Sharpe ratios are much used in finance, yet cannot be measured directly because price returnsare non-Gaussian . On the other hand, the number of records of a discrete-time random walk in a given time-interval follows a Gaussian distribution provided that its increment distribution has finite variance. As as consequence, record statistics of uncorrelated, biased, random walks provide an attractive new estimator of Sharpe ratios  . First, I derive an approximate expression of the expected number of price records in a given time interval when the increments follow Student's t distribution with tail exponent equal to 4 in the limit of vanishing Sharpe ratios . Remarkably, this expression explicitly links the expected record numbers to Sharpe ratios and and suggests to estimate the average Sharpe ratio from record statistics. Numerically, the asymptotic efficiency of a permutation estimator of Sharpe ratios based on record statistics is several times larger than that of the t-statistics for uncorrelated returnswith a Student's t distribution with tail exponent of 4.
Estimating Sharpe ratios requires the computation of the moments of price returns, which is problematic because the latter are heavy-tailed . On the other hand, the total duration of drawdowns of a time series, or equivalently the number of its upper price records, follows a Gaussian distribution that depends on its true Sharpe ratio. Reversely, this suggests an estimator of Sharpe ratios based the total duration of drawdowns. Its efficiency is several times larger than moment-based estimators for symmetric heavy-tailed price returns. Such type of data also leads mechanically to a larger number of expected price records, hence, to a smaller duration of drawdowns. Thus, for a given number of records, the absolute value of the estimated Sharpe ratios is smaller when price returns are heavy tailed. This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions, which implies that using them for investment decisions may amplify large price returns . 
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Sharpe ratios are much used in finance, yet cannot be measured directly because price returnsare non-Gaussian
Estimating Sharpe ratios requires the computation of the moments of price returns, which is problematic because the latter are heavy-tailed
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number of records of a discrete-time random walk in a given time-interval
total duration of drawdowns of a time series, or equivalently the number of its upper price records,
R
provided that its increment distribution has finite variance. As as consequence, record statistics of uncorrelated, biased, random walks provide an attractive new
that depends on its true Sharpe ratio. Reversely, this suggests an
A
based the total duration of drawdowns. Its efficiency is several times larger than moment-based estimators for symmetric heavy-tailed price returns. Such type of data also leads mechanically to a larger number of expected price records, hence, to a smaller duration of drawdowns. Thus, for a given number of records, the absolute value of the estimated Sharpe ratios is smaller when price returns are heavy tailed. This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions, which implies that using them for investment decisions may amplify large price returns
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First, I derive an approximate expression of the expected number of price records in a given time interval when the increments follow Student's t distribution with tail exponent equal to 4 in the limit of vanishing Sharpe ratios . Remarkably, this expression explicitly links the expected record numbers to Sharpe ratios and and suggests to estimate the average Sharpe ratio from record statistics. Numerically, the asymptotic efficiency of a permutation estimator of Sharpe ratios based on record statistics is several times larger than that of the t-statistics for uncorrelated returnswith a Student's t distribution with tail exponent of 4.