# Statistical distribution of Max Drawdown

Are there any good papers/ references on the statistical distribution of Max Drawdown over a specified amount of time given a specified Sharpe? Assuming returns are iid normally distributed

I’ve been running some Monte Carlo simulations but wondering if there is any theory

• Magdon-Ismail et al, Rej et al, among others. Jan 25, 2021 at 17:48
• Given the nature of your resonses to the already provided answer I think it would be helpful if you provided more details in the question about what you you are looking for (mathematically speaking). In the absense of a trading strategy, are you simply looking for the statistical distribution of the minimum of a sum of normal iid variables?
– Attack68
Feb 4, 2021 at 7:49

The distribution of drawdown is highly sensitive to the trading strategy you are running. The distributions of drawdown for a Black Swan strategy and carry strategy are very different. Only you know what you are doing. If you are good, drawdown will have thin upper tail. If you are not good, it may have fat upper tail (or its distribution may fail in other ways). No paper will be able to encompass all the possibilities.

You are on the right track simulating drawdown via Monte Carlo and via backtesting on the historical data.

UPDATE: not only is the assumption of iid Gaussian returns unrealistic; your question is ill-posed for the following reason. The distribution of drawdown can take many shapes depending on the notional rules. The way you

1. choose the notional of a new trade,