Maximum drawdown, and report when it happened

Question

Reporting the size of the worst drawdown is rarely enough; risk teams want to know when it happened so they can attribute it to a specific event. Given an equity curve, return the maximum drawdown fraction together with the index of the peak it fell from and the index of the trough it fell to.

equity = [100, 120, 90, 105, 60, 80]
-> (0.5, 1, 4)         # 50% drop, from the peak at index 1 (120) to the trough at index 4 (60)

Return (mdd, peak_index, trough_index) in $O(n)$ time and $O(1)$ space.

Accepted Answer

Run the standard drawdown sweep, but also track the index of the current running peak. Whenever a new running high appears, remember its index. Whenever the drawdown improves on the best seen, snapshot the current peak index (as the start) and the current index (as the trough). Tracing the example: the running peak becomes 120 at index 1; at index 2 (value 90) the drawdown is 0.25, recorded from peak index 1; at index 4 (value 60) the drawdown is (120-60)/120 = 0.5, which beats it, recording (1, 4); index 5 (value 80) gives only 0.333. Result (0.5, 1, 4). Time O(n), space O(1). The key is tha…

Maximum drawdown, and report when it happened

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