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Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution

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  • Adcock, C.J.
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    Abstract

    Recent advances in Stein’s lemma imply that under elliptically symmetric distributions all rational investors will select a portfolio which lies on Markowitz’ mean–variance efficient frontier. This paper describes extensions to Stein’s lemma for the case when a random vector has the multivariate extended skew-Student distribution. Under this distribution, rational investors will select a portfolio which lies on a single mean–variance–skewness efficient hyper-surface. The same hyper-surface arises under a broad class of models in which returns are defined by the convolution of a multivariate elliptically symmetric distribution and a multivariate distribution of non-negative random variables. Efficient portfolios on the efficient surface may be computed using quadratic programming.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 234 (2014)
    Issue (Month): 2 ()
    Pages: 392-401

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    Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:392-401

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    Web page: http://www.elsevier.com/locate/eor

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    Keywords: Finance; Multivariate statistics; Utility theory;

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