Risk-Adjusted Return When Returns Are Not Normally Distributed

Abstract

Recently, a number of authors have shown that by using dynamic trading strategies and/or investing in options, a portfolio's Sharpe ratio can be increased even when the portfolio manager has no “skill.” The increased Sharpe ratio results from creating a return distribution that is significantly different from normal and typically has significant negative skewness. The author presents a generalized approach to calculating the Sharpe ratio of an asset or a portfolio when the return distribution is not necessarily normal. The procedure adjusts the entire distribution of the asset's return so that it will match the return distribution of a benchmark (e.g., S&P 500). The Sharpe ratio of the adjusted return can then be directly compared to that of the benchmark. The author applies the procedure to simulated data and the historical data on hedge fund indices.