How autocorrelation inflates a reported Sharpe

Question

A strategy reports monthly returns with first-order autocorrelation $\rho = 0.2$ (returns are somewhat smoothed, common in illiquid or marked-to-model books). The manager annualizes the monthly Sharpe the usual way, by multiplying by $\sqrt{12}$ .

Why does positive autocorrelation inflate the reported annual Sharpe, and what is the corrected number?

Accepted Answer

Where the naive factor comes from. The \sqrt{12} rule assumes monthly returns are independent, so the variance of a 12-month sum is 12 times the monthly variance, and volatility scales by \sqrt{12}. But if returns are positively autocorrelated, the annual variance is larger than 12 monthly variances (the returns reinforce rather than cancel), so true annual volatility is higher and the true Sharpe is lower than \sqrt{12} times the monthly figure. Lo's correction. Andrew Lo (2002) gives the right annualization factor for a q-period Sharpe under autocorrelation: \eta(q) = \frac{q}{\sqrt{q + 2\s…

How autocorrelation inflates a reported Sharpe

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