Does Historical Performance Predict Future Performance?

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  • 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: .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...


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