Performance maximization of actively managed funds

Abstract

A growing literature suggests that, even in the absence of any ability to predict returns, holding options on the benchmarks or trading frequently can generate positive alpha. The ratio of alpha to its tracking error appraises a fund's performance. This paper derives the performance-maximizing strategy, which turns out to be a variant of a buy-write strategy, and the least upper bound on such performance enhancement. If common equity indices are used as benchmarks, the potential alpha generated from trading frequently can be substantial in magnitude, but it carries considerable risk. The statistical significance in estimated alpha is low, and the probability of a negative alpha is high. The performance enhancement from holding options can be significant – both economically and statistically – if the options' implied volatilities are higher than the volatilities of the benchmark returns. The performance-maximizing strategy derived in this paper is different from the strategies that switch portfolio exposure to the benchmarks. The exposure-switching strategies are not promising unless the switching is based on superior information.