QUANTITATIVE TOOL
Bailey & López de Prado (2012). How many trading days do you need for your Sharpe Ratio to be statistically significant? The answer depends on your SR, return distribution, and confidence level.
— WHY IT MATTERS
A strategy showing SR = 1.5 over 30 days tells you almost nothing. The confidence interval is so wide that the true SR could be anywhere from 0 to 3. The Minimum Track Record Length tells you exactly how many trading days you need before your observed Sharpe becomes statistically distinguishable from your threshold.
— CALCULATOR
Your strategy's annualized Sharpe Ratio. Most brokers show this in your account stats. A typical good strategy is between 1.0 and 2.0.
What are you trying to prove? Leave 0 to test "am I profitable at all?". Use 0.5 to test "do I beat buying & holding the S&P 500?". Use 1.0 to test "do I have genuine skill?".
Measures if your returns lean left or right. 0 = symmetric. Negative = occasional large losses. Most strategies: between −1 and 0.
Measures how often extreme moves happen. 3 = normal. Above 3 = more extreme days than expected. Most strategies: between 3 and 6.
How sure you want to be. 0.95 (95%) is the standard in finance.
— RESULTS
Trading days required for the observed SR to be statistically significant at your chosen confidence level.
Verdict
Your track record is too short. You need more data before drawing conclusions.
SR variance factor
1.0345
Accounts for skewness and kurtosis. Higher = more uncertainty.
Z-score threshold
1.6449
Critical value for the chosen confidence level.
— CONFIDENCE INTERVAL
How many trading days you currently have.
95% confidence interval for the Sharpe Ratio.
[-0.997, 2.997]
SR standard error
1.0191
Interval half-width
±1.9974
PSR(0)
83.68%
Probability that the true SR > 0.
— METHODOLOGY
The standard error of the Sharpe Ratio depends on the sample length and the shape of the return distribution: σ(ŜR) = √[(1 − γ₃·SR + ((γ₄−1)/4)·SR²) / (T−1)]. More data shrinks this error.
The MinTRL inverts the PSR formula: instead of asking "is T enough?", it asks "what T do I need?" Given SR, SR*, and the confidence level α, we solve for the minimum T such that PSR(SR*) ≥ α.
Negative skewness and fat tails increase the SR standard error, which means you need more data. A strategy with normal returns (γ₃=0, γ₄=3) requires less data than one with left-tail risk and fat tails.
— FORMULAS
MinTRL = 1 + [(1 − γ₃·SR + ((γ₄−1)/4)·SR²) / (SR − SR*)²] × z²_α
Minimum number of observations for the observed SR to be statistically significant at confidence level α. Returns trading days.
σ(ŜR) = √[(1 − γ₃·SR + ((γ₄−1)/4)·SR²) / (T−1)]
Estimation uncertainty. Accounts for skewness (γ₃) and kurtosis (γ₄). Shrinks as T grows.
SR ± z_{α/2} × σ(ŜR)
The range within which the true Sharpe Ratio lies with probability α. Narrower intervals mean more reliable estimates.
PSR(SR*) = Φ[(ŜR − SR*) / σ(ŜR)]
Probability that the true SR exceeds the threshold SR*. MinTRL is the T at which PSR(SR*) = α.
— REFERENCE
Bailey, D.H. & López de Prado, M. (2012). "The Sharpe Ratio Efficient Frontier." Journal of Risk, 15(2). — Bailey, D.H. & López de Prado, M. (2014). "The Deflated Sharpe Ratio." The Journal of Portfolio Management, 40(5), 94–107.
— FAQ
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