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

C.J. Adcock

European Journal of Operational Research, 2014, vol. 234, issue 2, 392-401

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.

Keywords: Finance; Multivariate statistics; Utility theory (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:234:y:2014:i:2:p:392-401

DOI: 10.1016/j.ejor.2013.07.011

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