Originally developed in 1966 by Nobel Memorial Prize winner Prof. William F. Sharpe, the Sharpe ratio has become ubiquitous in the financial industry. Applied to a series of returns, it can be interpreted as the units of return per unit of risk taken by the investment strategy that realized the returns in the series.

In the decades since Prof. Sharpe first proposed the measure, many different methods have come to exist for estimating the Sharpe ratio, gauging confidence intervals, and testing hypotheses. To help bring clarity to these varying approaches, Two Sigma’s Labs team recently performed an in-depth survey of the extensive literature on the Sharpe ratio and published its findings in the Technical Report *Sharpe Ratio: Estimation, Confidence Intervals, and Hypothesis Testing*.

Refined statistical ingenuity is needed to estimate the Sharpe Ratio in practice, due to the autocorrelation that is often present in real series of returns. The evaluation of confidence intervals also presents some challenges, due to the time-series nature of the data, that can be overcome with appropriate variants of the bootstrap approach. Different techniques based on the Generalized Method of Moments are instead used in determining the asymptotic variance of the estimator.

For a full discussion of these and other subtleties, as well as thoughts on potentially interesting directions for future research, read the full Technical Report here.