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Statistikk › Backtesting og evidens › The haircut

A ten year backtest replicates about 30% of its Sharpe ratio, and the parameter count is why

444 parameters|real data, 9% replicatedIn sample: 3.6Out of sample: 0.30.33 parameters|real data, 68% replicatedIn sample: 0.7Out of sample: 0.50.5444 parameters|simulated, 38% replicatedIn sample: 8.2Out of sample: 3.13.13 parameters|simulated, 0.9 to 0.6In sample: 0.9Out of sample: 0.60.6I utvalgetUtenfor utvalget

Sharpe ratios in sample and out of sample for the same twelve commodity futures and the same 36 signals, fitted two ways. Data May 1998 to December 2023, ten years in sample and three out, with ridge regularisation. The simulation rows are 10,000 realisations of the same setup.

The common rule is to halve an in-sample result. One derivation puts the expected replication ratio of a ten year backtest at 30%. On real commodity data a full regression with 444 parameters replicated 9% of its in-sample Sharpe while a three parameter panel replicated 68%.

About 30%Expected replication ratio of a ten year backtest
9%Replication ratio, 444 parameter model on real commodity data
68%The same data with a three parameter panel model
3.6 against 0.3In-sample Sharpe of the 444 parameter model against its out of sample Sharpe

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