Identifying Superior Performing Equity Mutual Funds

Transcription

1 Identifying Superior Performing Equity Mutual Funds Ravi Shukla Finance Department Syracuse University Syracuse, NY Phone: (315) First draft: March 1999 This revision: March 2000 Software used: L A TEX Please do not quote. Comments are welcome.

2 Identifying Superior Performing Equity Mutual Funds Abstract We find that high returns among large company U.S. equity mutual funds are earned by funds with low expense ratios, high three-year trailing returns, and negative trailing Jensen alphas. The top decile portfolio identified by the model outperforms the average fund by 3.46% per year. A drawback of the model is that if applied strictly it results in a high turnover (67%). However, a slightly relaxed version of the model results in only a 27% turnover while maintaining a 2.72% advantage over the average fund. Mutual fund selection usually proceeds in two steps: First, one creates a list of funds to suit an investment objective, and then, from this list, one selects a few funds that are expected to perform well. The first step is relatively easy, even though one needs to be cautious while choosing funds based on their stated objectives. 1 The second step is the problematic one. Financial magazines and web sites are filled with advice on how to identify funds that are expected to perform well. Recently, some research papers have also identified mutual fund attributes that can help select superior performers. The objective of this paper is to construct a simple model for identifying superior performing equity mutual funds using factors identified in earlier research. Specifically, we want to construct a model that is parsimonious and utilizes readily available information. Our results show that a model based on expense ratio, trailing returns, and trailing Jensen alpha has the ability to identify superior performing mutual funds quite reliably. The model, when applied strictly, has a significant portfolio turnover. However, a less strict implementation of the model results in a much lower and quite tolerable turnover with a small loss in portfolio returns. 1 The Model Our model is structured to forecast mutual fund annual returns one year into the future. For example, in December 1998, we forecast one-year returns that would be realized in December 1999 (over the investment period of January 1999 to December 1999). We proceed in the following steps: 1 See Brown and Goetzmann (1997), dibartolomeo and Witkowski (1997) and Kim, Shukla, and Tomas (1999) for a discussion of pitfalls associated with classifying mutual funds based on their stated objectives. 1

3 1. Estimate the model by regressing the realized returns at time t on mutual fund attributes at time t l, where l is the lag for the forecasting model. Specifically, we estimate the following cross-sectional model at time t: R j,t = γ 0,t + γ 1,t A j,1,t l + γ 2,t A j,2,t l + + γ k,t A j,k,t l + ε t (1) where R j,t is the realized return on fund j at time t and A j,k,t l is attribute k on fund j. Theγ s are the coefficients to be estimated in the regression model. 2. Forecast the returns at time t + l using the attributes at time t and coefficients ˆγ s estimated in step 1 as: ˆR j,t+l =ˆγ 0,t +ˆγ 1,t A j,1,t +ˆγ 2,t A j,2,t + +ˆγ k,t A j,k,t (2) To test the validity of the model, we examine the Pearson correlations and Spearman rank-order correlations between the predicted returns ˆR j,t+l and realized returns R j,t+l. Predicting fund returns may not be necessary for investors and institutions. 2 For practical purposes, it is sufficient if one can predict whether a mutual fund will be among the top or bottom 10% of the mutual fund population. To test the ability of the model to forecast at this practical level, we divide the funds, based on their predicted returns, into 10 decile portfolios: Decile 10 portfolio is an equally weighted portfolio of funds predicted to be in the top 10%. Decile 1 portfolio is an equally weighted portfolio of funds predicted to be in the bottom 10%. Other decile portfolios fall in the in-between deciles. In this paper, we use annual returns and a lag (l) of 4 calendar quarters. Therefore, our models are estimated by regressing returns for the year ending in quarter t on mutual fund attributes in quarter t 4. Then, using the regression coefficients estimated for equation (1) and the mutual fund attributes in quarter t, we forecast mutual fund returns for the year ending in quarter t +4. For example, we estimate a model by regressing annual returns realized in Quarter 4, 1997 on mutual fund attributes as of Quarter 4, Next, annual returns for mutual funds in quarter 4 of 1998 are forecast by using attributes in quarter 4, 1997 and the coefficients estimated in the regression model. The next question is which attributes should be used as predictors in our model. Existing research provides some guidelines on this issue: 1. Krum (1995) finds that portfolios managed by smaller firms may be better performers as firms lose their potential for high performance as they grow. 2. Lemak and Satish (1996) find that funds managed by managers with longer tenure have lower risk and higher performance measures. They also find that the expense ratios are lower and fund sizes are higher for funds managed by the same manager for long term. 2 In fact, expecting this level of precision is unrealistic because of the high level of randomness in the mutual fund returns. 2

4 3. Gruber (1996) shows that mutual fund performance can be predicted using observable variables. In particular, he provides the following evidence: (a) Lower expense ratio leads to higher returns. (b) Funds with high one-year trailing returns have high returns. (c) Funds with a high four-factor Jensen alpha type measure have high returns. The four factors are: difference between the S&P 500 return and the Treasury bill return (market premium), difference between the returns on a small cap portfolio and large cap portfolio (size premium), difference between the returns on a high growth portfolio and a value portfolio (growth premium), difference between the returns on a portfolio of corporate and government bonds and the Treasury bill (risk-premium). 4. Ang, Chen, and Lin (1998) examine the level and nature of efforts by funds that have experienced poor performance in the recent past. The poorer performers try harder by incurring more expenses, trading more often, and taking greater risk of loss. However, the authors find that higher returns are most reliably achieved by lower expenses. There is only a weak link between stock selection and subsequent returns. 5. Khorana and Nelling (1998) find that funds that have higher Morningstar ratings earn higher returns. Furthermore, they find evidence for persistence of Morningstar ratings, which may lead to persistence in fund returns. The mutual fund attributes we use in our performance prediction model are based on these results. 2 Data Our source for all data is the Morningstar Principia database. 3 This is an easily accessible, publicly available database. Our first database is for quarter 2 of 1993 (1993Q2) and the last one is for quarter 4 of 1998 (1998Q4), making a total of 23 quarters. Since our model has a lag of four quarters, we estimate the model 19 times (using returns for 1994Q2 to 1998Q4) and forecast returns four quarters into the future based on these estimates. Since the last available return is for quarter 1998Q4, we can test the predictive ability of the model using returns in 15 quarters: 1995Q2 to 1998Q4. The Morningstar Principia database contains almost one hundred different data fields for each mutual fund, including the data items of interest to us, which are fund returns, expense ratio, trailing returns, Jensen alpha, Morningstar rating, fund assets, and manager tenure. 3 Some of our data come from Morningstar OnDisc database, a precursor of Morningstar Principia database. 3

5 It is reasonable to expect that the model coefficients and even the mutual fund attributes that describe the model would be different for different types of mutual funds. In this paper, we construct a model for the U.S. large company equity funds. 3 Variable Selection The research cited earlier shows that five different attributes may be used to predict mutual fund performance: 1. Expenses: The expense ratio is available in the Morningstar Principia database. 2. Momentum: Gruber (1996) use a one-year trailing return to capture momentum. Other studies have used a three-year trailing return. Since Morningstar provides both one and three-year trailing returns, we will try both of them to find the better measure. 3. Performance: Khorana and Nelling (1998) use Morningstar rating which is available in the Morningstar Principia database. Gruber (1996) uses a four factor Jensen alpha. Other studies have used single factor (S&P 500) Jensen alpha. Morningstar provides the single factor alpha (S&P 500) estimated using three years of returns in its Principia database. In the interest of simplicity, we try the Jensen alpha provided in the Morningstar Principia database in addition to Morningstar rating. 4. Size of the managing firm: This variable is not available in the Morningstar Principia database. We use the total assets of the mutual funds as a proxy for the size of the managing firm with the assumption that large firms manage large funds. 5. Manager tenure: This variable is provided in Morningstar Principia database. We use a stepwise process to select the variables to be included in the model. Table 1 shows the details of our variable selection process. We start our search for the best model by trying individual variables. Clearly, expense ratio (Exp) is the single most important characteristic when it comes to future mutual fund returns. The average R 2 over the 19 quarters during which the model is estimated is 10.68% and the average F -statistic is The F -statistic is significant at the 5% level in 18 of the 19 quarters. As judged by the t-statistic, the regression coefficient is also significant at the 5% level 4 in 18 of the 19 quarters. 5 The second most important variable is momentum proxied by one-year trailing return (TR1Yr) or three-year trailing return (TR3Yr). Performance, represented by Jensen alpha (Alpha) or Morningstar rating (Rating), is the 4 Significance levels for t-statisticsinthepaperarebasedontwo-tailedtests. 5 F = t 2 for univariate regression models. Therefore, the significance count for F and coefficients is identical for all univariate regressions. 4

6 Table 1: Variable Selection A stepwise process is used to select the variables used in the model. Potential variables are first evaluated individually and then in combinations of two s, three s and four s. This table shows the summary of regression model estimations over 19 quarters. 5 Average Average N of signi- Number of significant coefficients Case R 2 F ficant F s Exp TR1Yr TR3Yr Alpha Rating Tenure Size 1A B C D E F G A B A B C D A B : Statistically significant at the 5% level.

7 next important variable. Fund size (Size) and manager tenure (Tenure) do not have a significant relationship with future returns. Next we try combinations of variables. First we try the two most important variables: expense ratio (Exp) and momentum (TR1Yr or TR3Yr). It appears that the two proxies for momentum TR1Yr and TR3Yr perform almost equally well (R 2 =57.26% and 55.12%). Next we try the combination of three variables: expenses, momentum and performance. Clearly, the combination of Exp, TR3Yr and Alpha has the highest average R 2 (69.13%), F (28.74) and the greatest number of occurrences of significant coefficients. Adding manager tenure (Tenure) or fund size (Size) to the three-variable model does not improve the model fit. In fact, the F value declines. 6 Therefore, we use a three-variable model with expense ratio (Exp), three-year trailing return (TR3Yr) and Jensen alpha (Alpha) as the forecasting attributes. 4 Model Fit The results from estimating the model with the three selected variables are shown in Table 2. Let us examine the results for the model period of quarter 4 of 1997 (1997Q4). The model is estimated using 697 funds. The R 2 for the regression model is 25% and the F -statistic for the regression is 76.70, which is statistically significant at the 5% level. The intercept is and is statistically significant at the 5% level. The coefficients of expense ratio, three-year trailing return and Jensen alpha are 3.03, 0.86 and 0.72, respectively, and are all statistically significant at the 5% level. The signs of the three coefficients show that lower expenses improve returns, higher returns are followed by higher returns (as expected from momentum effect), and trailing high abnormal performance funds earn lower returns. Examining the entire set of results, we see that the coefficient of expense ratio is always negative and statistically significant. The coefficient of threeyear trailing return is positive and statistically significant in 16 of 19 quarters. The coefficient of Jensen alpha is always negative, and is statistically significant in 16 of 19 quarters. The coefficients of expense ratio and three-year trailing returns are consistent with anecdotal evidence as well as prior research (e.g., Gruber (1996)). The coefficient of Jensen alpha is contrary to the conclusion in Gruber (1996). This finding led us to scrutinize the coefficient of performance variables more carefully. In results not reported here, we find that in univariate regression models, coefficients of Jensen alpha and Morningstar rating are mixed: some are positive while others are negative, with about as many positive coefficients being statistically significant as negative coefficients. When we estimate the multivariate model reported in Table 2 using Morningstar rating instead of Jensen alpha, we find that the coefficient of Morningstar rating is negative in 15 6 The slight increase in R 2 from case 3C to 4B is misleading. It is simply the effect of increased number of independent variables. Adjusted R 2 (not shown here) declines as a result of adding the new variable. This is also conveyed by the decrease in F -statistic. 6

8 Table 2: Model Estimation This table shows the results from estimating the following model for various quarters: R j,t = γ 0,t + γ 1,tExp j,t 4 + γ 2,tTR3Yr j,t 4 + γ 3,tAlpha j,t 4 + ε t where R j,t is the one-year return on mutual fund j at the end of quarter t, Exp j,t 4 is the expense ratio on fund j at the end of quarter t 4, TR3Yr j,t 4 is the return over the three-year period ending quarter t 4andAlpha j,t 4 is the one-factor (S&P 500) Jensen alpha estimated using returns over three years ending quarter t 4. t Funds R 2 (%) F ˆγ 0,t ˆγ 1,t ˆγ 2,t ˆγ 3,t 1994Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q : Statistically significant at the 5% level. 7

9 of the 19 quarters and is negative and statistically significant in 8 quarters. The coefficient is never positive and statistically significant regardless of whether Jensen alpha or Morningstar rating is used. The negative sign on Jensen alpha is consistent with the hypothesis that the risk-adjusted excess returns have a mean reverting behavior: Positive riskadjusted returns in one period are followed by negative risk-adjusted returns in the following period. Empirical results reported in Shukla and Trzcinka (1994) confirm this phenomenon. Overall, our model results suggest that high returns among large company U.S. mutual funds are earned on those funds which have lower expense ratios, have earned high total returns but negative risk-adjusted returns in the past. 5 Predictive Ability In the second step of our analysis, we apply the coefficients shown in Table 2 to the mutual fund attributes to obtain predicted mutual fund returns for four quarters in the future. As noted earlier, for most practical applications, it is sufficient to be able to predict the decile rank of a mutual fund. Therefore, funds are also assigned decile ranks based on their predicted returns, with decile 10 having the highest predicted return funds while decile 1 having the lowest predicted return funds. Table 3 shows the prediction results. Let us examine the results for 1998Q4 which reflects the returns predicted based on the model estimated in 1997Q4. There are 944 funds whose results were forecasted. The correlation between forecasted and actual returns is 0.38 and is statistically significant at the 5% level. The rank order correlation between the predicted and actual returns is 0.47 and statistically significant at the 5% level. A word of caution about the forecast results is in order. The level of returns forecast by the model is quite different from the actual level of returns realized. For example, for 1998Q4, the average forecast return for the entire sample of mutual funds is 34.85% while the average realized return is 21.61%. The disparity between the levels of forecast and realized returns is even larger in other quarters. The strength of the model, however, lies in explaining the variation and relative ranking of the various mutual funds. The returns on the decile portfolios are shown next. Consistent with the model prediction, decile 10 portfolio has the highest return (32.61%) and decile 1 portfolio has the lowest return (13.65%). The second highest return is realized on decile 9 portfolio followed by deciles 8, 7, 5, 6, 4, 3, 2, and 1. The rank correlation between the predicted decile ranks and actual decile ranks of these portfolios is Practical usefulness of the prediction mechanism can be assessed by measuring the return to an investor who invests in the top decile of funds rather than a random sample of funds representing the entire population of mutual funds. This difference is 11.00% per year. Scanning the results for 15 quarters 1995Q2 to 1998Q4 we see that most of the Pearson correlations between predicted and actual fund returns are around 8

10 Table 3: Test of Predictive Ability This table shows the results of using the model with expense ratio, three-year trailing returns, and Jensen alpha to predict one-year returns on mutual funds four quarters into the future. 9 Return of decile portfolio Forecast Quarter Funds r r s ρ s 1995Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Average : Statistically significant at the 5% level. r: Pearson correlation between predicted and realized fund returns. r s: Spearman rank order correlation between predicted and realized fund returns. ρ s: Correlation between decile portfolio numbers and their ranks. : Difference between realized average returns on decile 10 portfolio and the entire sample.

11 0.5 and most of the Spearman rank order correlations are around 0.4. More importantly, the correlations between the actual and predicted decile ranks are very high, the average being Except in 1996Q3, the strategy of investing in the highest predicted decile portfolio outperforms the average group of mutual funds. The average difference between the top decile portfolio and the average fund ( ) is 3.46% per year. 6 Portfolio Turnover The funds in the top predicted decile will change over time. Therefore, following the strategy of investing in the top decile portfolio of mutual funds will cause turnover in the portfolio. In this section, we assess the level of turnover created due to replacement of mutual funds while implementing this model. Consistent with the lag structure in the model, we assume that the mutual fund portfolio will be revised every 4 quarters. Different portfolio revision strategies are possible depending on the level of efficiency one desires from the mutual fund portfolio. First, the investor can perform a Full Overhaul of the portfolio and bring it up to the top decile portfolio based on the most recent model. The second strategy, referred to here as Decile 10 strategy, would be to replace only the funds that are no longer in the top decile by new top decile funds. A variation on the Decile 10 strategy is Decile 9 strategy, which is somewhat less strict and removes the funds only if they fall below decile 9 and replaces them with the new top decile funds. Table 4 shows the results from the three strategies described above. To understand the process fully, let us focus on the last row of this table. The model is estimated using the returns as of 1996Q4 (and attributes as of 1995Q4). Table 2 shows that this estimation involved 507 mutual funds. The model is used to forecast returns for 1997Q4 for 697 funds (see Table 3 for the number of mutual funds) using the attributes as of 1996Q4. Therefore, the top forecast decile consists of 70 mutual funds. Having created the portfolio in 1996Q4 and realized the returns in 1997Q4, the investor is considering revising the portfolio in 1997Q4 to get the best return in 1998Q4. The current model (estimated using 1997Q4 returns) forecasts the returns for 944 mutual funds and therefore the top decile consists of 94 mutual funds. Comparing the currently held portfolio with the most recent forecast, we find that 15 funds in the portfolio are below decile 10. Furthermore, six funds are not even in the full sample either because they have ceased to exist or there is insufficient information about the funds for them to be included in the model. The first revision strategy requires a Full Overhaul of the portfolio. It involves selling the 21 non-decile 10 funds entirely and fractions of the remaining = 49 funds and using the proceeds to buy = 45 funds to create an equally weighted portfolio of 94 mutual funds. This would involve a selling and buying 48% ( = 48%) of the portfolio. This portfolio earns a return of 32.61% in 1998Q4, which is the same as the return for decile 10 portfolio in 1998Q4 in Table 3. 10

12 Table 4: Portfolio Turnover In this table we show the results of portfolio revision strategies on the turnover and the realized portfolio return. Full Overhaul strategy brings the portfolio up to the top decile portfolio based on the most recent model. Decile 10 strategy replaces the funds that are no longer in the top decile by new top decile funds. Decile 9 strategy removes the funds only if they fall below decile 9 and replaces them by new top decile funds. Turnover refers to the percent of portfolio that needs to be replaced by new mutual funds. δ is the effect on the portfolio return relative to the Full Overhaul strategy. 11 Quarter for Full Overhaul Replace funds below decile 10 Replace funds below decile 9 Model Revision Return Turnover Return Turnover Return δ Turnover Return δ 1994Q2 1995Q2 1996Q Q3 1995Q3 1996Q Q4 1995Q4 1996Q Q1 1996Q1 1997Q Q2 1996Q2 1997Q Q3 1996Q3 1997Q Q4 1996Q4 1997Q Q1 1997Q1 1998Q Q2 1997Q2 1998Q Q3 1997Q3 1998Q Q4 1997Q4 1998Q Average Std Dev t-stat

13 The second revision strategy would be to keep the number of mutual funds in the portfolio unchanged at 70 and replace only the funds that have fallen below decile 10 with the top new members of the new decile 10 portfolio. This strategy results in sale and purchase of 30% of the portfolio ( = 30%) and a realized return of 34.43% in 1998Q4, which is 1.82% greater than the Full Overahul strategy. Across all quarters, the decile 10 strategy results in an average loss of 0.42% in return but avoids 67% 53% = 14% portfolio turnover. The reduction in return, however, is not statistically significant at the 5% level. The third strategy is to replace the funds that have fallen below decile 9 by the top new members of the new decile 10 portfolio. This strategy results in a turnover of 13% and a gain of 1.76% compared to the Full Overhaul strategy. On an average, the decile 9 strategy results in an average loss of 0.74% in return and avoids = 40% portfolio turnover. An annual turnover of 27%, just over a quarter of the portfolio, does not seem excessive for active investors yet it provides an excess return of 3.46% 0.74% = 2.72% over random fund selection. 7 Conclusion The empirical results in this paper demonstrate that it is possible to identify top performing mutual funds using publicly available mutual fund information, specifically, expense ratio, three-year trailing return and S&P 500-based Jensen alpha. In our sample, the top decile funds earn an extra return of 3.46% over what can be earned by investing in a random sample of the population of mutual funds. The level of turnover associated with following the model is high. However, one can reduce the turnover significantly by accepting a small reduction in the portfolio return by following a relaxed strategy. References [1] Ang, James S., Chen, Carl R., and Lin, James Wuh, 1998, Mutual fund managers efforts and performance, Journal of Investing, Volume 7, Number 4 (Winter), Pages [2] Brown, Stephen J. and Goetzmann, William N., 1997, Mutual fund styles, Journal of Financial Economics, Volume 43, Number 3 (15 March), Pages [3] dibartolomeo, Dan and Witkowski, Erik, 1997, Mutual fund misclassification: Evidence based on style analysis, Financial Analysts Journal, Volume 53, Number 5 (September/October), Pages [4] Gruber, Martin J., 1996, Another puzzle: The growth in actively managed mutual funds, Journal of Finance, Volume 51, Number 3 (July), Pages

14 [5] Khorana, Ajay and Nelling, Edward, 1998, The determinants and predictive ability of mutual fund ratings, Journal of Investing, Volume 7, Number 3 (Fall), Pages [6] Kim, Moon K., Shukla, Ravi K., and Tomas, Michael J., 1999, Mutual fund objective misclassification, Journal of Economics and Business. Forthcoming. [7] Krum, Ted, 1995, The performance advantage of small portfolio management firms, Journal of Investing, Volume 4, Number 1 (Spring), Pages [8] Lemak, David J. and Satish, Peruvemba K., 1996, Mutual fund performance and managers terms of service: Are there performance differences, Journal of Investing, Volume 5, Number 4 (Winter), Pages [9] Shukla, Ravi K. and Trzcinka, Charles A., 1994, Persistence performance in the mutual fund market: Tests with funds and investment advisers, Review of Quantitative Finance and Accounting, Volume 4, Number 2 (June), Pages