A mild 0.1 autocorrelation on a naive Sharpe of 1.2

Question

A strategy has monthly returns with a lag-1 autocorrelation of 0.1, and its naively annualized Sharpe ratio, computed as if returns were independent, is 1.2.

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

Accepted Answer

The setup. Even a mild positive autocorrelation slightly understates volatility and slightly overstates the Sharpe. The correction. For a first-order autocorrelation pattern with lag-1 correlation ho, the honest Sharpe is SR{	ext{true}} \approx SR{	ext{naive}} 	imes \sqrt{\frac{1-ho}{1+ho}}. Plug in the numbers. With ho = 0.1: \sqrt{\frac{0.9}{1.1}} = \sqrt{0.818} \approx 0.905,\qquad SR{	ext{true}} \approx 1.2 	imes 0.905 \approx 1.09. Interpretation. With only a mild 0.1 autocorrelation, the Sharpe barely moves, from 1.2 down to about 1.09, a haircut of under 10%. The correctio…

A mild 0.1 autocorrelation on a naive Sharpe of 1.2

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