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

Abstract

With the advent in recent years of large financial data sets, machine learning and high-performance computing, analysts can backtest 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 backtest overfitting.

The problem of performance inflation extends beyond backtesting. More generally, researchers and investors 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 over-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.

Keywords: Sharpe ratio, Non-Normality, Probabilistic Sharpe ratio, Backtest overfitting, Minimum Track Record Length, Minimum Backtest Length

JEL Classification: G0, G1, G2, G15, G24, E44