cannot lead to out-performance.
I find significant negative return for all portfolios except for the most active portfolio in the highest volatile environment. Apparently, active managers underperform during days where stocks returns are very dispersed. Most of these highly volatile days are during the climax of the economic crisis of 2008 to 2009, therefore the estimated alpha returns are also calculated on two different ways. I still find similar results by setting up larger ranges for the different CSV quintiles, which mean that the results are robust to a alternative measure of dispersion. Also the results are robust to a alternative sample period, by excluding the returns of 2008 and 2009. Therefore we can conclude that the climax of the economic crisis of 2008-2009 is not affecting the estimated alphas of the sample in such a way which leads to significantly different results.
recessionary months where she finds no outperformance in recessionary months as a whole, since no fund portfolio is able to achieve significant alphas during these months.Therefore it might be that mutual funds in my sample period cannot outperform during the economic crisis and are affected by the consequence of the crisis in the years following.
Finally, this paper has several limitations. Survivorship bias is present in my sample, since the sample only reports mutual funds that survived until the end of the period. Nevertheless, I assume that the reason for funds to drop out is because of lacking performance, which wouldn’t lead to increased fund’s performance if they would be in the sample.
Active mutual funds are not able to outperform over the full sample period, however because of the aspects of the zero sum game, there should also be “winners” who got the opposite position of these funds. These winners are funds who are out of the sample or individual investors. If individual investors are on the winning side, this will raise criticism whether actively managed mutual funds add value.
This research uses the single factor model to calculate fund’s R-squared to classify the five portfolios instead of the multifactor model of Amihud and Goyenko (2013). For example, one might argue that a fund is sorted into portfolio R5 but had to be sorted into portfolio R4 according to the multifactor model to calculate fund’s R-squared. However, the multifactor model also give biased results since values close to the last of the rolling regression observations are more sensitive. The method to classify fund’s activeness is a more or less a choice between both methods, therefore limitations with respect to the selection of activeness are inevitable.
In my paper, no other fund’s characteristics are taken into account besides fund’s activeness. I conclude that several portfolios of funds, which are selected on fund’s activeness, underperform during environments of very high and very low cross-sectional volatility. It might be interesting to make different portfolios on other fund or management characteristics like fund size, management tenure, manager’s skill or manager’s experience. These new portfolios can lead to different outcomes, and might be able to achieve outperformance in certain environments.
Appendix A
Table 5. FFC alphas for CSV environments based on monthly data
R1 R2 R3 R4 R5 All
High -2.74% -0.51% -0.46% 0.07% 0.31% -0.37%
Low -2.07% -1.57% -1.58% -1.26% -1.40% *-1.81%
All -0.85% -0.81% -1.46% -1.44% -1.38% *-1.23%
This table reports annualized portfolio alpha. Every month t, funds are sorted into five different portfolios (R1 to R5) based on their R-squared. After that, all months in the sample are sorted into two quantiles based on the level of , calculated following equation (1). For each portfolio the alpha is estimated by regressing the monthly portfolio returns on the monthly factor returns of the FFC model for each CSV quantile. A GARCH (1,1) model is used for this regression analysis to deal with ARCH-effects. ***,**,* denote significance at the 1%, 2.5% and 5% level, respectively.
Table 5 reports the FFC alphas based on monthly data for the same time period. A new dataset with monthly returns and monthly CSV is used to create dummy variables and portfolios. However only two CSV quintiles are created because of limited data points. By using monthly data instead of daily, the dataset is reduced by a factor (around) 21, since a month contains around 21 trading days. The highest quintile contain 40% of the highest CSV data points and the lowest quintile contain 40% of the lowest CSV data points.
References
Amihud, Y., & Goyenko, R. (2013). Mutual fund's R2 as predictor of performance. Review of Financial Studies, 26(3), 667-694.
Ankrim, E. M., & Ding, Z. (2002). Cross-sectional volatility and return dispersion. Financial Analysts Journal, 58(5), 67-73.
Byung, S. (2016). The usefulness of cross-sectional dispersion for forecasting aggregate stock price volatility. Journal of Empirical Finance, 36(1), 162-180.
Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82.
Cremers, K. J. M., & Petajisto, A. (2009). How active is your fund manager? A new measure that predicts performance. Review of Financial Studies 22(9), 3329-3365.
Cremer M., & Pareek A. (2016). Patient capital outperformance: The investment skill of high active share managers who trade infrequently. Journal of Financial Economics, 122(2), 288-306.
Daniel, K.., Grinblatt, M., Titman, S., & Wenners, R. (1997). Measuring mutual fund performance with characteristic-based benchmarks, Journal of Finance, 52(3), 1035–1058.
Elton, E. J., Gruber, M. J., & Blake, C. R. (2003). Incentive fees and mutual funds, Journal of Finance, 58(2), 779–804.
Elton, E.J., Gruber, M. J., & Blake, C. R. (2011). Holdings data, security returns, and the selection of superior mutual funds, Journal of Financial and Quantitative Analysis, 46(2), 341–367.
Engle, R. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50(4), 987-1007.
Fama, E. F. (1970). Efficient capital markets: a review of theory and emperical work, Journal of Finance, 383-417.
Fama, E. F., & French, K. R. (2010). Luck versus skill in the cross-section of mutual fund returns, Journal of Finance, 65(5), 1915-1947.
Grinblatt, M., & Titman, S. (1989) Mutual fund performance: An analysis of quarterly portfolio holdings, Journal of Business, 62(3), 393–416.
Grinblatt, M., & Titman,S. (1993). Performance measurement without Benchmarks: An Examination of Mutual Fund Returns, Journal of Business, 66(1), 47–68.
Jensen, M. C. (1968). The performance of mutual Funds in the period 1945–1964, Journal of Finance, 23(2), 89-416.
Kacperczyk, M., van Nieuwerburgh, S., & Veldkamp, L., (2014). Time-varying fund manager skill. Journal of Finance 69(4), 1455-1484.
Kosowski, R., (2011). Do mutual funds perform when it matters most to investors? US mutual fund performance and risk in recessions and expansions. Quarterly Journal of Finance 1(3), 607-664.
Pástor, Ľ., & Stambaugh, R., (2002). Investing in equity mutual funds. Journal of Financial Economics 6(1), 351-380.
Petajisto, A. (2003). Active share and mutual fund performance. Financial Analyst Journal 69(4), 73-93.
