How is drawdown calculated

Drawdown is calculated as the percentage decline from the running equity peak to the current value, and maximum drawdown is the largest such peak to trough drop in the sample. It is path dependent because the ordering of returns determines peaks and troughs. A backtest measures drawdown on only one realized historical path, so the deepest observed drawdown is not a bound on future risk. A broad numerical study quantifying the average gap between backtest and future maximum drawdown is not provided.

Drawdown is the decline from a prior equity peak to a subsequent trough. In a strategy equity curve, it is calculated by comparing the current portfolio value to the highest value reached up to that point. At each time step, the running peak is updated if a new high is made. The drawdown at that time is then the percentage drop from that running peak. Maximum drawdown is the most severe such peak to trough decline observed over the sample period.

This arithmetic makes drawdown path dependent. Two strategies can have the same set of returns and the same ending value, yet different ordering of those returns will produce different running peaks, different troughs, and different maximum drawdowns. Drawdown is therefore not determined only by average return, volatility, or terminal wealth. It depends on the sequence in which gains and losses occur.

That path dependence matters in backtesting because a backtest observes only one realized sequence from the historical sample. The measured maximum drawdown is the worst decline that happened along that particular path, not the worst decline that could occur across other plausible paths. If the sample omits a more adverse ordering of returns, a different market regime, or a more damaging sequence of losses, the observed maximum drawdown will be smaller than the strategy may experience later.

Sonar describes this limitation directly in its fundamentals material by distinguishing in sample testing from out of sample testing and by emphasizing that backtest quality depends on whether results survive unseen data rather than only fitting the sample used to build the strategy. That same logic applies to drawdown. A maximum drawdown measured on the development sample is conditional on the historical path used for construction and evaluation, so it cannot fully represent future path risk across unseen data or alternative market sequences.

The backtest overfitting audit is relevant because it is designed to test whether backtest statistics remain credible once selection bias and overfitting are considered. Sonar explains that overfitting can make in sample performance metrics look better than what is likely to persist out of sample. While the tool is presented around audit and robustness rather than a standalone drawdown theorem, its purpose is to quantify the extent to which backtest results can be overstated when many trials, specifications, or tuning choices are searched. Maximum drawdown is one of the statistics that can be made to look benign in sample for the same reason: the chosen specification is evaluated on a limited historical path and may not be exposed to the unseen adverse sequences that matter later.

The deflated Sharpe ratio glossary entry reinforces the same statistical point from another angle. Sonar explains that naive performance estimates can be inflated by multiple testing and non normality, and that a deflated measure adjusts for those distortions. Drawdown is not the Sharpe ratio, but the shared lesson is that a backtest statistic should not be read as a direct estimate of future reality when the research process has involved selection across many candidates. If many variants are tried, the selected strategy is likely to look better on observed data than it will on new data. That selection effect can understate future drawdown because the chosen path and specification have already benefited from historical luck.

For risk assessment, the practical implication is simple. Maximum drawdown in a backtest is a historical observation, not a hard bound on future loss depth. It is the deepest decline seen on one sample path. Because drawdown is path dependent and future market sequences are unseen, the deepest drawdown in the backtest can systematically understate the potential drawdown out of sample.

A numerical estimate of the size of the understatement is not available from the cited material.

Drafted with AI assistance from cited sources. Reviewed and approved by Sonar Sciences Quant & Research Team.