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Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution

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  • C. Adcock

Abstract

The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar mean-variance frontier, and which may be implemented using quadratic programming. Copyright Springer Science+Business Media, LLC 2010

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  • C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:221-234:10.1007/s10479-009-0586-4
    DOI: 10.1007/s10479-009-0586-4
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    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
    3. Landsman, Zinoviy, 2006. "On the generalization of Stein's Lemma for elliptical class of distributions," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1012-1016, May.
    4. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. C. J. Adcock, 2005. "Exploiting skewness to build an optimal hedge fund with a currency overlay," The European Journal of Finance, Taylor & Francis Journals, vol. 11(5), pages 445-462.
    7. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    8. Jones, M. C., 2002. "Marginal Replacement in Multivariate Densities, with Application to Skewing Spherically Symmetric Distributions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 85-99, April.
    9. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    10. Landsman, Zinoviy & Neslehová, Johanna, 2008. "Stein's Lemma for elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 912-927, May.
    11. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    12. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    13. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    14. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    15. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    16. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    17. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    18. Liu, Jun S., 1994. "Siegel's formula via Stein's identities," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 247-251, October.
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