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dc.contributor.authorBenhamou, Eric
dc.date.accessioned2019-05-15T10:38:44Z
dc.date.available2019-05-15T10:38:44Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18910
dc.language.isoenen
dc.subjectSharpe ratioen
dc.subjectStudent distributionen
dc.subjectcompounding effect on Sharpeen
dc.subjectAR(1)en
dc.subjectCramerRao bounden
dc.subject.ddc519en
dc.subject.classificationjelC.C1.C12en
dc.subject.classificationjelG.G1.G11en
dc.titleConnecting Sharpe ratio and Student t-statistic, and beyonden
dc.typeDocument de travail / Working paper
dc.description.abstractenSharpe 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.namePreprint Lamsadeen
dc.publisher.cityParisen
dc.identifier.citationpages23en
dc.relation.ispartofseriestitlePreprint Lamsadeen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02012448en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-04-30T12:04:20Z
hal.person.labIds989


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