A study on modeling the dynamics of statistically dependent returns

This paper develops a method to characterize the dynamic behavior of statistically dependent returns of assets via a scenario set. The proposed method uses heteroskedastic time series to model serial correlations of returns, as well as Cholesky decomposition to generate the set of scenarios such that the statistical dependence of different asset returns is preserved. In addition, this scenario generation method preserves marginal distributions of returns. To demonstrate the performance of the proposed method, a multi-period portfolio optimization model is presented. Then, the method is implemented through a number of stocks selected from New York Stock Exchange (NYSE). Computational results show a high performance of the proposed method from the statistical point of view. Also, results confirm sufficiency and in-sample stability of the generated scenario set. Besides, out-of-sample simulations, for both risk and return, illustrate a good performance of the proposed method.