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

• Published in: Annals of operations research Vol. 176; no. 1; pp. 221 - 234
• Main Author: Adcock, C. J.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2010; Springer; Springer Nature B.V
• Subjects: Adcock, C.J; Analysis; Business and Management; Capital assets; Combinatorics; Expected utility; Kurtosis; Normal distribution; Operations research; Operations Research/Decision Theory; Parameter estimation; Portfolio management; Pricing; Probability distribution; Skewness; Studies; Theory of Computation; Utility functions; Honduras; Efficient frontier; Multivariate Student distribution; Portfolio selection; Multivariate skew-normal distribution; Utility functions; Market model; Capital asset pricing model
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-009-0586-4

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.