Estimating the Dynamics of Mutual Fund Alphas and Betas

Consider an economy in which the underlying security returns follow a linear factor model with constant coefficients. While portfolios that invest in these securities will, in general, have a linear factor structure, it will be one with time-varying coefficients. However, under certain assumptions regarding the portfolio’s investment strategy, it is possible to estimate these time varying alphas and betas. Importantly, this can be done without direct knowledge of either the portfolio manager’s exact investment strategy or of the alphas and betas of the individual securities in which the portfolio invests. As other papers in the area of mutual fund performance measurement have found, overall there appears to be little evidence that, in aggregate, fund investors earn superior returns. Of course, even though the average fund may not produce a superior expected return, this need not be true of sub-populations. Using a dynamic coefficient model to find funds with superior expected returns produces fund of fund portfolios that substantially outperform the market benchmark. Furthermore, these portfolios outperform portfolios selected using the traditional OLS approach. Bootstrapped estimates indicate that the median return produced by the Kalman filter selected funds exceeds those selected via OLS by over 1.6% under the single factor market benchmark, and 1.2% under the four factor Carhart benchmark. JEL Classification: G12, G13. Over the last twenty years the mutual fund industry has grown at an incredible rate, and this has naturally attracted a lot of attention from the academic and financial community. Because most of these funds are actively managed two questions have arisen: First, does the average mutual fund produce superior returns? Second, can funds with superior future returns be identified ex-ante? For the most part the answer to the first question seems to be no, at least after expenses are taken into account (see, for example Lehmann and Modest (1987), Carhart (1997), Daniel, Grinblatt, Titman, and Wermers (1997), Wermers (2000), and Pástor and Stambaugh (2002a)). The answer to the second question is not as clear, with different studies coming to different conclusions. Hendricks, Patel, and Zechhauser (1993), and Brown and Goetzmann (1995) conclude that finding funds with future expected excess returns is a difficult but perhaps not impossible task. More recently Teo and Woo (2001) find that allowing for the trading restrictions imposed by a fund’s advertised investment style helps predict out of sample returns. In contrast, Carhart (1997) argues that whatever selection ability can be found is due to portfolio momentum rather than managerial ability. What most studies have in common is the maintained hypothesis that past factor loadings reasonably forecast future factor loadings. While this assumption may or may not be true at an individual security level, it seems rather unlikely to hold for managed portfolios. Investors presumably employ portfolio managers to move assets into and out of various sectors and securities as part of a dynamic strategy. Absent some mathematical coincidence, the simple act of shifting funds across securities will lead to time varying portfolio loadings on any benchmark. As noted by Admati and Ross (1985), and Dybvig and Ross (1985) a model with static coefficients may then lead to the erroneous conclusion that a manager with market timing abilities produces negative abnormal returns. In response, Grinblatt and Titman (1989a) (hereafter GT) propose a technique that can detect market timing abilities under such circumstances, and implement it in their 1994 paper. However, as Ferson and Schadt (1996) point out correlations between factor loadings and market returns may also be due to predictable changes in time varying expected returns, and thus implement a technique for handling this case. One might think that professional rating agencies might be able to select funds with superior performance. But Blake and Morey (2000) do not find any evidence MorningStar ratings help in this regard. Another approach has been to look at overseas data. Dahlquist, Engström, and Söderlind (2000) find they can, to a limited degree, identify Swedish mutual funds with future superior performance. Chevalier and Ellison (1999) examine whether or not measures related to the fund manager such as SAT scores can help predict superior stock picking ability. While they find the answer to that question is yes, the evidence that fund investors capture any of it is considerably weaker. Historically, stock returns with super normal returns in the previous six months, tend to outperform in the following six months. Thus, to the degree that managers simply hold onto a winning portfolio from one year to the next they will appear to outperform their benchmark. One exception is Grinblatt and Titman (1993). The methodology they use avoids a direct comparison against a specific portfolio, and instead uses an “endogenous” benchmark. However, their technique requires knowledge of the fund’s actual composition, which may not always be available. Ferson and Khang (2002) extend the technique to condition the portfolio betas on exogenous variables such as macro economic data. See Breen, Glosten, and Jagannathan (1989) for an empirical estimate of the potential value of such actions, and Mamaysky and Spiegel (2002) for a theoretical treatment.