Correct a naive Sharpe of 1.8 for a 0.25 autocorrelation

Question

A strategy has monthly returns with a lag-1 autocorrelation of 0.25, and its naively annualized Sharpe ratio, computed as if returns were independent, is 1.8.

Roughly what is the honest Sharpe ratio once you correct for the autocorrelation?

Accepted Answer

The setup. A lag-1 autocorrelation of 0.25 smooths the reported returns, understating volatility and inflating the Sharpe. The correction. For a first-order autocorrelation pattern with lag-1 correlation ho: SR{	ext{true}} \approx SR{	ext{naive}} 	imes \sqrt{\frac{1-ho}{1+ho}}. Plug in the numbers. With ho = 0.25: \sqrt{\frac{0.75}{1.25}} = \sqrt{0.6} \approx 0.775,\qquad SR{	ext{true}} \approx 1.8 	imes 0.775 \approx 1.39. Interpretation. A naive Sharpe of 1.8 becomes about 1.4 after correcting for a moderate 0.25 autocorrelation. The correction factor of 0.775 sits neatly betwe…

Correct a naive Sharpe of 1.8 for a 0.25 autocorrelation

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