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Andrew Lo's correction for the serial autocorrelation that inflates most hedge fund Sharpes.
Lo-adjusted Sharpe is Andrew Lo's 2002 correction to the standard Sharpe ratio that accounts for serial autocorrelation in returns. Hedge fund returns often exhibit positive autocorrelation due to stale pricing of illiquid assets, which artificially inflates Sharpe. The correction adjusts the denominator using the autocorrelation pattern.
Sharpe_Lo = Sharpe / sqrt(1 + 2·Σ(1−k/q)·ρ_k)SharpeLo = Sharpe / sqrt(1 + 2·Σk=1..q-1(1 − k/q)·ρk)The correction shrinks Sharpe when returns are positively autocorrelated and inflates Sharpe (slightly) when they are negatively autocorrelated. Most real-world Sharpe inflation comes from positive autocorrelation in illiquid assets.
Stale pricing makes everything look smoother than it is. If a fund holds illiquid real estate, private equity, or thinly-traded credit, its reported monthly returns will show artificial autocorrelation — losses leak out over multiple months instead of hitting in one. Volatility looks lower; Sharpe looks higher.
The Lo adjustment was made famous by its application to Bernie Madoff's books, which showed implausibly smooth returns consistent with no real strategy. Madoff's reported Sharpe was 2.5+; Lo-adjusted estimates were closer to 1.2.
A hedge fund reports a monthly Sharpe of 2.0. Lag-1 autocorrelation of monthly returns is 0.35; lag-2 is 0.15; later lags are noise.
For annualization (q=12), Lo correction factor ≈ sqrt(1 + 2·(0.917·0.35 + 0.833·0.15)) = sqrt(1 + 2·(0.321 + 0.125)) = sqrt(1.892) = 1.376
Sharpe_Lo = 2.0 / 1.376 = 1.45
The fund's "true" Sharpe is meaningfully lower than reported.
If your Lo-adjusted Sharpe is more than 20% below your reported Sharpe, the returns have meaningful autocorrelation and the original Sharpe is overstating skill.
Sharpe Ratio · Probabilistic Sharpe Ratio · Modigliani-squared (M²)
For funds with illiquid holdings, smooth-but-fake monthly returns, or strategies with positive serial correlation (mean-reverting strategies typically have negative autocorrelation and benefit from the adjustment).
Lo's 2002 paper uses up to q-1 lags where q is the annualization factor. For monthly returns annualized, that means 11 lags.
Yes — alongside standard Sharpe in the metrics panel. The gap between them is a signal of how much of the reported Sharpe was artifact.
Not always — strategies with negative autocorrelation (some mean-reversion systems) actually have artificially low standard Sharpe. Lo correction can raise their Sharpe.
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