A 0.3 autocorrelation guts a naive Sharpe of 1.5

Question

A credit book has monthly returns with a lag-1 autocorrelation of 0.3, and its naively annualized Sharpe ratio, computed as if returns were independent, is 1.5.

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

Accepted Answer

Why the naive Sharpe is too high. A lag-1 autocorrelation of 0.3 means returns are smoothed: this month partly echoes last month, so the reported volatility understates the true risk, and the Sharpe is overstated. The correction. For a first-order autocorrelation pattern with lag-1 correlation ho, the honest Sharpe is the naive one scaled by the volatility-inflation correction: SR{	ext{true}} \approx SR{	ext{naive}} 	imes \sqrt{\frac{1-ho}{1+ho}}. Plug in the numbers. With ho = 0.3: \sqrt{\frac{0.7}{1.3}} = \sqrt{0.538} \approx 0.734,\qquad SR{	ext{true}} \approx 1.5 	imes 0.734 …

A 0.3 autocorrelation guts a naive Sharpe of 1.5

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