Abstract
It is often very difficult to accurately measure dependence structure in multivariate distributions that exhibit asymmetry and heavy tail dependence. Hence, the use of copula models which have become popular nowadays because they take into account the skewness and tail dependence of asset returns. However, the use of copula is challenging in higher dimensions, because of inflexible structures. Thus, this study focuses on the decomposition of a multivariate distribution model into pairwise copula. Although vine copulas have many dimensions, this study focuses on the C- and D-vine models. Moreover, the research examines the application of the C- and D-vine models in portfolio optimization. The examination considers 6 JSE stock indices, namely, Beverage Index, Construction and Materials Index, Financial and Industrial 30, Healthcare Index, Mining Index, and Telecommunication Index – with daily data spanning from 05 January 1998 to 15 October 2014. The results of the Sharpe ratio indicate that the C- and D-vine copulas are better models for measuring the dependence structure in portfolio optimization. This is because these two models are able to decompose a multivariate probability density into bivariate copulas, thereby allowing the different structural behaviours of the pairs of variables to be modeled accurately. Similar results for the application of vine copula in portfolio optimisation have been shown in the literature review. This is evidence that the C- and D-vine copula models can be implemented in South Africa to measure accurately the dependence between returns with high excess skewness and kurtosis on a daily basis.
M.Com.