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Testing the predictability of mutual fund returns.


One of the most important concerns people have, secondary only to their family's health, is their financial security. The importance of this issue is easily recognized because of its impact on almost everyone in our society. The challenge to accumulate adequate assets to sufficiently maintain one's lifestyle while retired is affected by many variables. Apprehension about the long-term viability of social security, increasing life expectancies, escalating health care costs skewed toward the elderly and a desire to retire younger make this challenge tougher to accomplish. Unrealistic expectations based on extraordinary equity returns of 199596 also work to diminish the importance of proper decision making in planning one's financial future.

Three factors are directly attributable to attaining the goal of achieving financial security by the time one chooses or is forced to stop working. These factors are the amount of money a person saves while working, the length of time between when a person invests and begins to withdraw funds and the return a person earns while his money is invested. The first two constraints are bound by a person's attitude toward building a secure future, his income and his lifestyle. The third factor is substantially independent of these bounds and is of specific interest to this study.

For many investors, investing in mutual funds is a popular way to build assets for their retirement. They provide professional asset management, the ability to diversify with a small amount of capital, cost effective repositioning of assets as objectives change and relative ease of comparison.

Financial publications provide ample space for recommended funds on a regular basis. Information-system providers also track a multitude of fund characteristics and offer advice for a fee based on their analysis. This study is designed to evaluate frequently used fund characteristics through path analysis to determine if such characteristics have significant causal effects that can be successfully used as selection criteria.

Findings of Previous Studies

Published mutual fund selection studies span three decades. Jensen concluded that predictability of both average fund performance and individual fund performance for a sample of fund statistics encompassing 1945-64 was no better than random chance [8]. Bogle concluded that picking a winning fund is virtually impossible because reliance on past performance is of no apparent help [1]. Other studies had similar conclusions. Results of these analyses confirmed theories that annual mutual fund returns are influenced by a multitude of variables, many of which cannot be identified. Not only will these anonymous variables' beta coefficients change over time, but the variables themselves are not static.

Other studies provide differing conclusions of varying degrees. Goetzmann and Brown concluded that predictability of returns is much stronger in identifying poor performing funds. While this approach may help decrease the number of potential candidates in a selection process, it is less likely to successfully identify consistent winners.

Contrary findings were also identified. These studies found significant positive correlations between historical returns and current returns. Hendricks, Patel and Zeckhauser found that while past performance is not an assurance of future results, a statistically significant relationship exists [7]. Goetzmann and Ibbotson found that past returns are useful in predicting investment returns, risk adjusted alpha measures and relative rankings of peer group funds [4]. They sighted weaknesses in earlier studies resulting from a lack of attention to cross-sectional dependence of fund returns as a possible reason for their different conclusions.

Theorized Causal Relationship

As illustrated in Exhibit 1, the theory proposes that direct causal relationships exist between a fund's current relative performance and historical performance rankings as represented by the relative performance of a fund for the period being evaluated (CURRENT PER) and the relative performance of a fund for three years (RANK03) and five years (RANK05) prior to the year being evaluated. Frequently used predictors of performance are also believed to have direct causal effects with a fund's current relative performance. Since two of the endogenous variables are themselves relative rankings of different periods, they should also have significant causal relationships with all of the exogenous variables.

The rationale for choosing the four widely used exogenous variables is based on professional experience in the financial markets as a registered investment advisor and general investment theory from a variety of financial publications and classroom lectures on financial market theory. Many other latent or unidentifiable exogenous variables exist.

Relative rankings are used instead of actual returns to partial out outside influences affecting equity returns. A sample of annualized returns often has a high standard deviation and many outliers. The magnitude of outliers across differing periods would result in a substantial reduction in sample size if the data were not transformed into rankings. The objective of effective mutual fund selection is to identify those advisors who can outperform their peer group, not to predict absolute equity returns or to make judgments as to whether equities are an appropriate asset class in which to invest. A significant causal relationship between RANK03 and RANK05 is expected because RANK03 is a subset of RANK05. This relationship also suggests the probability of collinearity. If collinearity is significant, additional statistical analysis will be required.

Identifying significant indirect effects from exogenous variables that have a causal relationship with the endogenous variables previously described may improve the interpretative ability of the model. Commonly held assumptions that exist for RISK suggest that this variable will have a direct effect on all endogenous variables. RISK measures the consistency of performance directly and of ALPHA indirectly. Funds with greater consistency of performance take advantage of compounding more effectively than funds whose average non-annualized returns are similar, but lack consistency due to greater volatility.

Theory also suggests that a fund's size will have a positive causal effect on its relative ranking among its peer group. Large funds should gain economies of scale over small funds. Once a fund's critical mass is large enough to be effectively managed, the incremental resources required to manage an increased asset base should decline. These economies of scale should be reflected in a fund's relative returns, referred to as RANK03, RANK05 and CURRENT PER, regardless of market conditions. A fund's asset base should not have a causal relationship with ALPHA.

For parallel reasons, the amount of operating expenses (FEES) deducted from a portfolio should have similar effects on relative rankings. This relationship should not hold true for ALPHA, because it is only designed to measure the incremental returns earned through proper equity selection. Fund managers do not have to increase fees to increase profitability. Consistent performance in the upper percentiles of their peer group will be noticed by investors who will transfer assets from weaker performing funds, thereby increasing revenues for superior fund managers. Since these additional assets are less costly to manage, profits will rise.

Finally, a fund's degree of diversification (DEG OF DIVER) should influence its volatility. Diversification is defined as owning a mix of stocks that are not highly correlated with each other. The market will not reward investors for unsystematic risk which can be reduced through diversification. Better diversification will lead to reduced risk and improved performance. Therefore, diversification should have a causal relationship with RANK03, RANK05 and CURRENT PER but not with ALPHA.

Data Selection

The data set was compiled from FundWatch. Additional or missing information was collected from fund prospectuses and financial publications. Known differences in data collection procedures exist from one source to another. All information pertaining to the endogenous variables was available from FundWatch.

The initial data set included 222 mutual funds that were described by FundWatch as growth oriented and included funds in existence for sufficient time to have a historical five-year track record. From the data, outliers were identified in several of the variables. Cases outside a range three times the interquartile range were considered outliers. These observations tend to bias the results and reduce the overall reliability of the data. Three of the exogenous variables contained outliers.

The variable accounting for the greatest number of outliers was SIZE. Average fund size of all observations was $781 million. The standard deviation of these observations was $2.6 billion. The variable was heavily skewed and outlying cases were deleted to make this variable more normally distributed. The largest fund, Fidelity Magellan, had more assets than the combined assets of 169 smaller funds in the sample. Removing this single case lowered the average fund size by $163 million and its standard deviation by $1 billion. Other notable examples were the Janus Fund, Growth Fund of America, IDS New Dimension and Twentieth Century Ultra. In total, 41 cases were removed from the sample. The resulting distribution of assets is still somewhat skewed, but a further reduction of the sample size would not beneficially impact the study (Appendix [ILLUSTRATION FOR EXHIBIT 1.A OMITTED]).

Sixteen cases were removed because of outlying FEES. Funds with fees below 0.4 percent were usually index funds. Since index funds require no active management and therefore do not incur research costs, they charge lower management fees. The funds with the lowest fees included Elfun Trust, Vanguard Index, Vanguard Special Portfolio, Vanguard Extended Index and Fidelity US Equity Index. Funds with fees above 1.6 percent were also considered outliers. Funds with the highest fees included American Growth, Excel Value Fund, Centurion Growth, First Eagle of America and Beacon Hill. Upon deletion of the outliers, FEES was more normally distributed (Appendix [ILLUSTRATION FOR EXHIBIT 1.B OMITTED]).

Seventeen cases were deleted for DEG OF DIVER. Index and traditional growth funds comprised the majority of funds at the high extreme, including Stagecoach Corporation, Portico Equity, Fidelity U.S. Equity Index, Principal Preservation and Vanguard Quantitative. Funds that focus on small cap stocks and specialty funds dominated the bottom extreme. Because sector funds invest in stocks of a single or limited industry group, their portfolios are also likely to be less diversified. The five least diversified funds included American Capital Enterprise, Dreyfus Strategic, Pioneer Capital, Copley and Shadow Stock. Upon deletion of outliers, DEG OF DIVER was more normally distributed (Appendix [ILLUSTRATION FOR EXHIBIT 1.C OMITTED]).

The variables ALPHA, RANK03, RANK05 and RISK were relatively normally distributed, and sample size reduction was not necessary. After purging the data of outlying observations, the final sample size is 148 and remained sufficiently large to test the hypothesis.

As previously stated, a possible problem with collinearity between RANK03 and RANK05 was suspected. This problem is intuitive since RANK03 is a subset of RANK05. The calculated correlation coefficient is only 0.6. Under the circumstances, this degree of collinearity is acceptable. All other correlations are below 0.4 and are acceptable.

Empirical Findings

The first regression of the data isolated four variables having causal relationships with CURRENT PER (Appendix [ILLUSTRATION FOR EXHIBIT 2.A AND 2.B OMITTED]). RANK05, however, was not significant. This outcome is surprising since RANK03 was significant and is a subset of RANK05. Longer periods generally produce more predictable results by smoothing the effects of unusual occurrences. Despite this influence, RANK03 had a significant causal relationship while RANK05 did not. This finding lends evidence that predictive powers of historical returns are low. Running the regression analysis with these four significant variables provided path coefficients and the [R.sup.2]-value to calculate the specification error for CURRENT PER in the actual model shown in Exhibit 2.

The ALPHA node was then regressed on the remaining independent variables to identify significant causal relationships (Appendix [ILLUSTRATION FOR EXHIBIT 2.C AND 2.D OMITTED]). In the hypothesized model, the theory postulated a significant relationship between RISK and ALPHA. The regression validated that theory and also identified significant causal relationships between ASSETS and DEG OF DIVER with ALPHA. These results were not expected nor are they easy to explain. Since ALPHA is a reflection of a fund's return relative to the overall beta of a portfolio, it should not have any dependence upon the amount of assets in the fund or the standard deviation of its returns. The regression also confirmed the theory that FEES should not have a statistically significant relationship with ALPHA. Running the regression analysis with the three significant variables provided path coefficients and the [R.sup.2]-value to calculate the specification error for ALPHA in the path analysis model shown in Exhibit 2.

The next node evaluated was RANK03 (Appendix [ILLUSTRATION FOR EXHIBIT 2.E AND 2.F OMITTED]). As indicated by the hypothesized model, all exogenous variables should have a significant causal relationship with RANK03. RISK and ASSETS had significant causal relationships as theorized. FEES and DEG OF DIVER were shown to be insignificant. One possible interpretation for FEES is that the amount of management fees a fund manager charges is not a reflection of his ability to outperform his peers. Such a theory may provide an interesting topic for future research.

DEG OF DIVER is less easily explained. One of the basic rules of investment theory explains the importance of diversifying to improve investment returns and reduce risk. Following this theory, DEG OF DIVER should have a significant effect on RANK03 and RANK05, and by definition, it should not have a significant causal effect on ALPHA. These conflicting results add further skepticism about relying on these variables for fund selection. Running the regression analysis with the two significant variables provided path coefficients and the [R.sup.2]-value to calculate the specification error for RANK03 in the actual model shown in Exhibit 2.

The last variable evaluated was RANK05 (Appendix [ILLUSTRATION FOR EXHIBIT 2.G OMITTED]). Exogenous variables impacting RANK05 should behave similarly to those impacting RANK03. Since RANK05 includes all of RANK03 and two additional years, the significance should be slightly higher based on reduced impact of unlikely occurrences. The regression showed no relation to any other variable providing evidence that favors the publications concluding that past performance has no interpretive ability on future results. These findings are further supported with the relatively low correlation between RANK03 and RANK05. Of greater surprise was the lack of a causal relationship between RANK03 and RANK05. To account for this lack of significance, a high degree of randomness in the returns must exist. This randomness must be considerable, such that differences in two of the five years can cause a randomized impact on variables that would otherwise be perfectly correlated.

Final results of this analysis shown in Exhibit 2 illustrate the results of the path analysis conducted to test the hypotheses. The nodes for RANK05 and FEES were included to show the hypothesized model. Notice there are no paths leading to or away from RANK05 and FEES. Also, note the high specification error for ALPHA and RANK03. Attempts to partial out the almost limitless number of variables affecting annualized returns by using a ranking of performance were also not particularly beneficial.


The results of this analysis indicate that using historical performance and widely accepted indicators of performance as predictors of success in mutual fund selection are marginally successful at best. Significant specification errors, lack of consistency among regression coefficients and path signs that contradict widely accepted financial theories regarding diversification, risk, and cost show that investment selection success is impacted by random chance or unobserved variables far more than predictable patterns. The ability to generalize this model remains a topic of future research. Similar analysis should be conducted using data sets from other periods.

The evaluation here contains useful information that can assist investors in making wise selection choices. If historical results provide little insight to future success and the amount of assets a fund manager oversees is not an important factor, the investment selection process becomes quite clear. Identify those funds that charge very low management fees and select a diversified group of these funds. In some years, they will be top performers; in others, they will under perform their peer group, but in all years their costs will be lower. These cost savings will be compounded over lime and returns will be maximized.


1. Bogle, J.C. "Selecting Equity Mutual Funds." The Journal of Portfolio Management, Vol. 3, No. 1, 1992, pp. 94-100.

2. Bowlin, O.D. and W.P. Dukes. "The Dual Nature of Beta Responsiveness." Journal of Portfolio Management, Vol. 9, No. 2, 1983, pp. 51-56.

3. Coggin, T.D. and J.E. Hunter. "Problems in Measuring the Quality of Investment Information: The Perils of the Information Coefficient." FinanciaI Analysts Journal, Vol. 39, No. 3, 1983, pp. 25-33.

4. Goetzmann, W.N. and R.G. Ibbotson. "Do Winners Repeat?" Journal of Portfolio Management, Vol. 20, No. 2, 1994, pp. 9-18.

5. Grinblatt, M. and S. Titman. "The Persistence of Mutual Fund Performance, 1977-1984." Journal of Finance, 1992.

6. Grinold, R.C. "Is Beta Dead Again?" Financial Analysts Journal, Vol. 49, No. 4, 1993, pp. 28-34.

7. Hendricks, D., J. Patel and R. Zeckhauser. "Hot Hands in Mutual Funds: Short Run Persistence of Performance in Relative Performance, 1974-1988." Journal of Finance, 1993, pp. 93-100.

8. Jensen, M. "The Performance of Mutual Funds in the Period 1945-1964." Journal of Finance, 1968, pp. 389-416.

9. Lynch, P. "Beating the Street." Money, Vol. 22, No. 3, 1993, pp. 120-135.

10. Passerine, M.H. and A. Timmermann. "Forecasting Stock Returns: An Examination of Stock Market Trading in the Presence of Transaction Costs."Journal of Forecasting, Vol. 13, No. 4, 1994, pp. 335-367.

11. Rich, S.P. and W.R. Reichenstein. "Is the Stock Market Predictable?" Baylor Business Review, Vol. 12, No. 1, 1994, p. 11.

12. Thornburg, L. "Performance Measures that Work." HR Magazine, Vol. 36, No. 5, 1991, pp. 35-38.

13. Toolson, R.B. "Strategies for Buying and Selling Mutual Funds." Journal of Accountancy, Vol. 174, No. 4, 1992, pp. 37-42.
Appendix Exhibit 2. Regression Estimates

a. Dependent Variable: CURRENT PER
[R.sup.2] = 0.51 F = 19.46 Sign. = 0.00

Variable t Sign.

ALPHA 10.28 0.00
SIZE -1.74 0.08
DEG OF DIVER -2.35 0.02
FEES 0.30 0.76
RANK03 -3.41 0.00
RANK05 -0.46 0.65
RISK -5.75 0.00
(Constant) 6.30 0.00

b. Dependent Variable CURRENT PER
[R.sup.2] = 0.51 F = 19.46 Sign. = 0.00

Variable t Sign.
ALPHA 11.06 0.00
DEG OF DIVER -2.47 0.01
RANK03 -4.11 0.00
RISK -6.07 0.00
(Constant) 6.95 0.00

c. Dependent Variable: ALPHA
[R.sup.2] = 0.27 F = 8.11 Sign. = 0.00

Variable t Sign.

SIZE -2.52 0.01
DEG OF DIVER 3.57 3.57
FEES -1.36 0.17
RANK03 -0.13 0.90
RANK05 -0.14 0.89
RISK 5.34 0.00
(Constant) -2.61 0.01

d. Dependent Variable: ALPHA
[R.sup.2] = 0.25 F = 15.63 Sign. = 0.00

Variable t Sign.

SIZE -2.16 0.03
DEG OF DIVER 4.28 0.00
RISK 5.580 0.00
(Constant) -3.84 0.00

e. Dependent Variable: RANK03
[R.sub.2] = 0.17 F = 7.14 Sign. = 0.00

Variable t Sign.

SIZE -2.58 0.01
DEG OF DIVER 1.74 0.08
FEES -0.17 0.86
RISK -3.20 0.00
(Constant) 3.23 0.00

f. Dependent Variable: RANK03
[R.sup.2] = 0.15 F = 12.34 Sign. = 0.00

Variable t Sign.

SIZE -2.97 0.00
RISK -3.65 0.00
(Constant) 6.85 0.00

g. Dependent Variable: RANK05
[R.sup.2] = 0.07 F = 4.24 Sign. = 0.04

Variable t Sign.

SIZE -2.25 0.07
DEG OF DIVER -1.52 0.13
FEES 0.30 0.77
RISK -4.20 0.08
(Constant) 3.83 0.00
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Author:Walker, Gary A.
Publication:Review of Business
Date:Jun 22, 1997
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