CFA Institute
Does Historical Performance Predict Future Performance?Author(s): Ronald N. Kahn and Andrew RuddReviewed work(s):Source: Financial Analysts Journal, Vol. 51, No. 6 (Nov. - Dec., 1995), pp. 43-52Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479882 .Accessed: 21/07/2012 00:22
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Does Historical Performance Predict Future
Performance?
Ronald N. Kahn and Andrew Rudd
An investigation of the persistence of mutualfund performance indicates that investors need more than past performance numbers to pickfuture winners. In this study, style analysis was used to separatefund total returns into style and selection components. Performance was defined in terms of total returns, selection returns, and information ratios (ratios of selection return to selection risk). For eachfund type, two out-of-sample periods were established to investigate persistence of performancefrom one period to the next using regression analysis and contingency tables. The evidence supported persistence onlyforfixed-incomefund performance. This persistence is beyond any effects offundfees and expenses or data base survivorship bias. Unfortunately, this persistence edge cannot overcome the average underperformance offixed-incomefunds resultingfrom fees and expenses.
Who will be next year's winners? Conventional wisdom in the investment industry is that the
first place to look in trying to predict the future performance of mutual funds is past performance. But does it help to know last year's winners? Do winners repeat?
The idea that winners repeat is so obvious and popular, it has spawned an entire mini-industry de- voted to documenting past winners. Mutual fund performance reviews regularly appear in publica- tions from Barrons to Business Week to Consumer Re- ports. Services such as Momingstar and Lipper exist to publish mutual fund rankings. Pension plan con- sultants closely examine past performance before recommending managers, and successful managers proudly document their past performance. All this activity demonstrates that everyone choosing active managers, from pension plan sponsors to individual investors, is acting as if past performance predicts future performance. But does it?
In this article, we review the history of investiga- tion into this question and then present new results based on the performance of active equity and fixed- income managers of publicly available U.S. mutual funds during the past decade.1 We also discuss the investment implications of our results.
This study differs from previous studies in its use
of "style analysis" to monitor performance, min ac- counting for the effect of fund expenses and fees,3 in the use of multiple mutual fund data bases, and in the particular historical period investigated.
PREVIOUS RESEARCH Interest in mutual fund performance has a long his- tory, and many studies have investigated whether mutual funds, on average, outperform the market and whether the performance of the best managers is statistically significant. Those studies, however, do not address the question of persistence of perform- ance. Studies of performance persistence fall into two camps: those that do not find persistence and those that do.
Several studies have shown, based on different asset classes and different time periods, that per- formance does not persist. Jensen looked at the per- formance of 115 mutual funds over the 1945-64 pe- riod and found no evidence for persistence.4 Kritzman reached the same conclusion examining the 32 fixed-income managers retained by AT&T for at least ten years.5 Dunn and Theisen found no evi- dence of persistence in 201 institutional portfolios from 1973 to 1982.6 Elton, Gruber, and Rentzler showed that performance did not persist for 51 puLb- licly offered commodity funds from 1980 to 1988.7
Other studies have found that performance does persist. Grinblatt and Titman found evidence of per- sistence in 157 mutual funds during the 1975-84 period.8 Lehman and Modest reported similar results
Ronald N. Kahn is director of research at BARRA. Andrew Rudd is CEO of BARRA. This paper received the IMCA 1995 Journalism Award.
Financial Analysts Journal / November-December 1995 43
looking at 130 mutual funds from 1968 to 1982.9 In the United Kingdom, Brown and Draper demonstrated evidence for persistence usimg data on 550 pension managers from 1981 to 1990.l Hendricks, Patel, and Zeckhauser documented persistence of perform- ance in 165 equity mutual funds from 1974 to 1988.11 Recently, Goetzmann and Ibbotson showed evi- dence for persistence using 728 mutual funds over the 1976-88 period.12
PERFORMANCE MEASURES Mutual fund performance can be measured in sev- eral possible ways, including total or excess returns, risk-adjusted returns (alphas or selection returns), and information ratios (ratios of return to risk). Al- phas can be extracted from excess returns through the following regression:
rn (t) = Cn + 1 x rB (t) + En(t), (1)
where rn(t) is the monthly excess return to the fund in month t, rB(t) is the monthly excess return to the benchmark, and cn is the fund's estimated alpha. The information ratio is the annualized ratio of residual return to residual risk. In Equation 1, it is the ratio of alpha to the standard deviation of en(t), annualized.
The past studies of performance persistence have mainly defined performance using total returns or alphas. Lehman and Modest showed that the choice of benchmark can critically influence the re- sulting estimated alpha.13 Although the benchmark has a severe impact on individual fund alphas, it has somewhat less influence on fund performance rank- ings. In the context of arbitrage pricing theory mod- els, Lehman and Modest emphasized the importance of knowing the appropriate risk and return bench- mark.
STYLE ANALYSIS We looked at performance using both selection returns and information ratios. Selection (or style- adjusted) returns credit manager performance relative to a "style" benchmark. Generalizing on Equation 1, we estimated selection returns using only the portfolio's returns plus the returns to a set of style indexes; formally,
r(t) = X,wj Xfj(t) + Ni(t), (2)
where wj is the portfolio's weight in style j. These weights define the style benchmark, and (t) is the return in excess of that benchmark. We estimated these weights and the selection returns, W(t), using a quadratic program to minimize Var[w(t)] subject to the constraints that the weights are positive and sum
to 1. For equity funds, the style indexes include the
S&P 500 /BARRA value and growth indexes, the S&P midcap 400/BARRA value and growth indexes, and
14" the S&P small-cap 600 index, plus a Treasury bill index.
For fixed-income funds, the style indexes in- clude the Lehman Brothers intermediate govern- ment bond, long government bond, corporate bond, and mortgage indexes, the Salomon Brothers world government bond index, and a BARRA index of synthetic 30-year Treasury zero-coupon bonds, plus a Treasury bill index.
In contrast to alphas estimated via the uncon- strained regression (Equation 1), which are uncorre- lated (by mathematical construction) with the bench- mark, selection returns estimated with constraints on style weights can contain remaining market expo- sures. The beta of the equity style benchmark is bound by the betas of the lowest and highest index betas. Likewise, the duration of the fixed-income style benchmark is bounded by the durations of the lowest and highest duration indexes. This constraint can cause particular problems for fixed-income funds, which can exhibit durations far in excess of index durations. Hence, we included a 30-year zero- coupon index with a duration of 30 to mitigate this effect. With this index included, we found no corre- lation between selection returns and duration.
The style weights define the style benchmark as a weighted average of the style indexes. For perform- ance analysis, we estimated this style benchmark at time t, using returns in a 36- to 60-month trailing window (based on data availability), with a 1-month lag. Thus, the style benchmark at time t is based on returns from [(t - 2) to (t - 1), (t - 3) to (t - 2),...,(t - 61) to (t - 60)]. The selection return over the period from t to (t + 1) is then the portfolio return over that period minus the style benchmark return. This method for estimating the style benchmark ensures an out-of- sample selection return, and the one-month lag, in principle, allows the manager to know the relevant benchmark before time t.
We believe selection returns as estimated above to be the best estimate currently available (using only returns data) of a "level playing field" on which to compare manager performance. This formulation is an embellishment of Jensen's original idea of control- ling for market exposure before analyzing perform-
"15 ance. Style analysis controls for several investment styles. Looking forward, the investor chooses an ap- propriate style benchmark for investment and then selects managers to exceed that benchmark.
In the context of style analysis, the information ratio is the ratio of selection return mean to standard deviation, annualized. If investors wish to maximize the risk-adjusted selection returns defined in the standard mean-variance framework, oc Xw ), then they will always prefer the highest information ratio
44 Financial Analysts Joural / November-December 1995
managers.16 Looking forward, after choosing the style benchmark, investors will wish to select the managers with the highest information ratios.
SURVIVORSHIP BIAS One important issue for all of these studies is survi- vorship bias. The underlying data on fund perform- ance are not free of survivorship bias, and recently, Brown, Goetzmann, Tbbotson, and Ross showed that survivorship bias can significantly influence the evi- dence on persistence of performance.17 This impor- tant insight was not recognized in previous work on survivorship bias, which showed only that it was not a significant influence on studies of average mutual fund performance. This new insight has called into question much of the previous work on fund persist- ence of performance.
THE DATA We investigated U.S. active equity and fixed-income mutual funds included in both the Micropal and Morningstar data bases.18 In particular, we used all active domestic equity funds included in both data bases with data starting in January 1983 but excluded equity index funds. The 300 equity funds in our study included three convertible bond funds. For the fixed- income sample, we included all active taxable do- mestic bond funds that were in both data bases and had data starting in October 1988. We excluded junk bond funds, money market funds, international bond funds, index funds, and preferred stock funds.
To examine fund persistence, the data were sepa- rated into equity funds and fixed-income funds and analyzed separately. Separating the funds is clearly important when using standard alpha analysis (Equation 1), because their analyses should include very different benchmarks for the two fund types. Even after using style analysis to separate out selec- tion returns, however, equity and fixed-income funds should be analyzed separately because of their differing risk and return levels. Brown, et al. have shown that the survivorship bias effect on persist- ence of performance studies is accentuated by ana- lyzing a group of funds with divergent risk levels.19 Another reason for separating the two types of funds is that expenses are more important for fixed-income funds.
Because we calculated performance "out-of- sample" using monthly returns, we required an in- sample period of at least 36 months of data to define the style benchmarks. We then divided the remain- ing data into two out-of-sample periods for the per- sistence-of-performance study. Table 1 lists the peri- ods for the studies.
For each asset category, we tried to define the longest possible analysis period, consistent with the
Table 1. Study Periods Asset Category In-Sample Period 1 Period 2
Equity 1/83-12/87 1/88-12/90 1/91-12/93 Fixed Income 10/86-9/90 10/90-3/92 4/92-9/93
number of funds in the data base. Because more equity funds than fixed-income funds had long his- tories, the equity study extends further back in time. Even though the fixed-income in-sample period starts in October 1986, the sample included funds with data beginning in October 1988. We estimated their style benchmarks using a window that ex- panded until it included 60 months of data, a tech- nique we believe had no material effect on the results.
We can also characterize these analysis periods along other possibly important dimensions for our study. For example, equity Period 1 corresponds to a time when equity "value" managers outperformed "growth" managers, and Period 2 was a period when growth managers typically outperformed value managers. For the fixed-income study, both periods exhibited steadily falling interest rates.
To insure data integrity, the study included only funds that appear in both the Micropal and Morning- star data bases and for which the data from those two sources lead to substantially similar total returns, selection returns, and information ratios for each fund in each period.20 Adding these screens for data integrity did not ultimately change the conclusions concerning persistence of performance.
In addition to the returns data in the Micropal and Morningstar data bases, we used data on current fees (the expense ratios) contained in the Morning- star data base as of November 1994. We used these data to investigate the influence of expenses on per- sistence of performance.
METHODOLOGY Our first investigation of persistence used regression analysis, regressing Period 2 performance against Period 1 performance.
Performance (2) = a + b x Performance (1) + F, (3)
where "performance" can be cumulative total re- turns, cumulative selection returns, or information ratios. Positive estimates of the coefficient b with significant t-statistics are evidence of persistence: Pe- riod 1 performance contains useful information for predicting Period 2 performance.
We also used contingency tables to analyze per- formance persistence. For contingency analysis, we sorted the funds into winners and losers in Period 1 and winners and losers in Period 2. We distinguished
Financial Analysts Joumal / November-December 1995 45
winners from losers by ranking fund performance according to the performance measure of interest and defining the top half of the list as winners and the bottom half as losers. If the statistical evidence shows that winners in Period 1 remain winners in Period 2, the case for persistence of performance is proven. The contingency tables show the numbers of funds that were winners in both periods, losers in both periods, winners then losers, and losers then winners.
Because half the funds are winners and half are losers in each period by definition, if performance does not persist, the numbers in each bin should be equal. Evidence for persistence will be (statistically significantly) higher numbers in the diagonal bins (top left and bottom right). To analyze statistical significance, we calculated
2=_ (Oi-E )2 % - ~Ei
where Oi is the observed number in each bin and Ei is the expected number in each bin. X2 follows a chi-square distribution with 1 degree of freedom in the case of a two-by-two table and (R - 1) x (C - 1) degrees of freedom in an R by C contingency matrix.
EQUITY RESULTS Figures 1 through 3 are scatter plots of Period 2 equity fund performance versus Period 1 perform- ance for cumulative total returns, cumulative selec- tion returns, and information ratios respectively. The regression analysis found evidence of persistence at the 95 percent confidence level (t > 2) only when persistence is defined in terms of information ratios. In this case, the estimated coefficient is 0.141: For a
Figure 1. Equity Total Returns
1.20
1.00 0
0.80 0
. 0 0.0-000 0rw f
0
0.20 * 60a..& *
0.00.0 .0
-0.20 0
-0.40 I . l l I -1.00 -0.50 0.00 0.50 1.00 1.50 2.00
Period 1
Coefficient t-Statistic Slope -0.037 -0.81 Intercept 0.367 14.66
Figure 2. Equity Selection Retumrs
0.80
0.60 _
0.40 _ ; 0
0.20 L_
-0.20_ . ; .
-0.40
-0.60
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
Period 1
Coefficient t-Statistic Slope 0.076 1.19 Intercept 0.031 3.45
Figure 3. Equity Information Ratios
3.00
2.00 -.
C 1000 W. *
., 0.00 ~.*
-1.00 * *
-2.00
-3.00 I l l I -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00
Period 1
Coefficient t-Statistic Slope 0.141 2.34 Intercept 0.097 2.26
fund with an information ratio of 0.50 in Period 1 (roughly the top quartile), we would expect an infor- mation ratio of 0.07 in Period 2 (slightly above the median).
Tables 2 through 4 are the contingency table information for the total return, selection return, and information ratio data, respectively. Each table dis- plays the number of funds in each bin; the percent- ages of Period 1 winners and losers that become Period 2 winners and losers; the X2 statistic; and the probability, p, that random data could have gener- ated that high a X statistic.
None of these tables shows evidence of persist- ence. Table 2 shows the rather perverse result that the losers in Period 1 are likely winners in Period 2. Because this table uses total re\turns data, this appar- ent mean reversion is probably the result of value
46 Financial Analysts Joumal / November-December 1995
Table 2. Total Equity Returns Period 2
W L
62 88 W 41.3% 58.7%
Period 1 ________________ 88 62
L 58.7% 41.3%
x = 9.01, p = 0.003
Table 3. Equity Selection Returns Period 2
W L
79 71 W 52.7% 47.3%
Period 1_________________ 71 79
L 47.3% 52.7%
x = 0.85, p = 0.356
Table 4. Equity Information Ratios Period 2
W L
80 70 W 53.3% 46.7%
Period 1_________________ 70 80
L 46.7% 53.3%
%2 = 133, p = 0.248
outperforming growth in Period 1 and growth out- performing value in Period 2. We focused on selec- tion returns precisely to control for these style effects. We wanted to find if funds can consistently outper- form appropriate benchmarks.
FIXED-INCOME RESULTS Figures 4 through 6 are scatter plots of Period 2 fixed-income fund performance versus Period 1 per- formance for cumulative total returns, cumulative selection returns, and information ratios, respec- tively. In contrast to the results for equities, the fixed- income selection returns and information ratios both show evidence of persistence. The t-statistics are large in each case: 4.93 for selection returns and 6.06 for information ratios. For the information ratios, the estimated coefficient is 0.368. SO, for a fund with an
Figure 4. Fixed-income Total Returns
0.19
0.14 -
0.09 0
c,j 0.0 X-\
-t
.3-0.01
-0.06
-0.11
-0.16
-0.21 I l I . I -0.20 -0.10 0.00 0.10 0.20 0.30 0.40
Period 1
Coefficient t-Statistic Slope 0.069 1.55 Intercept 0.004 0.45
information ratio of 0.50 in Period 1 (once again roughly top quartile), we would expect an informa- tion ratio of 0.18 in Period 2.
Tables 5 through 7 analyze the same data using contingency analysis. Once again, the fixed-income selection returns and information ratios exhibit per- sistence of performance. The surprise is that the total returns data show no persistence evidence, because both periods experienced falling interest rates. The long-term funds should have consistently outper- formed the short-term funds, because rates were fall- ing during this entire period. Evidently, in our data base, the dispersion in fund duration must have been sufficiently small so that other influences masked this expected effect. We did check that the selection returns, with such styles accounted for, exhibited no correlation with fund durations.
The regression analysis and contingency table
Figure 5. Fixed-income Selection Retums 0.20
0.15 -
0.10 0
0.05 _-^. . * . 00
-0.05 -g 0.00 *
-0.10
-0.15
-0.20 I l l I I -0.28 -0.23 -0.18 -0.13 -0.08 -0.03 0.02 0.07 0.12 0.17
Period 1
Coefficient t-Statistic Slope 0.292 4.93 Intercept -0.015 -7.58
Financial Analysts Joumal / November-December 1995 47
Figure 6. Fixed-income Information Ratios 3.00
2.00 -
1.00 . % .
0.00 _:. / 0
-2.00 0
-3.00 -~~~~~~~~~~~~~~~.0 0 0
-4 00.0
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 Period 1
Coefficient t-Statistic Slope 0.368 6.06 Intercept -0.903 -13.40
analysis consistently show significant persistence of fixed-income selection returns and information ra- tios.
ACCOUNTING FOR FEES AND EXPENSES Our initial analysis of the equity and fixed-income fund returns showed little evidence of persistence among equity fund managers but strong evidence of persistence of selection returns and information ra- tios among fixed-income fund managers. One possi- ble (and uninteresting) source of persistence could be a strong persistence of strong underperformers,
Table 5. Fixed-income Total Retums Period 2
W L
51 46 W 52.6% 47.4%
Period 1 ___________________ 46 52
L 46.9% 53.1%
x2 = 0.62, p = 0.431
achieved through large fees and expenses. Our re- sults hint at this effect because the persistence ap- pears only for fixed-income funds, which have higher ratios of fees to expected outperformance.
To investigate the influence of fees and expenses on mutual fund performance persistence, we used November 1994 expense ratio data contained in the Morningstar data base. The Morningstar expense ratios include all expenses taken directly from the fund's net asset value. The returns data we analyzed
Table 6. Fixed-income Selection Returns Period 2
W L
61 36 W 62.9% 37.1%
Period 1 36 62
L 36.7% 63.3%
x2 = 13.34, p = 0.000
are net of these expenses. To estimate monthly returns gross of fees and
expenses, we assumed these annual expense ratios to be fixed in time and added (one-twelfth of) them back to each fund's return every month. Then, we reran our persistence studies using these gross return data.
Table 7. Fixed-income Information Ratios Period 2
W L
59 38 W 60.5% 39.2%
Period 1
38 60 L 38.8% 61.2%
x = 9.48, p = 0.002
For the equity funds, the gross return data show no evidence of persistence, and even the information ratios, which showed persistence using returns net of fees and expenses, no longer show evidence of persistence based on gross return data. (In this case, the t-statistic drops from 2.34 to 1.10.)
Fees also had a strong influence on information ratios. For the equity funds, using net returns, the mean information ratio is 0.12 with a standard devia- tion of 0.73 across the 300 funds. Using the gross return data, the mean information ratio rises to 0.36 with a standard deviation of 0.69. On average, man- agers seem to be capable of producing excellent port- folio returns, but investors do not benefit. The evi- dence for average outperformance among this group of equity funds mainly disappears when we subtract expenses.
We also saw a strong relationship between net return information ratios and fees. In Period 1, the highest fee fund has the lowest information ratio, and in Period 2, all the highest fee funds are among the lowest decile information ratios. Regressing net return information ratios against expense ratios, this relationship shows up with a t-statistic of -4.77 in
48 Financial Analysts Joumal / November-December 1995
Period 1 and -5.74 in Period 2. We also examined average fees for the four groups in Table 4. The group of funds labeled as losers in both periods exhibited significantly higher fees than the other three groups, which all exhibited similar fees. Given the lack of reliable persistence elsewhere among equity fund performance, the avoidance of high fees is clearly a defensible strategy.
With regard to fixed-income fund performance, gross of fees, the evidence for persistence remains but the strength diminishes. For fixed-income selec- tion returns, persistence t-statistics drop from 4.93 to 4.50 and X statistics drop from 13.34 to 9.48. For fixed-income information ratios, the persistence t- statistics drop from 6.06 to 4.74 and the x2 statistics drop from 9.48 to 6.28, all still significant.
The effect of fees and expenses on information ratios is quite dramatic for the fixed-income funds. The mean information ratios move from -0.87, with a standard deviation of 1.00 for net returns across the 195 funds, to a mean of -0.10 with a standard devia- tion of 0.89 when looking at gross returns. Clearly, the average expenses for fixed-income funds form a much larger fraction of typical risk undertaken than what we observed for equity funds.
According to these numbers, there is no evidence of average over- or underperformance among this group of fixed-income funds gross of fees, but the fees lead to a strong average underperformance when they are netted out. For these fixed-income funds, especially in Period 1, the relationship be- tween net return information ratios and expense ra- tios is strong; the highest fees correspond to the lowest decile information ratios. The t-statistic for this relationship is -4.56, although it drops to -0.61 in Period 2, when the single highest expense ratio fund is in the top quartile of information ratios. Cor- respondingly, in Table 7, the one group whose fees were significantly above the others were the funds labeled losers in Period 1 and winners in Period 2.
SURVIVORSHIP BIAS Brown, Goetzmann, Ibbotson, and Ross investigated the influence of survivorship bias on persistence studies.21 They argued that because of the existence of a distribution of strategies of differing volatili- ties,22 even in the absence of any true persistence, survivorship bias will generate the appearance that winners repeat. In effect, managers following high- volatility strategies but with no true skill will either by chance consistently show up as winners or be removed from the business through poor perform- ance. Note that this effect will influence returns more strongly than information ratios.
Brown et al. demonstrated this effect through a Monte Carlo simulation based on a universe of 600 managers with no skill (random returns), a reason-
able distribution of active risk levels, and perform- ance studies based on four years of simulated re- turns. They introduced survivorship bias using a cutoff figure: the percent of funds at the bottom of the performance rankings deleted each year. They then
Table 8. Brown et al. Resufts Average t-
Cutoff Average X2 Statistic
0% 1.04 (p = 0.308) 0.0 (p = 1.000) 5% 1.64 (p = 0.200) 2.0 (p = 0.0461)
10% 3.28 (p = 0.070) 3.4 (p = 0.0007) 20% 7.13 (p = 0.008) 4.7 (p = 0.0000)
showed how survivorship bias can influence persist- ence t-statistics and x2 statistics as a function of the cutoff. Table 8 summarizes results from their paper.
These results call into question our interpreta- tion of the statistical significance of our observed t-statistics and x2 statistics. Of course, we do not know an appropriate cutoff number that describes the number of funds going out of business because of poor performance, but it certainly exceeds zero. Roughly speaking, a 20 percent cutoff figure could explain most of our observed results, although a 10 percent cutoff figure could not. Recent work by Brown and Goetzmann showed cutoff figures of roughly 5 percent for common stock funds between 1976 and 1988.23 Clearly, the best way to resolve the survivorship bias problem is to collect and build data bases free of survivorship bias.
SUMMARY OF RESULTS Table 9 summarizes the results on persistence of performance. We found no evidence for persistence
Table 9. Persistence of Perfonnance Summary Significance of Persistence
Contingency Fund Statistic Table Regression
Equity Total return No No
N=300 Total + fee No No Selection return No No Selection + fee No No IR No Yes IR+ fee No No
Bond Total return No No
N= 195 Total + fee No No Selection return Yes Yes Selection + fee Yes Yes IR Yes Yes JR + fee Yes Yes
Financial Analysts Journal / November-December 1995 49
of performance among equity mutual funds, but we did find evidence of persistence of fixed-income se- lection returns and information ratios, even after accounting for expenses.
Overall, we ran 12 tests for persistence of per- formance, accounting for fees, at the 95 percent con- fidence level, and 4 of those tests showed positive results.
CONTEXT How do these empirical findings compare with those of the many similar studies, with a wide variety of conclusions, conducted during the past 25 years? Why do some studies find evidence of persistence and others do not?
This study uses style analysis to separate style returns from selection returns. Studies that look at alphas from regressions of fund returns against S&P 500 retums do not control for fund styles. This omis- sion can generate the appearance of persistence. For example, if value managers, in general, outperform the S&P 500 in both periods, the alpha-based studies will show persistence but the style-based studies will not. Our study examined whether the value manag- ers who outperform a value index in Period 1 also outperform a value index in Period 2. This funda- mental difference is one reason why our results may differ from those of other studies.
Other reasons for the discrepancy of results in- clude a variety of effects not sufficiently understood by many of these studies. Survivorship bias is a significant problem and quite difficult to overcome. Also, fees can significantly influence the results, gen- erating persistence of underperformance based on high expenses. Most previous studies have not ex- plicitly investigated the influence of fund expenses on performance persistence.
Equity and fixed-income funds should be sepa- rated because they involve very different bench- marks, as well as very different levels of risk and expected return. Combining equity and bond funds together in a persistence study can accentuate survi- vorship bias problems by greatly broadening the distribution of fund volatilities and can also cause problems when studying persistence of alphas. Fixed-income fund alphas defined relative to an eq- uity benchmark will closely resemble fixed-income total returns because the equity betas of typical fixed- income funds will lie close to zero. Persistence of total returns, however, is not usually of interest.
The integrity of the fund return data bases is also an issue for consideration. Relying on two data bases and studying only those records beyond question can improve the reliability of the study, even though for this particular study, deleting questionable re- cords did not change the final results.
Finally, of course, these persistence results may
be time dependent. Different studies have looked at different time periods. Active managers outperform consistently, however, based on their superior infor- mation. As their ideas become widely known, the outperformance disappears. If good ideas do not consistently appear over time but instead arrive episodically, then persistence will be stronger in some periods than in others.
Along these lines, few if any of these studies (including ours) distinguish funds from managers. Persistence could be more a property of managers, not funds, even though most funds have a charac- teristic approach to investing.
INVESTMENT IMPLICATIONS We found evidence for persistence of fixed-income fund performance and no evidence of persistence of equity fund performance. What are the investment implications of these results?
For equity funds, the implications are simple. With no persistence of selection returns, unless you have another basis for choosing future winners (i.e., your selection criteria include information other than historical performance), the solution is to index, per- haps to a set of style indexes weighted to match your investment objectives. Index funds should achieve at least average performance with low selection risk, low fees, low turnover, and low transaction costs. Because of their low costs, index funds typically per- form above the median of all funds with similar styles.
For fixed-income funds, we found significant evidence of persistence of selection returns. Selection of above-average managers based on past perform-
Figure 7. Expected Period 2 Seection Retums
Period 2 0.64UNO Winners
Selectio Return
62.9?%,/
Period 1 Winners
-3.13%, Period 2 Losers
Selection Return
50
ance appears to be possible, but this possibility re- quires more detailed analysis.
Table 5 shows that of the fixed-income funds with above-median selection returns in Period 1, 62.9 percent were above-median funds in Period 2. That percentage sounds like impressive odds for picking Period 2 selection returns. Beyond the winners-los- ers distinction, however, what returns could these funds achieve? The mean selection return of the Pe- riod 2 winners was 0.64 percent, while the mean selection return of the Period 2 losers was -3.13 per- cent. In other words, the losers lost much more than the winners won, as Figure 7 shows. So, the appro- priate use of historical information provides strong odds for beating the median, but unfortunately the median has negative selection return. In this case, Figure 7 implies an expected selection return in Pe- riod 2 of -0.76 percent for the Period 1 winners, with a standard deviation of 1.82 percent.24 This result should not be too surprising. Fees and transaction costs imply that average fund returns should under- perform benchmarks, and many studies have dem- onstrated this underperformance.
The investment implications for fixed-income funds, surprisingly, are similar to those for equity funds. Once again, index funds are a very attractive strategy. Presumably, index funds will consistently appear as winners when compared with the funds in this study.
There is also an implication for investors who still wish to choose fixed-income funds based on past
selection returns: Choose only one fund. Because the mean selection return is negative, diversifying across funds will simply accentuate that negative return. Assuming normality, by choosing only one winning Period 1 fund, the probability of having a positive Period 2 selection return will be 34 percent. For five equally weighted funds, the probability of positive selection return drops to 17 percent. In this portfolio problem, surprisingly, diversification does not pay.
CONCLUSIONS We investigated persistence of performance for eq- uity and fixed-income mutual fund managers and found evidence for persistence of fixed-income fund performance, even after controlling for fund style and management fees.
The investment implications for equity and fixed-income fund selection are similar. Given only past performance information, index funds look best for equity and fixed-income investments. Equity in- dex funds make sense because of the absence of persistence in equity fund performance. Fixed-in- come index funds make sense because, even though performance does persist, the average underperfor- mance of fixed-income funds more than cancels out the benefits of being able to choose above-average funds through persistence alone. Only with informa- tion beyond historical performance statistics should investors choose active managers.
NOTES 1. Elsewhere, we have reported preliminary research on the per-
formance of U.S. institutional portfolios. See Ronald N. Kahn and Andrew Rudd, "Practical Applications of Quantitative Theories," presentation at The Financial Planet Symposium, Paris, November 1994.
2. This methodology was originally suggested by Sharpe. See William F. Sharpe, "Asset Allocation: Management Style and Performance Measurement," The Journal of Portfolio Manage- ment, vol. 18, no. 2 (Winter 1992):7-19.
3. See John C. Bogle, "Selecting Equity Mutual Funds," The Jour- nal of Portfolio Management, vol. 18, no. 2 (Winter 1992):94-100. Bogle investigated the impact of expenses and fees but did not use style analysis.
4. M. Jensen, "The Performance of Mutual Funds in the Period 1945-1964," TheJournal of Finance, vol. 23, no.2 (May 1968):389- 416.
5. Mark Kritzman, "Can Bond Managers Perform Consistently?" The Journal of Portfolio Management, vol. 9, no. 4 (Summer 1983):54-56.
6. Patricia C. Dunn and Rolf D. Theisen, "How Consistently Do Active Managers Win?" The Journal of Portfolio Management, vol. 9, no. 4 (Summer 1983):47-50.
7. E. Elton, M. Gruber, and J. Rentzler, "The Performance of Publicly Offered Commodity Funds," Financial Analysts Jour- nal, vol. 46, no. 4 (July/August 1990):23-30.
8. M. Grinblatt and S. Titman, "The Evaluation of Mutual Fund
Performance: An Analysis of Monthly Returns," working pa- per 13-86, John E. Anderson Graduate School of Management, University of California at Los Angeles (1988).
9. Bruce N. Lehmann and David M. Modest, "Mutual Fund Per- formance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," The Journal of Finance, vol. 42, no. 2 (June 1987):233-65.
10. G. Brown and P. Draper, "Consistency of U.K. Pension Fund Investment Performance," working paper, University of Strath Clyde Department of Accounting and Finance (1992).
11. Darryll Hendricks, Jayendu Patel, and Richard Zeckhauser, "Hot Hands in Mutual Funds: Short-Run Persistence of Rela- tive Performance, 1974-1988," TheJournal of Finance, vol. 48, no. 1 (March 1993):93-130.
12. W.N. Goetzmann and Roger Ibbotson, "Do Winners Repeat?" The Journal of Portfolio Management, vol. 20, no. 2 (Winter 1994):9-18.
13. See "Mutual Fund Performance Evaluation." 14. For further reference, see the S&P 500 1993 Directory. 15. Jensen, "The Performance of Mutual Funds." 16. See Richard C. Grinold and Ronald N. Kahn, Active Portfolio
Management (Chicago: Probus Publishing, 1995), for further justification of this point.
17. Stephen J. Brown, William Goetzmann, Roger G. Ibbotson, and Stephen A. Ross, "Survivorship Bias in Performance Studies," The Review of Financial Studies, vol. 5, no. 4 (December
Financial Analysts Journal / November-December 1995 51
1992):553-80. 18. The Micropal data base is available from Micropal, Inc., 31 Milk
Street, Suite 1002, Boston, MA 02109, and the Momingstar data base is available from Morningstar, 225 West Wacker Drive, Chicago, IL 60606.
19. Brown, et al., "Survivorship Bias in Performance Studies." 20. We defined "substantially similar" to mean within 2.0 percent
for equity total and selection returns, 0.08 for equity informa- tion ratios, 0.8 percent for fixed-income total and selection retums, and 0.20 for fixed-income information retums; part of the difference between equity and fixed-income screens was
because of differing length periods. These screens reduced the qualifying equity funds from 365 to 300 and the qualifying fixed-income funds from 261 to 195.
21. "Survivorship Bias in Performance Studies." 22. This problem was part of our motivation for separately analyz-
ing equity funds and fixed-income funds. 23. S.J. Brown and William Goetzmann, "Performance Persist-
ence," New York University, Salomon Center Working Paper Series S-94-28 (September 1994).
24. -0.76 percent = 0.629 x 0.64 percent + 0.371 x -3.13 percent.
52 Financial Analysts Joural! November-December 1995
