1
An Empirical Investigation of U.S. Equity Funds
Author: Jun ChenStudent number: s2353172
Supervisor: Dr. R.M. Salomons Date: 26/06/2014
Master’s Thesis Finance University of Groningen
Abstract
This paper primarily evaluates and compares the daily and monthly performance of 586 U.S. equity-based actively managed mutual funds during the period 2004-2013. We employ three different benchmark models to measure the fund performance at the aggregate portfolio level and the individual fund level, respectively. Besides, we evaluate the performance of mutual funds according to four different subgroups, including growth, growth & income, income and small-cap funds.
The result reveals that fund managers do not have superior stock selection and market timing skills for all three return-based models at the aggregate portfolio level. And the extended Carhart’s (1997) four-factor model even underperforms the market proxy and wrongly times the market directions with daily data rather than monthly data. For funds with different investment objectives, most of them do not show superior performance, either. These results support the efficient market theory. In terms of the individual fund level, for all kinds of funds, the result demonstrates an improved evidence of stock selection skills with daily data rather than monthly data, but not that strong. On the other hand, most of fund managers are not good at timing the direction of the market. Conversely, they possess significantly negative market timing skills, especially for managers of income funds.In addition, using the Carhart’s (1997) four-factor TM and HM models, we find that fund managers are good at valuation timing.
JEL classification: G23
1. Introduction
Mutual funds have been growing significantly in recent decades. According to the statistics, assets held in mutual funds by U.S. households increased from $7.1 trillion to 13.6 trillion from mid-year 2000 to mid-year 2013 (Investment Company Institute, 2014). Since the public are increasingly interested in funds investment, the mutual fund performance has been widely examined in the finance area both theoretically and empirically. Such an evaluation becomes especially important for investors and managers, because it can help them allocate their investment funds more rationally and efficiently. This paper mainly examines the mutual fund performance from two aspects – security selection and market timing skills. Fama (1972) uncovers that the return on a portfolio can be derived from two parts, i.e. the return from security selection and the return from market timing. The abnormal return from stock selection is defined as the difference between the realized return and the expected return given the beta of the market portfolio. The market timing skill refers to the management ability to forecast market directions and adjust their exposures timely. That is, managers will increase fund exposures to market index in a rising market, while decrease fund exposures in a falling market.
market. Bollen and Busse (2001) find that fund managers’ market timing ability is enhanced with daily returns relative to monthly returns. Sehgal and Jhanwar (2008) find an improved ability of security selection with daily data rather than monthly data.
On the one hand, though large numbers of previous studies about mutual fund performance are based on monthly data, few are studied by high frequency data. On the other hand, Goetzmann, Ingersoll and Ivkovic (2000) suggest that the high frequency data has more explanatory power to fund returns than the low frequency one, because active portfolios are managed under a continuous time framework. Inspired by these two factors, the objective of this paper is to evaluate and compare the performance of U.S. equity-based mutual funds based on both daily and monthly frequency. Therefore, the alternative hypothesis of this paper can be stated as follows,
The tests of mutual fund performance using daily frequency have more powerful explanatory mechanisms than the tests using monthly frequency.
factor in this paper. The momentum factor captures the Jegadeesh and Titman (1993) momentum anomaly. Therefore, we totally utilize three different benchmark models to investigate the mutual fund performance. They are the one single factor TM and HM models, the Fama and French’s (1993) three-factor TM and HM models, and the Carhart’s (1997) four-factor TM and HM models, respectively.
Firstly, we measure the fund performance at the aggregate portfolio level. And then, we test the management stock selection and market timing skills at the individual fund level. Meanwhile, since mutual funds are classified as different objectives, to give investors and practitioners the evidence that whether superior strategies exist within a certain investment objective of mutual funds, we decompose the entire sample into four subgroups, which are growth, growth & income, income and small-cap funds. Thus, we conduct an evaluation and comparison according to these four funds with different investment objectives. Finally, in addition to test market timing skills, we employ the Carhart’s (1997) four-factor TM and HM models to measure style timing skills with daily data in order to know whether managers have alternative timing abilities, such as size timing, valuation timing, and momentum timing. Simply speaking, the size timing refers to adjust exposures between small and large capitalization firms, the valuation timing refers to adjust exposures between value and growth companies, and the momentum timing relates momentum investments to non-momentum investments.
(2007), though they find strong evidence of market timing and momentum timing abilities in addition to valuation timing skills.
The remainder of the paper is organized as follows. Firstly, Section 2 reviews some earlier articles on U.S. and international mutual fund performance. Secondly, the data collection and the main methodology are detailed in Section 3. Thirdly, empirical findings and the corresponding results analysis are presented in Section 4. And at last, Section 5 makes a final conclusion.
2. Literature review
Jensen (1968) investigates the annual performance of 115 open-end U.S. mutual funds over the period 1945-1964. He utilizes the capital asset pricing model (CAPM) to forecast the fund returns before deducting fund expenses and after. The market proxy is S&P 500, and the risk-free rate is one-year government bond. In his paper, he finds that fund managers have little stock selection abilities both before and after the management expenses. The average value of alpha estimated from net returns is -0.011, with 39 funds having positive alphas and 76 funds having negative alphas. The average value of alpha calculated from gross of return is -0.004, with 48 funds having positive alphas and 67 funds having negative alphas. His findings support the efficient market hypothesis.
Ippolito (1989) estimates the performance of 143 U.S. mutual funds over the period 1965-1984 and supports the opinion of the inefficient market theory. Under the assumption that the target beta is stable over the sample time period, he finds that managers can earn an abnormal return of 0.83 percent above the S&P 500 index after the management expenses. Totally, 12 out of 143 mutual funds show significantly positive alphas. When he evaluates the mutual fund performance with different proxies (the New York Stock Exchange index and an equally weighted stock-bond portfolio), outperformance is not changed.
Treynor and Mazuy (1966) measure the market timing ability of 57 U.S. open-end funds during the period 1953-1962 employing an extended statistical test. They state that the traditional CAPM model exhibits a constant risk parameter over the entire evaluation period. However, they argue that a fund management can beat the market by successfully forecasting market directions and adjusting their exposures accordingly. To more specific, managers can increase fund exposures when they anticipate good market conditions, while decrease fund exposures when they anticipate bad ones. For this reason, they add a quadratic term to the model to capture this market timing activity. Comparing the performance of 57 mutual funds with S&P 500, they show that only 1 out of 57 fund managers possesses superior market timing skills to anticipate major turn in the market.
Findings from Bollen and Busse (2001), however, indicate that daily returns have more explanatory power than monthly returns and that fund managers have a superior market timing ability. In their paper, the sample is composed of 230 U.S. mutual funds during the period 1985-1995. The risk-free rate and market proxy are the 90-day U.S. Treasury bill and the Center for Research in Security Prices (CRSP) value-weighted index, respectively. Inspired by Goetzmann et al. (2000), they evaluate and compare the managers’ market timing ability with daily and monthly data. Employing the Carhart’s (1997) four-factor TM model, they find that 40.8 percent of funds exhibit significantly positive market timing coefficients with daily frequency, whereas 33.5 percent of funds show significantly positive market timing parameters with monthly frequency. In addition, to remove spurious market timing abilities proposed by Jagannathan and Korajczyk (1986), they synthesize a new sample which has no timing skills. The results show that 31.7 percent of funds have significantly positive market timing coefficients with monthly returns, while 36.0 percent of funds have significantly positive market timing parameters with daily returns. When using the Carhart’s (1997) four-factor HM model, they present a similar result.
model implies that 62 per cent of funds have positive valuation timing skills, while 53 per cent of funds have positive momentum timing skills. They explain that the difference exists because of high transaction costs for the momentum stocks.
The above discussions do not present a consistent conclusion on the outperformance or underperformance of the mutual funds. In the international context, different findings spread. Bauer, Otten and Rad (2006) find that monthly equity funds in New Zealand cannot beat Worldscope index over the period of 1990 till 2003, and fund managers do not possess superior market timing abilities, either. In addition, Blake and Timmermann (1998) study the U.K. mutual fund industry, Casarin, Pelizzon and Piva (2008) evaluate the Italian equity funds, Gupta and Gupta (2004) investigate the Indian mutual fund schemes. They all support the efficient market hypothesis.
Contrary evidence is provided by Jhanwar and Sehgal (2008). They investigate Indian mutual fund schemes over the period 2000-2004, and they find that managers possess superior stock selection skills when using daily frequency. In their paper, they argue that multifactor benchmarks improve the fund performance measurement as
well because they capture the fund style characteristics.
3. Data collection and methodology
3.1 Data collection
replicate the market index and thus cannot capture any stock selection and market timing skills. Besides, funds which have no data after 2004 are removed as well. In addition to using S&P 500 as the market proxy, we extract the size, book-to-market, and momentum factors from the Kenneth French’s website since the Fama and French’s (1993) three-factor model and the Carhart’s (1997) four-factor model are utilized in the evaluation phase. Since more and more banks refuse to lend to each other during the financial crisis that occurred in 2007, the London Interbank Offered Rate (LIBOR) rises sharply. For this reason, many dealers consider overnight index swap (OIS) as a risk-free rate. Therefore, we use the 3-month overnight index swap as a risk-free rate in this paper because of the sample period which we choose.
The daily and monthly risk-free rate can be calculated as follows,
, (1)
, (2)
where is the annualized 3-month overnight index swap rate. and are the monthly and daily overnight index swap rate, respectively.
Table 1. Summary statistics for mutual funds and style returns during the period 2004-2013 In Panel A, columns 2-6 shows the characteristics of mutual funds with different investment objectives, including total equity funds, growth funds, growth & income funds, income funds and small-cap funds, respectively. The asset under management (AUM), refers to the total asset that a mutual fund runs, is obtained from Morningstar. The AUM data records each fund’s total assets on May 5th, 2014. The average returns, median returns and volatility are all annualized numbers. The daily and monthly mean returns (assuming 252 trading days) are firstly averaged across funds within each investment objectives, and then averaged over time, assuming that funds are equally weighted. Panel B demonstrates the style returns (annualized) with regard to the market index, size factor, value factor and momentum factor, respectively.
Panel A: mutual funds sample All equity funds Growth funds Growth & Income funds Income funds Small-cap funds No. of funds 586 177 149 140 120 AUM ($billion) 12.26 10.13 13.52 22.12 2.32 Daily (%) 3.04 4.03 2.88 1.28 3.86 Median(%) 9.78 14.54 10.67 3.38 9.39 (%) 17.02 19.37 18.90 7.93 22.94 Monthly (%) 3.15 4.17 2.98 1.32 3.99 Median(%) 12.60 15.38 13.09 5.20 15.01 (%) 14.12 15.63 14.89 7.95 19.34
Panel B: style factors
S&P 500 Size Value Momentum
Daily (%) 7.14 2.19 2.17 1.01 Median(%) 14.21 0.00 0.00 10.60 (%) 20.08 8.81 8.88 15.71 Monthly (%) 7.38 2.65 1.75 -0.16 Median(%) 17.54 -0.72 0.36 4.16 (%) 14.84 7.65 8.14 16.83
total assets. Among them, income funds manage the largest total assets, which amount to $22.12 billion. And small-cap funds have the smallest assets, which are $2.32 billion. The daily and monthly mean returns are firstly averaged across funds within each investment objectives, and then constructed over time, assuming that portfolios of funds are equally weighted. The average returns, median returns and volatility are all annualized numbers. In general, the total daily and monthly mean returns are 3.04 percent and 3.15 percent, respectively. The standard deviations for daily and monthly returns are 17.02 percent and 14.12 percent, respectively. Among funds with four investment objectives, we can find that growth funds have the highest daily and monthly average returns, whereas income funds have the lowest daily and monthly mean returns. The daily and monthly mean returns for growth funds are 4.03 percent and 4.17 percent, respectively. The daily and monthly mean returns for income funds are 1.28 percent and 1.32 percent, respectively. Besides, the small-cap funds have the highest daily and monthly volatility, whereas income funds have the lowest daily and monthly volatility. The daily and monthly volatility for small-cap funds are 22.94 percent and 19.34percent, respectively. The daily and monthly volatility for income funds are 7.93 percent and 7.95 percent, respectively. In Panel B, we observe that the average daily and monthly returns for the market proxy are 7.14 percent and 7.38 percent, respectively. Compared with the mutual funds returns, the result suggests that the mutual funds generally underperform the market index during the period 2004 till 2013. This surprising result is probably the consequence of financial crisis that occurred in 2007 and 2008.
3.2 Methodology
(CAPM). However, Grinblatt and Titman (1994) point out that fund performance is sensitive with regard to different benchmark proxies, even when the same measurement is employed. Therefore, we utilize three different benchmark models to evaluate the mutual fund performance in this paper. They are, respectively, one single factor TM and HM models, Fama and French’s (1993) three-factor TM and HM models and Carhart’s (1997) four-factor TM and HM models.
3.2.1 One single factor TM and HM models
The capital asset pricing model (CAPM) is the most common metric to measure the risk-adjusted portfolio performance. Jensen’s alpha, developed by Jensen (1968), measures the difference between the excess return on the fund and the excess return on the market portfolio given its systematic risk beta. Nevertheless, the CAPM is not appropriate if fund managers have the ability to adjust the portfolio exposure according to the market states, because it assumes that the beta is constant over the evaluation period. For this reason, Mazuy and Treynor (1966) extend the capital asset pricing model by adding a quadratic term to capture a possible non-linear relationship between fund portfolios and market returns. The regression equation is given by the following,
, (3)
where , , , and are the portfolio return, the risk-free rate, the
traditional estimate of systematic risk, the market return and the random error term, respectively. The regression intercept, , is the Jensen measure, which captures the stock selection ability. If the Jensen alpha is positive, it reveals that fund managers have abilities to pick up stocks. The coefficient of the quadratic term, , provides an estimate of the market timing ability. A significantly positive suggests that
fund managers have superior market timing skills.
estimating the market timing performance. The relationship can be estimated by the following equation using the dummy variable,
, (4)
where measures the management timing skills, and D is a dummy variable. D=0
when , otherwise D=-1. Therefore, the beta of portfolio is in the
rising market, and in the falling market. A significantly positive
reveals that fund managers have a superior market timing ability.
However, the limitation of the one single factor model is that it only considers the systematic risk. Since the mutual fund has different investment styles, one-factor model cannot sufficiently capture the fund’s characteristics and performance, and thus lead to an incorrect conclusion.
3.2.2 Fama and French’s (1993) three-factor TM and HM models
Fama and French (1993) raise the question on the accuracy of the CAPM model, because it assumes that a fund return can only be explained by a single market index, while fund investment category diversifies. Therefore, Fama and French (1993) propose to add size and book-to-market factors to improve the performance measurement. Inspired by this, the extended regression equation of the Mazuy and Treynor’s (1966) timing model is estimated as follows,
, (5)
According to the Fama and French’s (1993) three-factor model, the modified regression equation of the Henriksson and Merton (1981) model is calculated as follows,
, (6)
where and test the managers stock selection and market timing skills,
respectively. A significantly positive and , respectively, suggests that fund
managers have superior abilities to pick up stocks and time the direction of the market.
3.2.3 Carhart’s (1997) four-factor TM and HM models
Following Jegadeesh and Titman’s (1993) article on profitability of momentum strategies, Carhart (1997) adds a fourth factor to capture the momentum anomaly. The Mazuy and Treynor’s (1966) four-factor timing regression equation is measured as follows,
, (7)
where is the portfolio return that proxies for the momentum risk factor. It measures the excess return between the portfolio of past 12-month winners and the portfolio of past 12-month losers.
Correspondingly, the Henriksson and Merton’s (1981) four-factor model is calculated as follows,
, (8)
where and test the managers stock selection and market timing skills,
managers have superior abilities to pick up stocks and time the direction of the market.
To study managers’ style timing skills, we can extend the Carhart’s (1997) four-factor TM and HM models further. The regression equations are expressed as follows, respectively , (9) , (10) D=0 when >0; otherwise D=-1; D=0 when >0; otherwise D=-1; D=0 when >0; otherwise D=-1; D=0 when >0; otherwise D=-1;
where , , and are the market timing, size timing, valuation
timing, and momentum timing coefficients, respectively. Similarly, a significantly positive , , and present superior market timing, size timing,
valuation timing, and momentum timing skills, respectively.
4. Results and analysis
growth & income funds, income funds and small-cap funds, are evaluated and compared at both the daily and monthly frequency. Besides, using the Carhart’s (1997) four-factor TM and HM models, we apply daily tests to evaluate the management style timing skills at the individual fund level.
4.1 Aggregate portfolio level
Table 2 shows the regression results of the mutual fund performance during the period 2004-2013, using one single factor TM and HM models. Among funds with different investment styles, we assume that they are equally weighted. To overcome the heteroscedasticity and autocorrelation of daily and monthly returns, we employ the Newey and West (1987) heteroscedasticity and autocorrelation consistent standard errors test in this regression process. For all equity funds, firstly, monthly results show that fund managers are not good at selecting stocks and timing the market. The intercepts and market timing coefficients are all insignificant for both TM and HM models. The intercepts for the TM and HM model are -2.723 and -3.150 percent, respectively. The market timing coefficients are -0.293 and 0.019, respectively. When the daily frequency is used, the results do not change. The Jensen’s alpha for the TM and HM model are -0.706 and 0.462 percent, respectively, which are insignificant. The market timing coefficients are insignificant as well, which are -0.257 and -0.022, respectively. The results from both daily tests and monthly tests are consistent with the conclusion of Sharpe (1966), Jensen (1968), Mazuy and Treynor (1966), as well as Henriksson (1984), who are in favor of the theory of the efficient market. Furthermore, daily tests do not have more superior statistics power than monthly tests in the aggregate level.
Table 2. Regression results of one single factor TM and HM models:
,
where for the TM model, and f( =D( for
the HM model. , , and are the fund return, the market return and the risk-free rate,
respectively. The market index is S&P 500 and the risk-free rate is the 3-month overnight index swap. The daily and monthly tests results for equal-weighted portfolios of all equity funds, growth funds, growth & income funds, income funds and small-cap funds are provided. The intercepts are expressed as annualized returns (assuming 252 trading days in a year). Note that * represents the 5% significance level. In this test, we employ the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors test.
Fund group (%) Adj
All equity funds
Daily TM -0.706 0.835* -0.257 0.972 HM 0.462 0.823* -0.022 0.972 monthly TM -2.723 0.910* -0.293 0.920 HM -3.150 0.922* 0.019 0.920 Growth funds Daily TM -0.911 0.949* -0.129 0.970 HM 0.297 0.941* -0.017 0.970 monthly TM -2.508 1.009* 0.078 0.916 HM -2.999 1.027* 0.035 0.916 Growth & Income funds
the findings of Grinblatt and Titman (1989), who reveal that fund managers cannot earn a significantly positive abnormal net return for any kind of funds. For the income funds, the HM model demonstrates that daily tests can earn a significantly positive abnormal return of 2.078 percent. At the same time, all market timing parameters are either insignificant or significantly negative as well, suggesting that managers have an adverse market timing ability. Particularly, daily tests demonstrate that managers of income funds possess significantly inferior market skills with daily data for both TM and HM models.
Table 3 demonstrates the performance regression results using Fama and French’s (1993) three-factor TM and HM models. The daily and monthly tests demonstrate that fund managers do not have superior stock selection and market timing skills. All intercepts and market timing parameters are either insignificant or significantly negative. For instance, based on the TM model, monthly tests show that funds can earn a significantly negative abnormal return of 2.602 percent. And the market timing parameter is -0.211, which is insignificant. For the HM model, daily tests present a timing coefficient of -0.018, which is significantly negative. And the corresponding Jensen’s alpha is insignificant. Generally, fund managers are not good at picking up stocks and timing the market directions when the Fama and French’s (1993) three-factor TM and HM models are employed. The results are similar to the findings from the one single factor TM and HM models.
Table 3. Regression results of Fama and French’s (1993) three-factor TM and HM models:
,
where for the TM model, and =
for the HM model. , , and are the fund return, the market return and the risk-free
rate, respectively. The market index is S&P 500 and the risk-free rate is the 3-month overnight index swap. and are the portfolio return that proxies for size and book-to-market risk factors, respectively. The daily and monthly tests results for equal-weighted portfolios of all equity funds, growth funds, growth & income funds, income funds and small-cap funds are provided. The intercepts are expressed as annualized returns (assuming 252 trading days in a year). Note that * represents the 5% significance level. In this test, we utilize the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors test.
Fund group (%) Adj
All equity funds
daily TM -1.649 0.821* 0.249* -0.007 -0.130 0.988 HM -0.387 0.812* 0.249* -0.007 -0.018* 0.988 monthly TM -2.602* 0.868* 0.241* -0.071 -0.211 0.935 HM -3.108 0.876* 0.238* -0.067 0.001 0.935 Growth funds daily TM -1.128 0.960* 0.192* -0.119* -0.129 0.981 HM -0.435 0.949* 0.192* -0.119* -0.021* 0.981 monthly TM -2.145 0.990* 0.229* -0.192* -0.163 0.934 HM -2.415 0.992* 0.226* -0.190* -0.006 0.934
Growth & Income funds
TM and HM models, daily tests show that income funds and small-cap funds present a reverse sign of the intercepts.
Table 4 shows the regression results of the mutual fund performance from 2004 till 2013 with the help of the modified Carhart’s (1997) four-factor model. For the entire sample, monthly tests for both TM and HM models present that fund managers do not have superior skills to pick up stocks and time the direction of the market. The parameters are all insignificant. For the daily frequency, fund managers do not possess superior skills, either. Although market timing coefficients are significant, they are negative, which imply that managers time the market in a wrong direction. Generally speaking, utilizing the Carhart’s (1997) four-factor TM and HM models, daily tests show that managers do not show more superior performance than monthly tests. Conversely, fund managers possess a significantly negative stock selection and market timing abilities with daily data. It seems that it is not encouraging information for investors and practitioners.
Table 4. Regression results of Carhart’s (1997) four-factor TM and HM models:
,
where for the TM model, and =
for the HM model. , , and are the fund return, the market return and the risk-free
rate, respectively. The market index is S&P 500 and the risk-free rate is the 3-month overnight index swap. , and are the portfolio return that proxies for size, book-to-market and momentum risk factors, respectively. The daily and monthly tests results for equal-weighted portfolios of all equity funds, growth funds, growth & income funds, income funds and small-cap funds are provided. The intercepts are all annualized numbers (assuming 252 trading days in a year). Note that * represents the 5% significance level. In this test, we use the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors test.
Fund group (%) Adj
All equity funds
daily TM -1.694* 0.823* 0.248* -0.003 0.007* -0.125* 0.988 HM -0.493 0.814* 0.249* -0.002 0.006* -0.017* 0.988 monthly TM -2.498 0.861* 0.247* -0.069 -0.027* -0.252 0.936 HM -2.939 0.866* 0.242* -0.066 -0.025* -0.008 0.936 Growth funds daily TM -1.307 0.965* 0.189* -0.099* 0.028* -0.107 0.981 HM -0.030 0.956* 0.189* -0.099* 0.028* -0.017* 0.981 monthly TM -2.029 0.982* 0.235* -0.190* -0.029 -0.208 0.935 HM -2.225 0.981* 0.231* -0.189* -0.028 -0.015 0.935 Growth & Income funds
4.2 Individual fund level
In this second part, we evaluate the mutual fund performance at the individual fund level. First of all, we apply three alternative TM and HM models to measure the management stock selection and market timing skills with both daily and monthly frequency. And secondly, we employ the Carhart’s (1997) four-factor TM and HM models to test style timing skills with only daily frequency.
4.2.1 Stock selection and market timing
In Table 5, we utilize the one single factor TM and HM models to calculate the proportion of mutual funds that have positive and negative intercepts and market timing coefficients, respectively. Besides, the fraction of mutual funds whose Jensen alpha and marking timing coefficients are significantly positive and negative is reported as well. For both daily and monthly tests, we apply the Newey and West (1987) heteroscedasticity and autocorrelation consistent standard errors statistics to prevent heteroscedasticity and autocorrelation.
Table 5. Fractions of intercepts and market timing coefficients
In this table, we estimate equations from equation (3) and (4), labeled as the TM and HM model, respectively. We employ the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors statistics to overcome the heteroskedasticity and autocorrelation. The fraction of intercepts and market timing coefficients are classified as one of the following subgroups: significantly positive (++), positive (+), negative (-) and significantly negative (--). The table shows the fractions of mutual funds that belong to one of these four subgroups during the period 2004-2013. Note that MTC means market timing coefficients, and the tests are evaluated at the 5% significance level.
Monthly Daily Monthly Daily
+ - + - ++ -- ++ --
All equity fund
TM 0.106 0.894 0.406 0.594 0.000 0.142 0.000 0.029 HM 0.184 0.816 0.582 0.418 0.002 0.104 0.094 0.009 MTC TM 0.474 0.526 0.268 0.732 0.050 0.111 0.010 0.177 HM 0.543 0.457 0.241 0.759 0.027 0.032 0.000 0.184 Growth fund TM 0.141 0.859 0.395 0.605 0.000 0.073 0.000 0.000 HM 0.181 0.819 0.531 0.469 0.000 0.017 0.085 0.000 MTC TM 0.565 0.435 0.418 0.582 0.073 0.040 0.000 0.011 HM 0.565 0.435 0.390 0.610 0.040 0.023 0.000 0.136
Growth & Income fund
TM 0.081 0.919 0.174 0.826 0.000 0.302 0.000 0.096 HM 0.134 0.866 0.322 0.678 0.000 0.248 0.040 0.034 MTC TM 0.550 0.450 0.470 0.530 0.081 0.087 0.034 0.128 HM 0.577 0.423 0.275 0.725 0.047 0.000 0.000 0.128 Income fund TM 0.050 0.950 0.571 0.429 0.000 0.114 0.000 0.000 HM 0.207 0.793 0.886 0.114 0.000 0.114 0.243 0.000 MTC TM 0.129 0.871 0.071 0.929 0.000 0.300 0.007 0.564 HM 0.421 0.579 0.136 0.864 0.007 0.100 0.000 0.450 Small-cap fund TM 0.150 0.850 0.517 0.483 0.000 0.075 0.000 0.000 HM 0.225 0.775 0.625 0.375 0.008 0.042 0.000 0.000 MTC TM 0.650 0.350 0.025 0.975 0.033 0.025 0.000 0.033 HM 0.608 0.392 0.100 0.900 0.008 0.008 0.000 0.017
positive coefficients shrinks, whereas the number of funds that have significantly negative parameters increases. The results suggest an inferior market timing ability for fund managers, and thus resulting in a bad return.
Among four different subgroups, both models reveal that the number of funds that have positive intercepts increase when the daily frequency is applied, particularly for the income funds. Although the TM model does not show that daily tests improve the stock selection skills, the HM model witnesses an increased number of funds that possess superior selection abilities, except the small-cap funds. At the same time, both TM and HM models imply that the proportion of funds that have negative and significantly negative intercepts decreases a lot. For the market timing coefficients, the result presents a contrary trend. Neither the TM model nor the HM model exhibits a superior market timing ability. Particularly, daily tests show that income funds have prominently negative market timing skills. For the TM model, tests show that about 56.4 percent of funds have inferior market timing skills. For the HM model, tests report that about 45.0 percent of funds have bad market timing abilities. These findings imply that fund managers possess less superior market timing abilities, but more inferior market timing skills with daily frequency instead of monthly frequency.
Table 6. Fractions of intercepts and market timing coefficients
In this table, we estimate equations from equation (5) and (6), labeled as the TM and HM model, respectively. We employ the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors statistics to overcome the heteroskedasticity and autocorrelation. The fraction of intercepts and market timing coefficients are classified as one of the following subgroups: significantly positive (++), positive (+), negative (-) and significantly negative (--). The table shows the fractions of mutual funds that belong to one of these four subgroups during the period 2004-2013. Note that MTC means market timing coefficients, and the tests are evaluated at the 5% significance level.
Monthly Daily Monthly Daily
+ - + - ++ -- ++ --
All equity fund
TM 0.164 0.836 0.305 0.695 0.007 0.164 0.014 0.106 HM 0.222 0.778 0.498 0.502 0.131 0.005 0.118 0.055 MTC TM 0.340 0.660 0.328 0.672 0.038 0.162 0.014 0.181 HM 0.485 0.515 0.270 0.730 0.017 0.048 0.015 0.229 Growth fund TM 0.254 0.746 0.362 0.638 0.023 0.079 0.045 0.051 HM 0.311 0.689 0.554 0.446 0.011 0.028 0.164 0.023 MTC TM 0.395 0.605 0.316 0.684 0.040 0.102 0.000 0.096 HM 0.441 0.559 0.271 0.729 0.006 0.028 0.000 0.249
Growth & Income fund
TM 0.074 0.926 0.121 0.879 0.000 0.309 0.000 0.195 HM 0.134 0.866 0.221 0.779 0.000 0.262 0.034 0.054 MTC TM 0.483 0.517 0.497 0.503 0.087 0.101 0.020 0.067 HM 0.570 0.430 0.322 0.678 0.054 0.013 0.013 0.107 Income fund TM 0.143 0.857 0.536 0.464 0.000 0.079 0.000 0.000 HM 0.050 0.950 0.879 0.121 0.000 0.107 0.243 0.000 MTC TM 0.136 0.864 0.086 0.914 0.000 0.300 0.007 0.471 HM 0.379 0.621 0.143 0.857 0.000 0.100 0.000 0.457 Small-cap fund TM 0.167 0.833 0.183 0.817 0.000 0.208 0.000 0.200 HM 0.233 0.767 0.317 0.683 0.008 0.150 0.008 0.167 MTC TM 0.317 0.683 0.417 0.583 0.008 0.175 0.033 0.108 HM 0.567 0.433 0.350 0.650 0.008 0.058 0.058 0.092
cannot improve the explanatory power. However, daily tests are more powerful than monthly tests in explaining the significantly negative market timing parameters.
For funds with different investment objectives, we can conclude that generally fund managers’ stock selection skills are improved when the daily frequency is employed rather than the monthly data. Conversely, they do not have superior skills to time the market directions. What’s more, compared with monthly tests, daily tests present a significantly negative market timing abilities for all kinds of funds, particularly for income funds. Daily tests report that around 47.1 percent and 45.7 percent of income funds have significantly negative market timing parameters for the TM model and the HM model, respectively. These findings are consistent with results revealed by the one single factor TM and HM models.
Table 7. Fractions of intercepts and market timing coefficients
In this table, we estimate equations from equation (7) and (8), labeled as the TM and HM model, respectively. We employ the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors statistics to overcome the heteroskedasticity and autocorrelation. The fraction of intercepts and market timing coefficients are classified as one of the following subgroups: significantly positive (++), positive (+), negative (-) and significantly negative (--). The table shows the fractions of mutual funds that belong to one of these four subgroups during the period 2004-2013. Note that MTC means market timing coefficients, and the tests are evaluated at the 5% significance level.
Monthly Daily Monthly Daily
+ - + - ++ -- ++ --
All equity fund
TM 0.158 0.842 0.292 0.708 0.005 0.164 0.003 0.097 HM 0.232 0.768 0.469 0.531 0.005 0.123 0.096 0.044 MTC TM 0.324 0.676 0.352 0.648 0.027 0.177 0.014 0.172 HM 0.462 0.538 0.295 0.705 0.019 0.049 0.012 0.208 Growth fund TM 0.271 0.729 0.333 0.667 0.017 0.085 0.011 0.051 HM 0.339 0.661 0.492 0.508 0.011 0.028 0.085 0.011 MTC TM 0.373 0.627 0.395 0.605 0.011 0.113 0.000 0.062 HM 0.424 0.576 0.328 0.672 0.006 0.028 0.000 0.209
Growth & Income fund
four-factor TM and HM models are used.
Among funds with different investment objectives, we can reach a result consistent with Table 5 and 6. In general, daily tests enhance managers’ skills to pick up stocks, whereas daily tests do not show evidence of superior market timing abilities, and even significantly inferior market timing skills, particularly for income funds.
With all three different models, it is not difficult to find that fund managers generally have negative and even significantly negative market timing skills. Warther (1995), Edelen (1999), Bollen and Busse (2001) uncover that the significantly negative market timing parameters can be explained by the cash flow hypothesis, which states that investors wish to increase their subscriptions when the market is rising, but fund managers cannot invest timely, and thus leading to a lower beta. As a consequence, results from previous tables with regard to market timing parameters may be biased downwards as a result of the cash flow hypothesis.
4.2.2 Style timing
In this part, we estimate the management market timing, size timing, valuation timing, and momentum timing skills with daily data at the individual fund level. Unlike Swinkels and Tjong-A-Tjoe (2007), who test the market timing, size timing, valuation timing and momentum timing skills separately, this paper tests these style timing skills at the same time employing equations (9) and (10). Adams, Chen and Taffler (2013) explain that this move can effectively isolate the impact of each timing factors, because investors and fund managers are normally interested in the overall performance of mutual funds.
significantly positive valuation timing parameters. The HM model presents a similar result. About 65.7 percent of funds demonstrate positive valuation timing abilities, and 7.5 percent of them show significantly positive parameters. However, fund managers generally do not present market timing, size timing and momentum timing skills. With regard to size and momentum timing skills, the results for both TM and HM models show that more than half of funds have negative timing coefficients, and funds that have significantly negative timing parameters exceed the corresponding funds that have significantly positive timing parameters.
Table 8. Fractions of market, size, valuation, momentum timing coefficients
In this table, we estimate equations from equation (9) and (10), labeled as the TM and HM model, respectively. We employ the Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors statistics to overcome the heteroskedasticity and autocorrelation. The fraction of market timing, size timing, valuation timing and momentum timing coefficients are classified as one of the following subgroups: significantly positive (++), positive (+), negative (-) and significantly negative (--). The table shows the fractions of mutual funds that belong to one of these four subgroups during the period 2004-2013. Note that MTC means market timing coefficients, and the tests are evaluated at the 5% significance level.
Daily TM Daily HM
+ - ++ -- + - ++ --
All equity fund
Market 0.503 0.497 0.041 0.044 0.369 0.631 0.017 0.167 Size 0.160 0.840 0.019 0.186 0.261 0.739 0.012 0.135 Valuation 0.623 0.377 0.102 0.026 0.657 0.343 0.075 0.002 Momentum 0.369 0.631 0.041 0.104 0.464 0.536 0.026 0.048 Growth fund Market 0.571 0.429 0.068 0.006 0.429 0.571 0.000 0.119 Size 0.107 0.893 0.000 0.350 0.153 0.847 0.011 0.294 Valuation 0.678 0.322 0.130 0.011 0.689 0.311 0.062 0.000 Momentum 0.373 0.627 0.045 0.062 0.542 0.458 0.023 0.034
Growth & Income fund
managers do not often claim to implement market timing and momentum strategies. And the growth-oriented fund managers are inclined to invest in large capitalization stocks. Thus, managers may have valuation timing skills under this circumstance.
5 Conclusion
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