You are in a drawdown. When should you start worrying?

TL;DR

This paper provides a quantitative method to determine when a trading drawdown is truly concerning, using probability distributions for drawdown length and depth in Brownian motion models, highlighting common underestimations by managers and investors.

Contribution

It introduces a precise probabilistic framework for assessing drawdown severity and duration, improving decision-making in trading strategy evaluation.

Findings

Quantitative thresholds for worrying drawdowns derived from Brownian motion models

Managers and investors tend to underestimate drawdown risks

Provides exact probability distributions for drawdown characteristics

Abstract

Trading strategies that were profitable in the past often degrade with time. Since unlucky streaks can also hit "healthy" strategies, how can one detect that something truly worrying is happening? It is intuitive that a drawdown that lasts too long or one that is too deep should lead to a downward revision of the assumed Sharpe ratio of the strategy. In this note, we give a quantitative answer to this question based on the exact probability distributions for the length and depth of the last drawdown for upward drifting Brownian motions. We also point out that both managers and investors tend to underestimate the length and depth of drawdowns consistent with the Sharpe ratio of the underlying strategy.