Minimum Sample Size Required to Verify a Claimed Sharpe Ratio

Minimum Sample Size Formula

To determine how many observations are required to assess, with confidence level \(1 - \alpha\), that a trading strategy achieves a claimed target Sharpe ratio, the following approximation can be used (adapted from Aldridge, 2013):

\[n_{\min} = \left( \frac{q_{1 - \frac{\alpha}{2}}^{2}}{SR^{2}} \cdot m \right)\left( 1 + 0.5 \cdot \frac{SR^{2}}{m} \right)\]

where:

\(SR\) – Sharpe ratio for the period of interest (e.g., annual \(SR\));

\(n_{\min}\) – minimum number of observations required for a \(1 - \alpha\) confidence interval;

\(q_{1 - \frac{\alpha}{2}}\) – quantile of order \(1 - \frac{\alpha}{2}\) of standard normal distribution;

\(m\) – number of return observations per Sharpe ratio period.

Worked Example

If we want 90% confidence (\(1 - \alpha = 0.90\)) that a trading strategy attains a claimed yearly Sharpe ratio of 1.5, and returns are observed monthly (\(m = 12\)), then using \(q_{0.95} = 1.645\) the minimum required number of monthly observations is \(n_{\min} = 15.785\). This implies that the strategy should be tested for at least 16 months to verify the claimed Sharpe ratio with the intended confidence.

For a related approach to determining required sample size for strategy validation, see the G*Power-based method.

For a deeper treatment of the minimum sample size problem in backtesting, see Scientific Backtesting.

Reference

Aldridge, I. (2013). High-frequency trading: A Practical Guide to Algorithmic Strategies and Trading Systems (2nd ed.). John Wiley & Sons.