# Testing Sharpe ratio: luck or skill?

## TL;DR

This paper develops statistical tests to evaluate whether observed Sharpe ratios in asset management are due to skill or luck, accounting for estimation errors, auto-correlation, and sample size effects.

## Contribution

It introduces new methods to assess the statistical significance of Sharpe ratios, including adjustments for auto-correlation and sample size, enhancing the evaluation of fund performance.

## Key findings

- Provides reference tables for minimum Sharpe ratios for significance
- Quantifies the skill percentage at various Sharpe levels and auto-correlation
- Highlights the impact of auto-correlation on Sharpe ratio significance

## Abstract

Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected returns and the volatilities are unknown numbers and need to be estimated statistically. This means that the Sharpe ratio used by funds is likely to be error prone because of statistical estimation errors. In this paper, we provide various tests to measure the quality of the Sharpe ratios. By quality, we are aiming at measuring whether a manager was indeed lucky of skillful. The test assesses this through the statistical significance of the Sharpe ratio. We not only look at the traditional Sharpe ratio but also compute a modified Sharpe insensitive to used Capital. We provide various statistical tests that can be used to precisely quantify the fact that the Sharpe is statistically significant. We illustrate in particular the number of trades for a given Sharpe level that provides statistical significance as well as the impact of auto-correlation by providing reference tables that provides the minimum required Sharpe ratio for a given time period and correlation. We also provide for a Sharpe ratio of 0.5, 1.0, 1.5 and 2.0 the skill percentage given the auto-correlation level.