Asymmetry and Performance Metrics for Equity Returns

Abstract

An assumption of symmetric asset returns, together with globally risk averse utility functions, is unappealing for fund managers and other activist investors, whose preferences switch between risk aversion on the downside and risk seeking on the upside. A performance return criterion is originated that is more consistent with the implicit Friedman-Savage utility ordering. Adapted from recent developments in the income distribution literature, the proposed metric weights the lower versus upper conditional expected returns, while a dual spread or dispersion metric also exists. The resulting performance metric is easy to compute. A point of departure is the conventional Sharpe performance ratio, with the empirical comparisons extending to a range of existing performance criteria. In contrast, the proposed W-metric results in different and more embracing performance rankings.