dc.contributor.author Benhamou, Eric dc.date.accessioned 2019-05-15T10:38:44Z dc.date.available 2019-05-15T10:38:44Z dc.date.issued 2018 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/18910 dc.language.iso en en dc.subject Sharpe ratio en dc.subject Student distribution en dc.subject compounding effect on Sharpe en dc.subject AR(1) en dc.subject CramerRao bound en dc.subject.ddc 519 en dc.subject.classificationjel C.C1.C12 en dc.subject.classificationjel G.G1.G11 en dc.title Connecting Sharpe ratio and Student t-statistic, and beyond en dc.type Document de travail / Working paper dc.description.abstracten Sharpe ratio is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the excess return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected returns and the volatilities are unknown numbers and need to be estimated statistically.This means that the Sharpe ratio used by funds is subject to be error prone because of statistical estimation error. Lo (2002), Mertens (2002) derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic theory under several sets of assumptions (independent normally distributed - and identically distributed returns). In this paper, we provide the exact distribution of the Sharpe ratio for independent normally distributed return. In this case, the Sharpe ratio statisticis up to a rescaling factor a non centered Student distribution whose characteristics have been widely studied by statisticians. The asymptotic behavior of our distribution provides the result of Lo (2002). We also illustrate the fact that the empirical Sharperatio is asymptotically optimal in the sense that it achieves the Cramer Rao bound. We then study the empirical SR under AR(1) assumptions and investigate the effect ofcompounding period on the Sharpe (computing the annual Sharpe with monthly datafor instance). We finally provide general formula in this case of heteroscedasticity and autocorrelation. en dc.publisher.name Preprint Lamsade en dc.publisher.city Paris en dc.identifier.citationpages 23 en dc.relation.ispartofseriestitle Preprint Lamsade en dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-02012448 en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.ssrncandidate non en dc.description.halcandidate non en dc.description.readership recherche en dc.description.audience International en dc.date.updated 2019-04-30T12:04:20Z hal.person.labIds 989
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