Effective Return, Risk Aversion and Drawdowns

Abstract

We derive two risk adjusted performance measures for investors with risk averse preferences. Maximizing these measures is equivalent to maximizing the expected utility of an investor. The first measure, X(eff), is derivedassuming a constant risk aversion while the second measure, R(eff),is based on a stronger risk aversion to clustering of losses than of gains. The clustering of returns is captured through a multi-horizon framework. The empirical properties of X(eff), R(eff) are studied within the context of real-time trading models for foreign exchange rates and their properties are compared to those of more traditional measures like the annualized return, the Sharpe Ratio and the maximum drawdown. Our measures are shown to be more robust against clustering of losses and has the ability to fully characterize the dynamic behavior of investment strategies.