Performance and risk aversion of funds with benchmarks: A large deviations approach

Abstract

Mutual fund performance is often measured relative to a designated benchmark portfolio. This paper provides a simple method of ranking portfolios' probabilities of outperforming a benchmark portfolio. Ranking fund performance in this way is identical to ranking each fund's portfolio with an expected generalized power utility index, that uses a fund and benchmark-specific risk aversion parameter implied by the fund's portfolio choice. When the difference between funds' log returns and those of the benchmark are from different Gaussian processes, we derive different modifications of the selection Sharpe ratio (1994) associated with Roll's (1992) Tracking Error Variance (TEV)-e±ciency notion. We develop feasible nonparametric and parametric estimators of a fund's performance index value, and the implied degree of risk aversion of the equivalent expected generalized power utility. We apply these estimators to rank the small fraction of mutual funds that (from the results of an hypothesis test) could outperform the S&P 500 index in the long run, and to estimate the implied degrees of risk aversion of their managers. Our procedure produces more plausible and precise estimates of managerial risk aversion than other recent estimates.