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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.

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.

Suggested Citation

  • Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.
  • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:392-401
    DOI: 10.1016/j.ejor.2013.07.011
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    Cited by:

    1. repec:eee:ecosta:v:3:y:2017:i:c:p:91-111 is not listed on IDEAS
    2. Yue, Wei & Wang, Yuping, 2017. "A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 124-140.
    3. repec:gam:jecnmx:v:5:y:2017:i:2:p:18-:d:97715 is not listed on IDEAS
    4. repec:eee:stapro:v:137:y:2018:i:c:p:297-303 is not listed on IDEAS
    5. Babaei, Sadra & Sepehri, Mohammad Mehdi & Babaei, Edris, 2015. "Multi-objective portfolio optimization considering the dependence structure of asset returns," European Journal of Operational Research, Elsevier, vol. 244(2), pages 525-539.
    6. Eling, Martin, 2014. "Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 45-56.
    7. repec:eee:ejores:v:263:y:2017:i:2:p:510-523 is not listed on IDEAS
    8. repec:eee:ejores:v:261:y:2017:i:2:p:606-612 is not listed on IDEAS
    9. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.

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