Palashvan reports a monthly Sharpe ratio of 0.35, annualised to 1.21 with the square root of 12, but its monthly returns have a lag-one autocorrelation of 0.4 because illiquid positions are marked slowly. What is the corrected annual Sharpe, and what does the smoothing hide?

The honest annual Sharpe ratio is about 0.83, not 1.21: the smoothing hides roughly a third of the risk-adjusted return. With autocorrelation of 0.4, a year's variance is 2.15 times what twelve independent months would give, so annual volatility is about 10.2%, not 6.93%. Unsmoothing the returns first gives a similar 0.79. Smoothing also hides drawdowns, market exposure and the timing of losses.

Picture a thermometer that reports the average of today and the past few days instead of today's reading. A sudden cold snap shows up as a gentle slide over a week, so each day's change looks small, and anyone who scaled the daily changes to guess the yearly range would underestimate it. Slow marking does the same to a fund's returns: a loss is booked across several months, so each month looks calm while the year is not. The square root rule assumes each month is independent, so that variances add: twelve months give twelve monthly variances. When this month resembles last month, the covariances between months add as well, and they are positive.

Work it through. With 0.4 at lag one, 0.16 at lag two and so on, the covariance terms add 13.8 monthly variances to the twelve. The year's variance is 2.15 times the naive figure, so annual volatility is 1.47 times larger: about 10.2% rather than 6.93%. The mean is unaffected, still 8.4% a year, so the Sharpe ratio becomes 8.4 over 10.2, about 0.83. That removes 32% of the headline. The autocorrelation is no accident of sampling: with 96 months its standard error is about 0.10, so 0.4 sits four standard errors from zero.

Cross-check by undoing the smoothing. If each reported return is a blend of this month's true return and last month's reported one, with weight 0.4 on the past, the true returns are more volatile than the reported ones by the square root of (1 + 0.4) / (1 - 0.4), a factor of 1.53. Recover the true series, annualise it with the plain square root rule, and the Sharpe is 0.79, close to the 0.83 from the variance formula. Two methods built on different assumptions landing near 0.8 is a better answer than either alone.

Three things, each worth more to an allocator than the Sharpe itself. Drawdowns are understated, because a true 8% fall that is booked over four months never shows as one bad month. Market exposure is understated, because a regression of this month's fund return on this month's market return misses the part of the fall that is booked next month; adding lagged market returns to the regression usually shows a much larger total beta. And investors who redeem after a crash leave at a stale, too high price, which transfers value from those who stay. The test asked for one number, but the reason the number matters is that smoothing makes an illiquid fund look like a low-risk one.

Report the corrected Sharpe of about 0.83 with the method, and the annual volatility of about 10%. Ask for the regression of fund returns on current and lagged market returns, and for the worst rolling twelve-month return, not the worst single month. The limitation to state: the correction assumes autocorrelation decays geometrically from 0.4, and a fund whose marks are stale in a crash, when dealer quotes dry up, may be smoother exactly when it matters, so 0.83 is a ceiling as much as an estimate.