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Drawdown recovery maths

The asymmetric arithmetic of getting back to even: the gain required grows faster than the loss that caused it.

Required gain = 1 / (1 - drawdown) - 1. Ten per cent down needs 11.1% back. Twenty needs 25%. Thirty-three needs 50%. Fifty needs 100%. Seventy-five needs 300%. Ninety needs 900%.

Read the curve rather than the individual numbers. Up to roughly 20% the penalty is manageable; past 30% it accelerates sharply; past 50% recovery requires a different order of performance from anything that produced the loss in the first place. This is the entire quantitative argument for loss limits, and it does not depend on any view about markets.

Time compounds the damage. A 40% drawdown needing 66.7% to recover, in a strategy that compounds 15% a year, takes about three and a half years of flawless execution - assuming the edge survived whatever caused the loss. See time-to-recovery and underwater-curve.

Related: max-drawdown, time-to-recovery, underwater-curve, monthly-loss-limit

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

An equity curve and its drawdownAn account balance rising over a year, falling from a peak to a trough, then climbing back to the old peak.ACCOUNT EQUITY$20k$12k$8k024681012TIME (MONTHS)PEAK $16,000TROUGH $12,000DRAWDOWN−25%RECOVERY
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.

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