 The large-sample distribution of the maximum Sharpe ratio with and without short salesRoss Maller, Steven Roberts and Rabee Tourky Journal of Econometrics, 2016, vol. 194, issue 1, 138-152 Abstract: In the Markowitz paradigm the portfolio having maximum Sharpe ratio is optimal. Previously the large sample distribution of this statistic has been calculated when short sales are allowed and sample returns and covariance matrix are asymptotically normally distributed. This paper considers the more complex situation when short sales are not allowed, and provides conditions under which the maximum Sharpe ratio is asymptotically normal. This is not always the case, as we show, in particular when the returns have zero mean. For this situation we obtain upper and lower asymptotic bounds (in distribution) on the possible values of the maximum Sharpe ratio which coincide when the returns are asymptotically uncorrelated. We indicate how the asymptotic theory, developed for the case of no short sales, can be extended to handle a more general class of portfolio constraints defined in terms of convex polytopes. Via simulations we examine the rapidity of approach to the limit distributions under various assumptions. Keywords: Optimal portfolio; Maximum Sharpe ratio; Asymptotic distribution; Asymptotic normality; Short sales (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:194:y:2016:i:1:p:138-152 DOI: 10.1016/j.jeconom.2016.04.003 Access Statistics for this article Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson More articles in Journal of Econometrics from Elsevier |
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