Losing money with a high Sharpe ratio

TL;DR

This paper demonstrates that a high Sharpe ratio can coincide with losing all money, emphasizing the importance of understanding return bounds and the timing of losses in risk-adjusted performance metrics.

Contribution

It analyzes the maximum achievable Sharpe and Sortino ratios for investors with bounded returns who experience losses, clarifying conditions under which high ratios occur despite losses.

Findings

High Sharpe ratios can occur even when all money is lost.

Losses are often associated with a period of near-total loss.

Bounded return assumptions influence the maximum Sharpe and Sortino ratios.

Abstract

A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost. This note explores the best achievable Sharpe and Sortino ratios for investors who lose money but whose one-period returns are bounded below (or both below and above) by a known constant.