Sharpening Sharpe Ratios

The Statistics of Sharpe Ratios

The building blocks of the Sharpe ratio—expected returns and volatilities— are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, I derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic t...

A Note on Trader Sharpe Ratios

Traders in the financial world are assessed by the amount of money they make and, increasingly, by the amount of money they make per unit of risk taken, a measure known as the Sharpe Ratio. Little is known about the average Sharpe Ratio among traders, but the Efficient Market Hypothesis suggests that traders, like asset managers, should not outperform the broad market. Here we report the findin...

Improving Sharpe Ratios and Stability of Portfolios by Using a Clustering Technique

This paper proposes a method which combines a clustering technique with asset allocation methods, to improve portfolio Sharpe ratios and weights stability. The portfolio weights are computed based on cluster members and cluster portfolios, which are decided by an optimal cluster pattern. The optimized cluster pattern tells the belonging of assets to particular clusters, which is identified by u...

Sharpe Ratio Practice Note

The Sharpe Ratio Efficient Frontier

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) 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 b...