The deflated Sharpe ratio
A Sharpe ratio does not know how many times you tried. The deflated Sharpe, from Bailey and Lopez de Prado, puts that number into the arithmetic, along with the length of the record and the shape of the returns. It usually turns an impressive figure into an ordinary one.
What it needs, and which input people get wrong
Four inputs: the observed Sharpe, the length of the track record, the skew and kurtosis of the returns, and the number of trials. The first three come out of your data. The fourth comes out of your memory, and that is the problem.
The trial count means every variant you evaluated, including the ones abandoned within seconds. A parameter sweep of twelve lookbacks by five thresholds is sixty trials, not one, even if you only looked closely at the winner. Reconstructing the figure afterwards always undercounts, which is why the honest version of this number has to be logged while you work.
Some implementations go further and estimate an effective number of trials, on the grounds that sixty near-identical variants of one idea are not sixty independent bets. That is the more defensible treatment, and it is rarer.
The bar rises with the search
The dominant term is the multiple-testing correction, and you can apply it by hand. Under a Bonferroni correction at 5 percent, this is the t-statistic a result must clear for a given number of candidates tested. Computed at build time, not quoted.
| Variants tested | Required t-statistic |
|---|---|
| 1 | 1.96 |
| 10 | 2.81 |
| 50 | 3.29 |
| 200 | 3.66 |
| 1,000 | 4.06 |
| 5,000 | 4.42 |
How much search your result can absorb
Your t-statistic is roughly the Sharpe times the square root of the number of years. Set that against the table above and you get the number of variants your result would survive. This is the single most sobering calculation in backtesting.
| Annual Sharpe | Years | t-stat | Survives up to |
|---|---|---|---|
| 0.8 | 3 | 1.39 | 1 variants |
| 1.0 | 3 | 1.73 | 1 variants |
| 1.0 | 10 | 3.16 | 31 variants |
| 1.5 | 5 | 3.35 | 62 variants |
| 2.0 | 3 | 3.46 | 93 variants |
| 2.5 | 2 | 3.54 | 122 variants |
Read the third row. A ten-year record with a Sharpe of 1.0 stops being significant once you admit to about 31 variants. A serious parameter sweep passes that in an afternoon, which is why the trial count is not a technicality.
Who ships it
3 of the 20 platforms assessed report a deflated or probabilistic Sharpe: Minerva, QuantConnect, VectorBT. Of those, 2 also feed a multiple-testing correction into it, which is the part that does the work. A probabilistic Sharpe computed with a trial count of one is only correcting for track length.
Assessed from vendor documentation on ourpublished rubric.
What to do with it
- Log trials as you go. One line per variant. This single habit is worth more than any tool on this page.
- Compute your t-statistic. Sharpe times the square root of years. Compare it to the bar for your trial count.
- Check the shape of the returns. Negative skew and fat tails deflate hard. If your equity curve is a smooth line with occasional cliffs, the raw Sharpe is flattering you.
- Do not tune to the deflated number. Optimising against your own validation metric turns the metric into another thing you overfitted.
Frequently asked questions
What does the deflated Sharpe ratio actually do?
It asks a different question from the raw Sharpe. Instead of how good did this look, it asks how likely is a result this good to appear by chance, given how many candidates were tested, how long the record is, and how skewed and fat-tailed the returns are. The output is a probability that the true Sharpe is above the benchmark, not a return figure.
What inputs does it need?
The observed Sharpe, the length of the record, the skew and kurtosis of the returns, and the number of trials. The last one is the one people get wrong, because it means every variant tested and discarded, not just the ones written down.
Why does skew matter?
A strategy that makes small gains steadily and occasionally loses a lot has negative skew and fat tails. Its Sharpe overstates its quality, because the ratio only sees mean and standard deviation. The deflation penalises exactly this shape, which is why option-selling and carry strategies deflate hardest.
Is a deflated Sharpe above 0.95 a green light?
It means the result clears one specific bar, that the true Sharpe is above the benchmark with 95 percent confidence given the declared trial count. It says nothing about capacity, costs at your size, regime change, or whether your trial count was honest. It is a filter that removes obvious luck, not a verdict.
Can I compute it without a platform?
Not exactly, but you can get most of the value from the trial-count part alone, which is the dominant term. Compute your t-statistic as Sharpe times the square root of years, then compare it against the corrected bar for the number of variants you tested. The table on this page is computed from that arithmetic. Of the 20 platforms assessed here, 3 ship a deflated or probabilistic Sharpe and 2 feed a trial count into it.
Related
Educational content only, not investment advice. The tables illustrate published statistics and are not a judgement on any specific strategy.