How much does smoothing inflate a Sharpe of 2.0?

Question

A fund holds illiquid positions whose monthly returns show a lag-1 autocorrelation of 0.2 (a sign of smoothed or stale marks). Its naively annualized Sharpe ratio, computed as if returns were independent, is 2.0.

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

Accepted Answer

Why smoothing inflates the Sharpe. Illiquid or stale marks make each month's return look partly like last month's, which is positive autocorrelation. Smoothed returns understate the true bumpiness of the strategy: the reported volatility is too low, so the reported Sharpe (return over volatility) is too high. The naive \sqrt{12} annualization silently assumes independent months and misses this. The correction. For returns following a simple first-order autocorrelation pattern with lag-1 correlation \rho (each lag k correlation being \rho^k), the true long-horizon volatility is larger than the…

How much does smoothing inflate a Sharpe of 2.0?

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