Deflated Sharpe ratio calculator
Inputs and results
Enter each figure per period: one period is the interval of one return in the track record, such as a day or a month. The default inputs are the worked example of the DSR paper.
The inputs in the link were not read, so the fields keep the paper's example. Each fault is listed below.
Results
- Annual Sharpe ratio, SR · sqrt(periods per year)
- PSR at the benchmark SR*
- MinTRL, in observations
- MinTRL, rounded up to the next observation
- MinTRL, in years
- Standard deviation of the trials' Sharpe ratios, σ(SR) = sqrt(V), per period
- σ(SR) per year, σ(SR) · sqrt(periods per year)
- SR0, the expected maximum Sharpe ratio of N trials with no skill, per period
- DSR, the PSR at the benchmark SR0
Assumptions behind the DSR
- Null dispersion V
- Number of trials
- How N was counted
- Version of the method
Each field needs a number, except V, which can be left empty.
T must be at least 2 observations.
Kurtosis must be at least 1 + skewness². Normal returns have kurtosis 3, an excess kurtosis of 0.
For these inputs, 1 − γ3 · SR + (γ4 − 1) / 4 · SR² is 0 or negative, so PSR, MinTRL and DSR are not defined.
The confidence level must lie strictly between 0.5 and 1.
MinTRL is defined when SR exceeds SR*. With SR at or under SR*, no track record length reaches the confidence level.
N must be an integer of at least 1.
V must be 0 or positive, or left empty.
Periods per year must be a positive number.
The note on how N was counted takes at most 120 characters, without control or text-direction characters.
Link to these inputs
The link carries the numbers in the fields above, the note on N and the version of the method in its address. It holds no return series.
Sensitivity of the DSR to N
With the inputs above and V = 0.002 per period, the DSR is 0.999997 at N = 1, 0.9004 at the entered N = 100 (the marked point), and 0.3389 at N = 10,000. SR0 rises with N, so the DSR falls as N grows.
| N | SR0 per period | DSR |
|---|---|---|
| 1 | 0.0000 | 0.999997 |
| 2 | 0.0232 | 0.9999 |
| 5 | 0.0533 | 0.9986 |
| 10 | 0.0704 | 0.9939 |
| 20 | 0.0850 | 0.9816 |
| 50 | 0.1018 | 0.9462 |
| 100 (entered) | 0.1132 | 0.9004 |
| 200 | 0.1237 | 0.8374 |
| 500 | 0.1365 | 0.7314 |
| 1,000 | 0.1456 | 0.6399 |
| 2,000 | 0.1542 | 0.5449 |
| 5,000 | 0.1649 | 0.4229 |
| 10,000 | 0.1727 | 0.3389 |