Maximum drawdown from a return series

Question

Often you are handed periodic returns, not the equity curve itself. Given simple returns $r_1, r_2, \dots, r_n$ (as decimals, so $0.10$ means $+10\%$ ), the equity after period $k$ is the running product $\prod_{t \le k}(1 + r_t)$ . Find the maximum drawdown, the largest peak-to-trough fractional drop, of the equity curve those returns generate.

returns = [0.10, -0.20, 0.05, -0.30, 0.10]
-> 0.412         # peak 1.10 down to trough 0.6468

Return the maximum drawdown as a fraction, in $O(n)$ time and $O(1)$ space. Do not materialize the whole equity array.

Accepted Answer

Compound the returns into a running equity level as you go, starting from 1, and run the standard drawdown sweep on that level, carrying the running peak and the worst relative drop. There is no need to store the curve: each return updates equity in place. Tracing the example: equity goes 1.10, 0.88, 0.924, 0.6468, 0.71148; the running peak is 1.10 from period 1 on; the drawdowns are 0, 0.20, 0.16, 0.412, 0.353, so the answer is about 0.412 (a 41.2% drop from the 1.10 peak to the 0.6468 trough). Time O(n), space O(1). One subtlety: with simple returns the correct compounding is multiplicative…

Maximum drawdown from a return series

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