Autocorrelation-adjusted Sharpe calculator
How does positive autocorrelation change a Sharpe ratio scaled over twelve periods?
With a per-period Sharpe of 0.1, square-root scaling over 12 periods gives 0.346. If adjacent returns have a lag-one correlation of 0.2 under an AR(1) model, Lo's aggregation formula lowers the twelve-period figure to 0.288.
Annualize a periodic Sharpe ratio with a stated autocorrelation and horizon using Lo's aggregation identity. Inspect AR(1) dependence over a horizon.
Aggregation under serial dependence
The model assumes a stationary AR(1) return process whose lag-k correlation is rho to the power k. The periodic mean and variance are treated as known estimates.
SR(q) = q × SR(1) / sqrt(q + 2 sum[k=1..q−1] (q−k) rho^k)Positive serial correlation raises aggregated variance and lowers the horizon Sharpe relative to square-root-of-time scaling. Negative correlation reverses that comparison.
Twelve-period sensitivity check
For a per-period Sharpe of 0.1, rho = 0, and q = 12, the result is 0.346410. Setting rho = 0.2 reduces it to 0.287885 because adjacent returns move together.
The ordinary square-root rule applies when all nonzero-lag covariances vanish. The AR(1) coefficient exposes the dependence assumption hidden by treating monthly returns as independent observations. A positive coefficient matters most when the horizon contains many adjacent observations. A negative coefficient can raise the converted ratio, although a strongly negative value should prompt a check of the sampling and pricing process. Enter the periodic Sharpe directly: do not enter an annualized figure, or the horizon effect will be applied twice. The output is a ratio for a chosen aggregation horizon; it does not measure whether the estimated mean differs from zero. For inference, the sample size, higher moments and uncertainty of the autocorrelation estimate must also be considered. As a sensitivity check, compare zero, modest positive and modest negative rho while keeping the same periodic Sharpe.
What this conversion leaves out
The output converts a Sharpe ratio across horizons; it supplies no confidence interval for the estimate. An AR(1) model may miss long memory, volatility clustering and changing correlation.
Lo's derivation
Lo, A. W. (2002), The Statistics of Sharpe Ratios, Financial Analysts Journal 58(4), 36–52. The page uses his time-aggregation identity with AR(1) lag correlations. Original or institutional source.
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To cite the autocorrelation-adjusted Sharpe calculator in a paper, a report or a post, copy the reference below. Its address is https://stochastly.com/tools/autocorrelation-adjusted-sharpe-calculator.
Stochastly (2026). Autocorrelation-adjusted Sharpe calculator [web calculator]. https://stochastly.com/tools/autocorrelation-adjusted-sharpe-calculatorThe method behind the autocorrelation-adjusted Sharpe calculator comes from the paper below: cite that paper for the method, and the reference above for the autocorrelation-adjusted Sharpe calculator itself.
Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal 58(4), 36-52.