Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution
•This paper extends Stein’s lemma for the multivariate extended skew-t distribution.•Efficient portfolios are located on a mean–variance–skewness efficient surface.•This surface is a direct extension of Markowitz’ efficient frontier.•The multivariate models introduced by Simaan admit the same proper...
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| Published in | European journal of operational research Vol. 234; no. 2; pp. 392 - 401 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
16.04.2014
Elsevier Sequoia S.A |
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| Online Access | Get full text |
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| Abstract | •This paper extends Stein’s lemma for the multivariate extended skew-t distribution.•Efficient portfolios are located on a mean–variance–skewness efficient surface.•This surface is a direct extension of Markowitz’ efficient frontier.•The multivariate models introduced by Simaan admit the same properties.•There are also mean–variance–skewness efficient hyper-surfaces.
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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| AbstractList | 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. [PUBLICATION ABSTRACT] •This paper extends Stein’s lemma for the multivariate extended skew-t distribution.•Efficient portfolios are located on a mean–variance–skewness efficient surface.•This surface is a direct extension of Markowitz’ efficient frontier.•The multivariate models introduced by Simaan admit the same properties.•There are also mean–variance–skewness efficient hyper-surfaces. 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. 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. |
| Author | Adcock, C.J. |
| Author_xml | – sequence: 1 givenname: C.J. surname: Adcock fullname: Adcock, C.J. email: c.j.adcock@shef.ac.uk organization: The University of Sheffield, Sheffield University Management School, 9, Mappin Street, Sheffield S1 4DT, UK |
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| Snippet | •This paper extends Stein’s lemma for the multivariate extended skew-t distribution.•Efficient portfolios are located on a mean–variance–skewness efficient... Recent advances in Stein's lemma imply that under elliptically symmetric distributions all rational investors will select a portfolio which lies on Markowitz'... |
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| SubjectTerms | Computation Finance Investment policy Mathematical analysis Mathematical models Multivariate analysis Multivariate statistics Operational research Portfolio investments Probability distribution Quadratic programming Random variables Studies Utility theory Vectors (mathematics) |
| Title | Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution |
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