Expected Maximum Drawdown

A backtest reports one number for maximum drawdown: the single worst peak-to-trough decline that happened to occur along that one historical path. But that path is just one random draw from many that could have happened — run the same strategy with a different sequence of lucky and unlucky days, and you'd get a different worst drawdown. Expected maximum drawdown answers the more useful question: averaged over many possible paths with the same underlying return distribution, what is the typical size of the worst drawdown you should expect?

For a process with drift $\mu$ and volatility $\sigma$ per period, over $T$ periods, expected maximum drawdown grows roughly with $\sigma\sqrt{T}$ when drift is near zero, and the relationship gets more favorable (smaller drawdowns relative to horizon) as positive drift dominates. The key qualitative fact worth remembering is that expected maximum drawdown grows with the length of time observed, not just with volatility — a strategy watched for 10 years will very likely show a materially worse "worst drawdown" than the same strategy watched for 1 year, purely because there are more opportunities for an unlucky streak, with nothing about the strategy itself having changed.

For example, a strategy with an annualized Sharpe ratio of 1.0 might show a historical max drawdown of 12% over a 3-year backtest, but simulating thousands of alternate 3-year paths with the same drift and volatility could reveal an expected maximum drawdown closer to 18-20% — meaning the actual backtest path happened to be unusually kind, and a live deployment should be sized for the larger number, not the smaller one that was observed.