Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

Advanced10 min read · updated 26 September 2026 · 8 sources

The deflated Sharpe ratio (DSR) answers a question that a measured Sharpe ratio on its own leaves open: how likely is it that the result reflects genuine skill rather than luck, a short history, skewed returns or the best of many variants tried? Here you will learn the building blocks: the standard error with skewness and kurtosis, the probabilistic Sharpe ratio, the minimum track record length and the haircut according to Harvey and Liu, each with a recalculated example.

Why a Sharpe ratio alone is not enough

A Sharpe ratio from historical returns is an estimate. Three things make it more uncertain than it looks: the history is short, the returns are not normally distributed, and the strategy shown is often the best of many tested. The article backtest overfitting shows how high the best Sharpe ratio turns out by chance alone when, in truth, none of the variants has any skill. This article goes one step further and calculates the probability that a specific Sharpe ratio lies above a threshold. Skewness, kurtosis and the number of trials all count.

The standard error with skewness and kurtosis

For independent, normally distributed returns, Lo (2002) derived the standard error of the Sharpe ratio. If the returns are skewed or have fat tails, two terms are added. Bailey and López de Prado (2012) use them in this form, which goes back to a derivation by Elmar Mertens; Opdyke (2007) derives the distribution in general for non-normally distributed returns:

For the normal distribution, γ₃ = 0 and γ₄ = 3; the numerator becomes 1 + SR̂² / 2, Lo's formula. Negative skewness and high kurtosis increase the standard error. Many strategies that regularly deliver small gains and occasionally large losses have exactly these properties.

Probabilistic Sharpe ratio

The probabilistic Sharpe ratio (PSR) of Bailey and López de Prado (2012) is the probability that the true Sharpe ratio lies above a threshold SR*, given the estimated Sharpe ratio, the length of the series, and the skewness and kurtosis:

Minimum track record length

Solving the PSR for T gives the minimum track record length (MinTRL): the number of periods after which a measured Sharpe ratio lies above the threshold with confidence 1 − α (Bailey and López de Prado 2012).

Deflated Sharpe ratio: accounting for many trials

The PSR assumes that only one strategy was tested. Bailey and López de Prado (2014) therefore replace the threshold with the Sharpe ratio that the best of N variants without any real edge would be expected to achieve. This threshold SR₀ depends on the number of independent trials and on the dispersion of their Sharpe ratios:

The article backtest overfitting gives the same approximation with the standard error 1 / √T; here you use the actual dispersion of the variants. Over ten years, assuming no edge, it is around 0.3 p.a., and the example uses this value.

In practice, the difficult part is the number N. Similar variants (such as moving averages over 9 and 10 months) are not independent; the effective number of trials is smaller than the number of runs. You estimate it by grouping similar variants into clusters. If you set N too low, you overestimate the DSR.

The Harvey and Liu haircut

Harvey and Liu (2015) take the route via multiple testing: they convert the Sharpe ratio into a t-statistic and a p-value, adjust the p-value for the number of tests and convert back. The percentage reduction is called the haircut. There are several methods for the adjustment, such as Bonferroni, Holm or methods for the false discovery rate; the example shows Bonferroni, the simplest variant.

Advanced: assumptions and extensions

• Independent returns: all the formulas assume that returns are independent and identically distributed. With autocorrelation (smoothed valuations, trend strategies), even annualising with √12 overstates the Sharpe ratio; Lo (2002) gives a correction factor (see Sharpe ratio).
• Data frequency: according to Bailey and López de Prado (2012), series with negative skewness and high kurtosis benefit from reporting results at the highest frequency at which returns are still independent.
• Uncertain moments: skewness and, above all, kurtosis can only be estimated roughly from 120 months; a single crash month changes them considerably. Calculate PSR and MinTRL with several plausible values.
• Comparing two strategies: whether one Sharpe ratio is significantly above another is tested with a test for the difference that takes the correlation of the two return series into account (Opdyke 2007).
• Minimum length of a backtest: Bailey et al. (2014) show how quickly a high Sharpe ratio arises in a backtest when there are many variants, and derive the minimum length a backtest must have for a given number of variants.
• Measuring overfitting directly: the probability of backtest overfitting of Bailey et al. (2016) checks how often the best variant in one section of the data ends up at or below the median in another. It does not need a number of independent trials, only the returns of all variants.

What research shows

Lo (2002) showed that hedge fund Sharpe ratios can be overstated by up to 65% because of autocorrelated monthly returns, and that rankings change considerably after the correction. Bailey and López de Prado (2012) introduced the PSR and MinTRL and used them to show that series with negative skewness and fat tails need a longer history. Bailey and López de Prado (2014) added the correction for selection bias under multiple testing to arrive at the deflated Sharpe ratio. For factor research, Harvey et al. (2016) called for t-statistics above 3.0 rather than above 2, and Harvey and Liu (2015) carried the idea over to individual backtests with the haircut and a profit hurdle. All these papers share the same message: without the number of trials and the length of the series, a Sharpe ratio cannot be put into context.

Limitations and common mistakes

• Using annualised values: all the formulas require the Sharpe ratio per period. If you plug in 1.0 instead of 0.289, you massively overestimate the PSR.
• Excess kurtosis instead of kurtosis: the formulas need the kurtosis, which is 3 for the normal distribution. If you use the excess kurtosis, the standard error comes out too small.
• Forgetting discarded variants: N includes all tested variants, including those you did not show, and also those of your colleagues if everyone is researching on the same data.
• Treating the 95% threshold as a law of nature: the threshold is a convention. A DSR of 88% does not mean the strategy is worthless, but that the data does not reliably prove skill.
• Looking only at the Sharpe ratio: a high PSR says nothing about drawdowns, capacity or costs. Also check the maximum drawdown and skewness and kurtosis.

How Portfolio Lab calculates

In the Backtest results, the Overfitting check tab calculates for each portfolio the standard error of the Sharpe ratio with skewness and kurtosis, the PSR, the minimum track record length and the DSR. You enter the number of variants tried and the dispersion of their Sharpe ratios yourself; in addition, there is the probability of backtest overfitting across the portfolios. How this is calculated in detail is described in the overfitting check methodology. The metrics table in the backtest also shows the ingredients: the annualised Sharpe ratio from the excess returns per period, the skewness and the “Excess kurtosis” of the period returns, and the start and end dates. For the formulas, divide the Sharpe ratio by √12 for monthly data (by √252 for daily data) and add 3 to the excess kurtosis. How the values are derived is described in the metrics methodology. For out-of-sample tests, Optimisation in “Rolling (walk-forward)” mode estimates the weights using only data up to each point in time; the factor statistics under Factors show a t-statistic for each factor premium.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.