Why Maximum Drawdown Depends on Strategy and Portfolio Rules
Summary
The document asks whether the maximum drawdown over a fixed horizon has a theoretical distribution under iid normally distributed returns with a specified Sharpe ratio. The replies emphasize that drawdown depends on the return-generating process and the strategy’s trading and portfolio rules. Decisions about opening, resizing, scaling, or limiting positions change portfolio mark-to-market behavior and therefore affect drawdown outcomes.
The suggested practical approaches are Monte Carlo simulation and historical backtesting, while recognizing that iid Gaussian returns are an unrealistic simplification for many strategies. Such assumptions may be a rough model for an asset or static portfolio, but they do not describe a rebalanced portfolio without specifying how rebalancing works. The discussion supplies no general distribution, paper, or quantitative result; its main lesson is that a useful drawdown model must reflect the strategy and its notional rules.
Key ideas
- Maximum drawdown distributions depend on the strategy and the rules used to size and manage positions.
- Monte Carlo simulation and historical backtesting are suggested ways to examine drawdown behavior.
- An iid Gaussian return assumption is a limited approximation for many trading strategies.
- Rebalancing changes portfolio returns and must be specified before modeling drawdowns.
- No universal drawdown distribution is established by the discussion.
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# Statistical distribution of Max Drawdown # 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 ## Answer by Denis Ryabich (score 2) https://quant.stackexchange.com/a/60940 I assume Michael meant distribution of maximum negative returns of iid Normal distribution. I guess the word drowdowns is meant to represent sequence of max negative returns, not the drowdowns of any specific strategy ## Answer by stans (score 0) https://quant.stackexchange.com/a/60661 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 - choose the notional of a new trade, - readjust the notionals of the open trades on any given day affects the distribution of the portfolio mark-to-market. Do you ever double down? Do you ever scale down? Are you saying: "If I have 10 trades open already, the 11-th one is not allowed no matter what"? Or are you assuming unlimited balance sheet? As naive as is, the iid Gaussian framework can be distantly related to returns on a particular asset or static portfolio. However, the framework is completely inapplicable to a portfolio which is rebalanced. Everything depends on how you rebalance. Everything depends on your strategy.
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