Mutual funds' risk adjusted performance.

Brooks, Mark ; Tompkins, Daniel L.

INTRODUCTION

From the first one created in the 1920's to the thousands that are available today, mutual funds are a popular investment vehicle. When investors look at mutual funds, they need to consider two characteristics, risk and return. In an ideal world, there would be high returns with no risk. Unfortunately, that's not how the investment world works. All too often, risk is often mentioned in terms of the classification of the fund (aggressive growth, growth, income, balanced, and international are categories often used). Mutual funds are split into different objective categories to suit each investor's needs. For example, a retired person will be interested in income preservation with lower risk while a college student would seek out aggressive growth higher risk.

Once mutual funds are classified by their objectives, it is ranked on how its return compares to the other funds in the category. Whether a fund is miss-classified, or the reward-to-risk performance of a fund, usually isn't considered.

In order for investors to increase returns, they need to increase risk. But with greater risk there's a possibility of taking a greater loss. There are several ways to adjust performance for risk. First, we can use the Sharpe Ratio:

([R.sup.p] - [R.sub.f])/ [sigma]

Where,

[R.sub.p] = Return on the (Risky) Portfolio

[R.sub.F] = Return on the Risk-free Rate

[sigma] = Standard deviation of the risky portfolio.

I.e., the Sharpe Ratio measures the Excess return (return on the portfolio minus the risk-free rate of return) per unit of risk, with the standard deviation of the risky portfolio used as the measure of risk. With the Sharpe ratio, the higher the index value, the better the portfolio. A negative index number can only result from a return on the portfolio below the risk-free rate of return.

The second measure is the Treynor Ratio. The Treynor Ratio is similar the Sharpe Ratio, but it uses beta as a measure of risk:

([R.sub.p] - [R.sub.f])/ [beta]

Where,

[R.sub.p], [R.sub.f] are the return on the portfolio and the Risk-free rate (as before), and [beta] = The systematic risk measure

In general, the higher the Treynor Ratio, the better the portfolio. However, negative results need to be carefully interpreted. Beta, the measure of systematic risk can be negative as well as positive. Thus a negative number could be the result of a very well diversified portfolio.

A third measure of risk-adjusted performance is [M.sup.2] (M-squared) by Modigliani and Modigliani (1997). [M.sup.2] takes the opportunity cost of a risky portfolio to adjust portfolios to a risk level of an unmanaged benchmark, such as the S&P 500:

[M.sup.2] = ([[sigma].sub.index]/[[sigma].sub.p]) * ([R.sub.p]-[R.sub.f]) + [R.sub.f]

Where,

[[sigma].sub.index] = Standard deviation (volatility) of unmanaged benchmark

[[sigma].sub.p] = Standard Deviation (volatility) of risky portfolio

[R.sub.p], [R.sub.f] are the return on the portfolio and the Risk-free rate (as before), and

The Risk Adjusted Performance is measured with basis points, thus one is able to compare one fund's performance against other funds. Like the Sharpe Ratio, [M.sup.2] uses the portfolio's standard deviation as the measure of risk. The only difference between the Sharpe Ratio and [M.sup.2] is the use of basis points as the measurement units. [M.sup.2] aims to answer the question, "Am I being fully compensated for the risk that I am taking on?" As Hopkins and Akins (1999) state, the risk that investors are concerned with is volatility, specifically, the volatility of the portfolio compared to the volatility of a stated benchmark. With [M.sup.2] we can make this comparison.

Several studies have examined mutual fund returns. Werner (2000) examines the performance of aggressive growth, growth, growth and income, and balanced funds. He finds that lower net return achieved by mutual funds is caused by non- stock holdings of the funds, expenses and transaction costs. Blake and Morey (2000) find that funds rated low by Morningstar generally do have relatively low future performance but funds rated the highest by Morningstar don't outperform funds in the next to highest or median categories. Rao (2001) examines the impact of distribution fees. DiBartolomeo and Witkowski (1997) find that 40% of mutual funds are misclassified, 9% seriously so. They cite ambiguity of classification systems and competitive pressures as the major reasons for misclassification. Kim, Shukla, and Tomas (2000) agree that a majority of mutual funds are misclassified (with a third seriously misclassified), but they disagree that fund managers are gaming their objectives (deviating from stated objectives in order to achieve a higher ranking).

DATA

Data was provided by the October, 1999 Value Line Mutual Fund Survey. Our data set includes all mutual funds categorized as either an aggressive growth, balanced, foreign, growth, growth and income, or income fund by the Value Line Mutual Fund Survey. To be included in the sample, the fund must have been in existence for at least ten years and complete information on the fund must be available. This study covers the returns over the October 1989 to October 1999 period. We choose this period because it includes the recession of 1990-1991 as well as the bull market of the late 1990s. We examined the following variables in this study: [M.sup.2] The Modigliani and Modigliani [M.sup.2] measure of risk adjusted return. Return for each fund was calculated as the ten-year average return, based on the ten-year total return, and the ten-year standard deviation for the fund and the S&P 500. TURN the percentage average yearly turnover of the portfolio. STOCK The percentage of the portfolio kept in stocks. CASH The percentage of the portfolio kept in money market securities EXP The average annual expense ratio for the firm. This ratio (expressed as a percentage of the total return) is the amount the management firm charges the mutual fund shareholders for administrative, research, and trading expenses. MGMT The percentage charged the fund holder for management fees. TEAM A dummy variable, 1 if team managed, 0 otherwise representing whether or not the fund was managed by a group (team) or a single manager. TEN Tenure. For funds managed by an individual, the number of months that individual has been in charge of the fund. 12b-1 The percentage charged by the fund for this fee. LOAD A dummy variable, 1 if no-load, 0 if load representing whether or not the fund charge a sales fee (load) to the investors in the fund. MAXLOAD, For Load funds, the percentage charged in each of these MINLOAD, categories. REDEMPT, DEFERRED AG A Dummy variable, 1 if an aggressive growth fund, 0 otherwise. BA A Dummy variable, 1 if a balanced fund, 0 otherwise. FO A Dummy variable, 1 if a foreign fund, 0 otherwise. GR A Dummy variable, 1 if a growth fund, 0 otherwise. IN A Dummy variable, 1 if an income fund, 0 otherwise.

Table 1 provides the descriptive statistics for the variables, [M.sup.2], TEN, LOAD, TURN, STOCK, CASH, EXP, MGMT, and 12b-1. Table 2 provides the descriptive statistics for M2 for each type of mutual fund.

RESULTS

Our first investigation is the hypothesis that there will be no differences in [M.sup.2] between the types of mutual funds. To test this, a two-tailed Z-test is used. Table 3 presents the finding for this set of results. With the exception of the exception of the growth fund/foreign fund pairing, all of the results were significant. Thus an investor can see that the risk adjusted return will differ depending on the type of fund one chooses to invest. Somewhat surprisingly, aggressive growth funds have the highest [M.sup.2], followed by the foreign and growth funds, and then by the growth and income, income, and balanced funds. It is somewhat surprising that the aggressive growth funds do have a better risk-adjusted performance than the growth funds, because this is the category where the most risk is taken. The performance of the market in the 1996-1999 period may have skewed these results a bit. However, none of the categories provided a risk-adjusted return that was higher than investing in a risk-free security.

To further examine these results we conducted a series of regression analysis. The first regression used all 474 funds and examined the [M.sup.2] in terms of the variables TEAM, LOAD, TURN, STOCK, CASH, EXP, MGMT, 12B-1, AG BA, FO, GR, and IN. Thus we choose all the variables that were pertinent to all of the funds. As Table 4 shows, this regression, significant at the five-percent level, has an adjusted R-squared of .55. However, the only variables to be significant are CASH, and the dummy variables for type of fund: AG, BA, FO, GR, and IN. Those variables with a negative relationship with [M.sup.2] are TEAM, LOAD, IN, and BA. These results could be expected. Funds that are managed by committee, or charge their shareholders a sales fee, should do worse than other funds. Also, the Balanced and income fund invest in many types securities with lower rates of return (and less risk.) However, there are some surprising results. Though the cash variable is insignificant, many investors would expect that putting more of the assets into money market securities would reduce the returns. These results suggest that the risk-reducing attributes of cash investments outweigh their drag on returns. Another surprise was the coefficient for EXP. Though this variable is insignificant, it is counter to the usual advise of selecting funds with lower fees. Perhaps the fees charged by some managers are justified by their ability to find optimal investments.

A second regression was done for the 366 funds managed by a single manager. It is often suggested that investors should look at the experience of the fund manager. If this is important, tenure, the length of time a manager has been in place with the fund, should be important. For this regression we used the same variables as the first, with the exception of using TEN in place of TEAM. Table 5 provides these results and shows that the equation is significant. Tenure, along with stock, cash, the variables for fund type are significant. The relationship for tenure is, however, a very slight negative relationship. This suggest that either it is the total experience possessed by a fund manager, not just the time at a particular fund, or perhaps some fund managers may have stayed too long. CASH and STOCK both have positive affects on M2. This suggests that it is the including other investments (such as bonds) decreases the risk-adjusted returns for a fund. Other variables that have a negative relationship with [M.sup.2] are LOAD, IN, and BA, though LOAD is insignificant.

Last, we looked at load funds and the how the various sales fees (load) will affect the risk-adjusted return. Thus, we added variables MAXLOAD, MINLOAD, REDEMPT, and DEFERRED to the analysis, while deleting TEN. As seen in Table 6 the regression equation is significant at the five percent level. However, none of the variables relating to the load fees are significant. The only significant variables in this equation are STOCK and CASH. And, as in the previous equation, both have a positive affect on [M.sup.2]. Though insignificant, MINLOAD and DEFERRED have slightly negative effects on [M.sup.2] and MAXLOAD and REDEMPT have slightly positive effects.

CONCLUSION

We examined the returns for 474 mutual funds classified as either aggressive growth, balanced, foreign, growth, growth and income, or income funds. Using [M.sup.2] as the measure of risk-adjusted return, we found that aggressive growth funds provide the highest risk-adjusted return. The other variables that affect the risk-adjusted mutual fund return are the percent invested in stock and cash equivalents. These results suggest that investors only need to examine the percent of the assets invested in stock and cash, as well as the type of fund to be sure that they're getting the best results for the amount of risk they're willing to take.

REFERENCES

Blake, C. R. & M. R. Morey. (2000). Morningstar Ratings and Mutual Fund Performance, Journal of Financial and Quantitative Analysis, 35 (Sept), 451-483.

DiBartolomeo, D. & E. Witkowski. (1997). Mutual Fund Misclassification: Evidence Based on Style Analysis, Financial Analysts Journal, 53 (September/October), 32-43.

Kim, M., R. Shukla & M. Tomas. (2000). Mutual Fund Objective Misclassification, Journal of Economics and Business, 52 (Jul/Aug), 309-323.

Malkiel, B. (1995). Returns From Investing in Equity Mutual Funds, Journal of Finance, 50, 549-572.

Modigliani, F. & L. Modigliani. (1997). Risk-Adjusted Performance, Journal of Portfolio Management,

Payne, T. H., L. Prather & B. William. (1999). Value Creation and the Determinants of Equity Fund Performance, Journal of Business Research, 45 (May), 69-74.

Rao, S. P. U. (2001). Economic Impact of Distribution Fees on Mutual Funds, American Business Review, 19 (Jan), 1-5.

Werner, R. (2000). Mutual Fund Performance, Journal of Finance, 55(August), 1655-1695.

Mark Brooks, Rochester Institute of Technology

Daniel L. Tompkins, Niagara University Table 1 Descriptive Statistics for Data Set [M.sup.2] Ten Load Mean 0.031 85.617 0.580 Standard Error 0.000 3.923 0.023 Median 0.032 62.000 1.000 Mode 0.033 43.000 1.000 Std. Deviation 0.006 75.047 0.494 Kurtosis 11.912 3.819 -1.902 Skewness -2.434 1.555 -0.326 Minimum -0.015 1.000 0.000 Maximum 0.041 495.000 1.000 Count 474 366 474 Largest(1) 0.041 495.000 1.000 Smallest(1) -0.015 1.000 0.000 Confidence (95%) 0.001 7.714 0.045 Turn Stock Cash Mean 0.747 0.873 0.045 Standard Error 0.042 0.009 0.003 Median 0.580 0.947 0.030 Mode 0.580 0.000 0.000 Std. Deviation 0.908 0.191 0.068 Kurtosis 139.161 9.065 77.546 Skewness 9.264 -2.815 6.655 Minimum 0.000 0.000 -0.098 Maximum 15.280 1.030 0.985 Count 474 474 474 Largest(1) 15.280 1.030 0.985 Smallest(1) 0.000 0.000 -0.098 Confidence (95%) 0.082 0.017 0.006 Exp Mgmt 12B-1 Mean 0.012 0.673 0.203 Standard Error 0.000 0.011 0.013 Median 0.011 0.680 0.170 Mode 0.010 0.750 0.000 Std. Deviation 0.006 0.230 0.275 Kurtosis 65.917 3.324 2.418 Skewness 5.446 0.619 1.725 Minimum 0.000 0.000 0.000 Maximum 0.089 1.960 1.000 Count 474 474 474 Largest(1) 0.089 1.960 1.000 Smallest(1) 0.000 0.000 0.000 Confidence (95%) 0.001 0.021 0.025 Table 2: [M.sup.2] AG BA FO Mean 0.035996 0.022511 0.032702 Standard Error 0.000362 0.000587 0.000242 Median 0.036187 0.022163 0.032554 Standard Deviation 0.002429 0.004149 0.001512 Kurtosis -0.449057 0.599028 3.536058 Skewness -0.408445 0.265406 1.321643 Range 0.009988 0.021287 0.007420 Minimum 0.031224 0.012103 0.030126 Maximum 0.041212 0.033390 0.037546 Count 45 50 39 Largest(1) 0.041212 0.033390 0.037546 Smallest(1) 0.031224 0.012103 0.030126 Confidence (95%) 0.000730 0.001179 0.000490 GI GR IN Mean 0.029751 0.032513 0.025683 Standard Error 0.000446 0.000262 0.001222 Median 0.030488 0.032818 0.027869 Standard Deviation 0.004109 0.003819 0.007917 Kurtosis 21.190113 15.655587 18.164681 Skewness -4.007569 -3.024015 -4.021193 Range 0.030967 0.031267 0.046053 Minimum 0.004145 0.006985 -0.014858 Maximum 0.035112 0.038253 0.031194 Count 85 212 42 Largest(1) 0.035112 0.038253 0.031194 Smallest(1) 0.004145 0.006985 -0.014858 Confidence (95%) 0.000886 0.000517 0.002467 Table 3 Results of Z-tests for d AG/BA z 19.0683 * P(Z<=z) two-tail 0 z Critical two-tail 1.9600 AG/FO BA/FO z 7.2489 * -15.7788 * P(Z<=z) two-tail 4.23E-13 0 z Critical two-tail 1.9600 1.9600 AG/GI BA/GI FO/GI z 10.8459 * -9.8277 * 5.6652 * P(Z<=z) two-tail 0 0 1.47E-08 z Critical two-tail 1.9600 1.9600 1.9600 AG/GR BA/GR FO/GR z 7.7657 * -15.5671 * 0.5185 P(Z<=z) two-tail 8.22E-15 0 0.6041 z Critical two-tail 1.9600 1.9600 1.9600 AG/IN BA/IN FO/IN z 8.1109 * -2.3407 * 5.6135 * P(Z<=z) two-tail 4.44E-16 0.0192 1.99E-08 z Critical two-tail 1.9600 1.9600 1.9600 z P(Z<=z) two-tail z Critical two-tail z P(Z<=z) two-tail z Critical two-tail z P(Z<=z) two-tail z Critical two-tail GI/GR z -5.3382 * P(Z<=z) two-tail 9.41E-08 z Critical two-tail 1.9600 GI/IN GR/IN z 3.1279 * 5.4656 * P(Z<=z) two-tail 0.0018 4.63E-08 z Critical two-tail 1.9600 1.9600 * Significant at 5% level. Table 4 Regression involving all 474 funds Regression Statistics Multiple R 0.75283 R Square 0.56675 Adjusted R 0.55450 Square Standard Error 0.00374 Observations 474 ANOVA df SS MS Regression 13 0.00842 0.00065 Residual 46 473 0.01486 Coefficients Std Error t Stat Intercept 0.01804 0.00135 13.34443 * TEAM -0.00088 0.00379 -0.23292 LOAD -0.00045 0.00044 -1.02399 TURN 0.00011 0.00024 0.45107 STOCK 0.01209 0.00115 10.52786 * CASH 0.00388 0.00278 1.39595 EXP 0.04588 0.04525 1.0139 MGMT 0.00043 0.00090 0.47759 12b-1 0.00038 0.00081 0.46308 AG 0.0056 0.00077 7.29767 * GR 0.00258 0.00057 4.52999 * IN -0.00311 0.00078 -4.00997* BA -0.00363 0.00082 -4.44880* FO 0.0021 0.0008 2.6705 * Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA F Significance F Regression 46.28751 * 4.63E-75 Residual P-value Lower 95% Upper 95% Intercept 1.44E-34 0.01539 0.02070 TEAM 0.81593 -0.00834 0.00657 LOAD 0.30638 -0.00130 0.00041 TURN 0.65215 -0.00036 0.00058 STOCK 2.29E-23 0.00984 0.01435 CASH 0.1634 -0.00158 0.00934 EXP 0.31116 -0.04304 0.13481 MGMT 0.63317 -0.00134 0.00220 12b-1 0.64353 -0.00122 0.00197 AG 1.29E-12 0.00409 0.00711 GR 7.53E-06 0.00146 0.00370 IN 7.08E-05 -0.00463 -0.00159 BA 1.08E-05 -0.00523 -0.00202 FO 0.00784 0.00057 0.00372 * Significant at 5% level. Table 5 Single Manager Funds Regression Statistics Multiple R 0.75599 R Square 0.57152 Adjusted R Square 0.55570 Standard 0.00370 Error Observations 366 ANOVA df SS MS Regression 13 0.00641 0.00049 Residual 352 0.00481 1.3658E-05 Total 365 0.01122 Coefficient Standard Error t Stat s Intercept 0.01385 0.00182 7.61595 * TEN -9.00E-06 2.67E-06 -3.3801 * 2 LOAD -0.0003 0.0005 -0.71191 TURN 0.0002 0.0003 0.76502 STOCK 0.0170 0.0016 10.77648 * CASH 0.0101 0.0031 3.24224 * EXP 0.0269 0.0496 0.54223 MGMT 0.0007 0.0010 0.67016 12B-1 0.0008 0.0009 0.91021 AG 0.0054 0.0008 6.77103 * GR 0.0024 0.0006 3.79809 * INC -0.0025 0.0009 -2.82922 * BAL -0.0024 0.0010 -2.36857 * FOR 0.0019 0.0009 2.21188 * Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA F Significance F Regression 36.11602 * 6.7357E-57 Residual Total P-value Lower 95% Upper 95% Intercept 2.43E-13 0.01028 0.01743 TEN 0.00081 -1.43E-05 -3.78E-06 LOAD 0.47699 -0.00131 0.00061 TURN 0.44477 -0.00030 0.00069 STOCK 0.00000 0.01388 0.02008 CASH 0.00130 0.00397 0.01620 EXP 0.58800 -0.07061 0.12437 MGMT 0.50320 -0.00131 0.00266 12B-1 0.36334 -0.00092 0.00250 AG 0.00000 0.00384 0.00699 GR 0.00017 0.00115 0.00361 INC 0.00493 -0.00432 -0.00078 BAL 0.01840 -0.00440 -0.00041 FOR 0.02762 0.00022 0.00367 * Significant at 5% level. Table 6 Load Fund Results Regression Statistics Multiple R 0.81367 R Square 0.66206 Adjusted 0.63635 R Square Standard Error 0.00358 Observations 199 ANOVA df SS MS Regression 14 0.00462 0.00033 Residual 184 0.00236 1.28E-05 Total 198 0.00698 Coefficients Standard t Stat Error Intercept 0.01899 0.00405 4.68341 * STOCK 0.01076 0.00172 6.26243 * CASH 0.00857 0.00356 2.40830 * EXP 0.14693 0.07854 1.87076 MGMT 0.00044 0.00174 0.25273 12B-1 0.00173 0.00143 1.21567 AG 0.00276 0.00389 0.7091 GR 0.00024 0.00384 0.06145 INC -0.00678 0.00388 -1.74821 BAL -0.00689 0.00393 -1.75451 FOR -0.00106 0.00397 -0.26781 MAXLOAD 0.00027 0.00024 1.11358 MINLOAD -0.00069 0.00089 -0.77531 REDEMPT 0.00122 0.00120 1.01323 DEFFERED -0.00001 0.00032 -0.02753 Regression Statistics Multiple R 0.81367 R Square 0.66206 Adjusted 0.63635 R Square Standard Error 0.00358 Observations 199 ANOVA df SS MS Regression 14 0.00462 0.00033 Residual 184 0.00236 1.28E-05 Total 198 0.00698 Coefficients Standard t Stat Error Intercept 0.01899 0.00405 4.68341 * STOCK 0.01076 0.00172 6.26243 * CASH 0.00857 0.00356 2.40830 * EXP 0.14693 0.07854 1.87076 MGMT 0.00044 0.00174 0.25273 12B-1 0.00173 0.00143 1.21567 AG 0.00276 0.00389 0.7091 GR 0.00024 0.00384 0.06145 INC -0.00678 0.00388 -1.74821 BAL -0.00689 0.00393 -1.75451 FOR -0.00106 0.00397 -0.26781 MAXLOAD 0.00027 0.00024 1.11358 MINLOAD -0.00069 0.00089 -0.77531 REDEMPT 0.00122 0.00120 1.01323 DEFFERED -0.00001 0.00032 -0.02753 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA F Significance F Regression 25.74855 * 4.12E-36 Residual Total P-value Lower Upper 95% 95% Intercept 5.47E-06 0.01099 0.02699 STOCK 2.61E-09 0.00737 0.01415 CASH 0.01701 0.00155 0.01559 EXP 0.06297 -0.00803 0.30188 MGMT 0.80076 -0.00299 0.00387 12B-1 0.22567 -0.00108 0.00454 AG 0.47916 -0.00492 0.01043 GR 0.95107 -0.00734 0.00781 INC 0.0821 -0.01443 0.00087 BAL 0.08101 -0.01464 0.00086 FOR 0.78915 -0.00890 0.00677 MAXLOAD 0.26691 -0.01463 0.00074 MINLOAD 0.43915 -0.00245 0.00107 REDEMPT 0.31228 -0.00116 0.00360 DEFFERED 0.97807 -0.00064 0.00062 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA F Significance F Regression 25.74855 * 4.12E-36 Residual Total P-value Lower Upper 95% 95% Intercept 5.47E-06 0.01099 0.02699 STOCK 2.61E-09 0.00737 0.01415 CASH 0.01701 0.00155 0.01559 EXP 0.06297 -0.00803 0.30188 MGMT 0.80076 -0.00299 0.00387 12B-1 0.22567 -0.00108 0.00454 AG 0.47916 -0.00492 0.01043 GR 0.95107 -0.00734 0.00781 INC 0.08210 -0.01443 0.00087 BAL 0.08101 -0.01464 0.00086 FOR 0.78915 -0.00890 0.00677 MAXLOAD 0.26691 -0.01463 0.00074 MINLOAD 0.43915 -0.00245 0.00107 REDEMPT 0.31228 -0.00116 0.00360 DEFFERED 0.97807 -0.00064 0.00062 * Significant at 5% level.