Great year, bad Sharpe? A note on the joint distribution of performance and risk-adjusted return

Matteo Smerlak

Papers from arXiv.org

Abstract: Returns distributions are heavy-tailed across asset classes. In this note, I examine the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using both synthetic and real data, I show that, all other things being equal, the investments with the best in-sample performance are never associated with the best in-sample Sharpe ratios (and vice versa). This counter-intuitive effect is unrelated to the risk-return tradeoff familiar from portfolio theory: it is, rather, a consequence of asymptotic correlations between the sample mean and sample standard deviation of heavy-tailed variables. In addition to its large sample noise, this non-monotonic association of the Sharpe ratio with performance puts into question its status as the gold standard metric of investment quality.

Date: 2023-02, Revised 2024-06
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