Performance and Risk Aversion of Funds with Benchmarks

Abstract

Abstract This chapter provides a simple method of ranking mutual funds’ probabilities of outperforming a benchmark portfolio. We show that ranking fund performance in this way is identical to ranking each fund’s portfolio with a generalized entropy, equivalent to an expected generalized power utility index that uses a risk-aversion coefficient specific to that fund. When the return differential between fund and benchmark portfolio (log gross) returns follows a Gaussian process, this ranking is equivalent to using a simple modification of the Information Ratio (1998). We develop and apply feasible parametric and nonparametric estimators to rank the performance of 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 fund-specific risk-aversion coefficients required for the ranking. We also argue that an auxiliary hypothesis that fund managers attempt to maximize the outperformance probability is no less plausible than an extant alternative behavioral hypothesis and is more parsimoneously parametrized.