The Sharpe ratio efficient frontier

David H. Bailey and Marcos López de Prado

Abstract

ABSTRACT

We evaluate the probability that an estimated Sharpe ratio will exceed a given threshold in the presence of nonnormal returns. We show that this new uncertainty-adjusted investment skill metric (called the probabilistic Sharpe ratio) has a number of important applications. First, it allows us to establish the track-record length needed for rejecting the hypothesis that a measured Sharpe ratio is below a certain threshold with a given confidence level. Second, it models the trade-off between track-record length and undesirable statistical features (eg, negative skewness with positive excess kurtosis). Third, it explains why track records with those undesirable traits would benefit from reporting performance with the highest sampling frequency such that the independent and identically distributed assumption is not violated. Fourth, it permits the computation of what we call the Sharpe ratio efficient frontier, which lets us optimize a portfolio under nonnormal, leveraged returns while incorporating the uncertainty derived from track-record length. Results can be validated using the Python code in the appendixes.