How to Compute a Deflated Sharpe Ratio

Gather the five inputs

The deflated Sharpe ratio needs five numbers: the observed Sharpe, the sample length in periods, the return skewness, the return excess kurtosis, and the trial count. The first four describe the backtest you ran; the fifth describes the search that produced it. Missing the trial count is the most common failure, and without it the deflation cannot be done honestly. Assemble all five before computing anything.

Use the Sharpe at the same frequency as your return observations. Mixing an annualized Sharpe with a daily sample length corrupts the standard error.

Use the Deflated Sharpe Ratio Calculator: Bailey & López de Prado deflated Sharpe — corrects observed Sharpe for selection bias across K trials. Reports deflated Sharpe, PSR (probability of skill).

Count the trials, including informal ones

The trial count is the number of distinct strategies you evaluated against the data: every grid point, every entry rule, every universe filter, every threshold you nudged after seeing a result. Informal tuning counts. If you changed a parameter because the backtest looked better, that is a trial. The deflated Sharpe uses the trial count to estimate the maximum Sharpe you would expect from pure luck across that many attempts, which becomes the bar your real Sharpe must clear.

When unsure, overcount rather than undercount. A conservative trial count makes the deflation stricter, which is the safe direction.

Use the Backtest Overfitting Score: Upload a backtest trade log and compute Probability of Backtest Overfitting (PBO), Deflated Sharpe Ratio, and the odds your edge survives live trading.

Compute the expected maximum Sharpe from luck

Given the trial count, the formula estimates the expected maximum Sharpe ratio you would see by selecting the best of that many independent random strategies. This benchmark grows with the number of trials: search a thousand variants and the best one will have a respectable Sharpe by chance alone. The deflated Sharpe measures how far your observed Sharpe sits above this luck benchmark, not above zero.

The luck benchmark rises fast at first and then slowly. Going from 1 to 100 trials matters far more than from 100 to 200, which is why the first few sweeps are the most damaging.

Adjust for skew and kurtosis

The standard error of a Sharpe ratio is not the textbook value when returns are skewed or fat-tailed, which financial returns almost always are. Negative skew and high kurtosis inflate the true uncertainty of the Sharpe estimate. The deflated Sharpe plugs the third and fourth moments into the standard error so the test reflects the actual shape of your returns rather than assuming a normal distribution that does not hold.

Strategies that sell tail risk often show high Sharpe with strong negative skew. The skew adjustment is exactly what catches these flattering-but-fragile backtests.

Read the probability and decide

The output is a probability between zero and one: the chance the true Sharpe is positive given the search you performed. The conventional threshold to consider a strategy worth capital is 0.95. A backtest with a raw Sharpe of 1.5 can deflate well below 0.95 once a few hundred trials and fat tails are priced in. If you clear the bar, the edge is plausibly real; if you do not, the result is most likely a selection artifact.

Treat a marginal value near 0.95 as a fail, not a pass. The cheapest way to raise it is more data or fewer trials, never a higher raw Sharpe found by searching harder.