Stats › Backtesting et preuves › Drawdown maths
Recovery takes three times as long as the fall, whatever your Sharpe ratio
| Sharpe 1.0 | Sharpe 1.5 | |
|---|---|---|
| Expected annual profit | $10m | $15m |
| Annual standard deviation | $10m | $10m |
| Maximum quantile loss at 95% | $6,763,859 | $4,509,239 |
| Time to reach it | 0.676 years | 0.300 years |
| Total time under water | 2.706 years | 1.202 years |
| Ratio of the two | 3 to 1 | 3 to 1 |
Two worked examples at 95% confidence with monthly observations, assuming independent normally distributed profit and loss. Raising the Sharpe ratio from 1.0 to 1.5 cuts the worst expected loss by a third and cuts the time under water by more than half, but it does not change the three to one ratio between recovery and decline.
For a strategy with a Sharpe ratio of 1, the worst expected loss at 95% confidence arrives after 0.68 years and the strategy stays under water for 2.7 years. The ratio is three to one, and under the model's assumptions it does not depend on the Sharpe ratio at all.
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