Validation

DSR

Deflated Sharpe Ratio

Why

The more trials you run, the easier it is to meet a Sharpe that looks high. First compute the highest Sharpe that pure-noise trials are expected to hit. Then see how far the observed Sharpe sits above that luck line.

Formula

The Deflated Sharpe Ratio of Bailey and López de Prado, 2014. The input is the per-fill net percent on the discovery-sample user book. The sealed sample is not included.

Percent of one fill

Cash = (exit price − entry price) × quantity × contract multiplier − fee cash − funding cash
The price term for a short is the opposite

r = this fill's cash / equity before this fill
Reported percent = r × 100

Fees: taker 0.05 and maker 0.02 are percentage points. Cash = notional × rate / 100. Slippage of 10 basis points is applied to the fill price. Funding is 0.0001 per 8 hours, paid by a long and received by a short.

Observed Sharpe

SR = mean(r) / std(r)

std is the sample standard deviation. The denominator is T − 1. T is the number of fills. It is not annualized. It is not divided again by the notional.

Independent trials

N = ρ + (1 − ρ) × K

K is the number of tries in the entry family. ρ is the average correlation among those tries. When that family cannot be estimated, N is recorded as 1. The raw grid count is not used, and N is not divided by 30 again.

The luck line

γ ≈ 0.5772156649
V = 1 / (T − 1)

SR₀ = √V × ( (1 − γ) × Φ⁻¹(1 − 1/N) + γ × Φ⁻¹(1 − 1/(N × e)) )

Φ⁻¹ is the quantile function of the standard normal. e is the base of the natural logarithm. When N ≤ 1, SR₀ = 0. When the expression above is negative, it is floored at 0.

The adjusted probability

DSR = Φ( (SR − SR₀) × √(T − 1) / √(1 − γ₃×SR + (γ₄ − 1)/4 × SR²) )

Φ is the cumulative distribution function of the standard normal. γ₃ is the skewness of this series of r. γ₄ is the kurtosis. The kurtosis of a normal distribution is 3. The SR in the denominator is the same observed Sharpe as the SR in the numerator.

When SR₀ is replaced by 0, the same expression is the probabilistic Sharpe without a trial adjustment. The version that deducts the trials is the DSR.

When there are fewer than 2 fills, the variance is 0, or a price is not a finite number, this row has no DSR. It is not recorded as 0.