A robust and efficient estimator of Sharpe ratios based on price records
Sharpe ratios are much used in finance, yet cannot be measured directly because price returns are 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 returns with a Student's t distribution with tail exponent of 4.
Year of publication: |
2015-05
|
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Authors: | Challet, Damien |
Institutions: | arXiv.org |
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