Quantifying the risk of portfolios containing stocks and commodities

Abstract

In this study, we used copula method in order to model the multivariate return distributions of stock portfolios and, in this manner, to implement this model for risk measure evaluations in practice. Copulas are used to describe the dependence between random variables thus, are enjoyed to model the marginals separately and to represent the dependence structure between them. We also modeled the multivariate return distributions of stock portfolios diversi ed with commodities, precious metals, crude oil etc. and tted a set of copulas to the joint return data. With this aim, we selected 20 stocks from New York Stock Exchange, gold and crude oil and constructed stock portfolios, stock portfolios with gold, stock portfolios with crude oil and stock portfolios with gold and crude oil in order to analyze whether the copula method ts the multivariate return distributions of selected portfolios. In order to check the validity of the models, we implemented daily and weekly back testing using 20 di erent values. We found that t distribution and generalized hyperbolic distributions are very nice models for modeling individual nancial instruments returns and the t copula is the best copula to represent the dependence structure between nancial instruments returns. We used this model to calculate the risks of portfolios and observed that adding gold decreases the risk of portfolios where crude oil behaves like an ordinary stock.