The Deflated Sharpe Ratio:Correcting for Selection Bias, BacktestOverfitting, and Non-Normality

Abstract

With the advent in recent years of large financial data sets, machine learning, and high-performance computing, analysts can back test millions (if not billions) of alternative investment strategies. Backtest optimizers search for combinations of parameters that maximize the simulated historical performance of a strategy, leading to back test overfitting. The problem of performance inflation extends beyond back testing. More generally, researchers and investment managers tend to report only positive outcomes, a phenomenon known as selection bias. Not controlling for the number of trials involved in a particular discovery leads to overly optimistic performance expectations. The deflated Sharpe ratio (DSR) corrects for two leading sources of performance inflation: Selection bias under multiple testing and non-normally distributed returns. In doing so, DSR helps separate legitimate empirical findings from statistical flukes.