AlphaAssayMinimum Track Record Length, explained — with a calculator
Minimum Track Record Length (MinTRL) answers the question every track record dodges: how many observations do you need before a given Sharpe ratio is statistically above a benchmark, at a confidence you choose? A Sharpe of 1.0 looks tradeable, but at 95% confidence it takes roughly 2.7 years of daily data to prove it clears zero — and a Sharpe of 0.5 takes over a decade. MinTRL turns „impressive-looking" into „provable yet, or not". It is the inverse of the Probabilistic Sharpe Ratio: instead of asking how confident you are at a given length, it asks how long you need for a target confidence. Bailey and López de Prado (2012). The calculator runs entirely in your browser.
The calculator
The default inputs (Sharpe 1.0, benchmark 0, 95% confidence) reproduce the 685-observation row in the table below — same formula, same defaults.
How long does a Sharpe ratio take to prove?
| observed Sharpe | benchmark SR* | confidence | MinTRL (daily) |
|---|---|---|---|
| 0.5 | 0 | 0.95 | ≈ 2,730 obs · 10.8 years |
| 1.0 | 0 | 0.95 | ≈ 685 obs · 2.7 years |
| 1.5 | 0 | 0.95 | ≈ 306 obs · 1.2 years |
| 2.0 | 0 | 0.95 | ≈ 173 obs · 0.7 years |
| 1.0 | 0.5 | 0.95 | ≈ 2,734 obs · 10.9 years |
The lesson is brutal and useful: a mediocre Sharpe over a short window is not evidence, however green the equity curve. Raising the bar you must beat (SR* from 0 to 0.5) explodes the history you need.
The formula, step by step
Step 1 — de-annualise your Sharpe and benchmark: ŜR = SR / √(periods per year).
Step 2 — the required length.
MinTRL = 1 + (1 − γ₃·ŜR + ((γ₄−1)/4)·ŜR²) · ( Z_α / (ŜR − SR*) )²,
where Z_α is the standard-normal quantile of your target confidence (0.95 → 1.645). The result
is a number of observations; divide by periods-per-year for calendar time.
Step 3 — the catch. If your Sharpe does not exceed the benchmark, no finite history proves it — the formula diverges, and the honest answer is „never, at this Sharpe". Skew and fat tails only make the required length longer.
Why does this end the „just give it more time" argument?
Because it puts a number on it. If your family has already spent its deflation budget and your Sharpe still needs eleven more years to clear zero, more time is not a plan. MinTRL, PSR and deflation are the same statistics from three angles, and all three run inside the AlphaAssay battery — which is why a fail can tell you to stop, not just to wait.