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Drawdown-Based Stop-Outs and the 'Triple Penance' Rule

Read the paperopens papers.ssrn.com in a new tab

What they found

The authors derive the statistical relationship between a strategy's Sharpe ratio, its expected maximum drawdown, and the time it takes to recover. For a strategy with normally distributed returns and no autocorrelation, the time to recover from the maximum drawdown is on average three times as long as the time it took to reach it, hence 'triple penance'. They show how to set drawdown-based stop-out limits at a chosen confidence level so that a stop-out is triggered only when the drawdown is inconsistent with the strategy's assumed properties, rather than by ordinary bad luck.

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.

What you can use

  • Expect recovery from a drawdown to take about three times as long as the drawdown took to develop; plan capital and patience accordingly.
  • A drawdown that is unusual for your strategy's Sharpe ratio is evidence the strategy is broken; one that is normal is not, and stopping out on it is a mistake.
  • The paper gives formulas to compute what drawdown you should expect at a given confidence level, which is the right way to set a stop-out.

Caveats

Assumes normal, independent returns; real strategies with fat tails and serial correlation have worse drawdown properties. SSRN version linked.

Tags: risk, drawdown, stop-out, sharpe-ratio

Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.