A heavy 0.4 autocorrelation halves a naive Sharpe of 2.5

Question

A real-estate fund reports monthly returns with a lag-1 autocorrelation of 0.4, and its naively annualized Sharpe ratio, computed as if returns were independent, is 2.5.

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

Accepted Answer

The setup. A lag-1 autocorrelation of 0.4 is high, typical of appraisal-based or infrequently marked assets, and it heavily smooths reported returns, badly understating true volatility. 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 = 0.4: \sqrt{\frac{0.6}{1.4}} = \sqrt{0.429} \approx 0.655,\qquad SR{	ext{true}} \approx 2.5 	imes 0.655 \approx 1.64. Interpretation. A glittering naive Sharpe of 2.5 collapses to about 1.6 once the heavy smoothing…

A heavy 0.4 autocorrelation halves a naive Sharpe of 2.5

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