Robust Omega ratio optimization using regular vines

Abstract

We study the robust portfolio optimization model for the Omega ratio when the joint ambiguity in the returns distributions is modeled utilizing copulas. We propose the copula formulation of the Omega ratio and use it to formulate the worst-case robust optimization model. Furthermore, we propose a Markov chain predicated filtering strategy to filter a set of fewer assets from a large pool of available assets in the market to amend the performance of the conventional Omega ratio model. We propose an R-vine copula Autoregressive Moving Average Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) model for the joint distribution of assets returns. We obtain the standardized residuals for each return series of the filtered assets using the ARMA-GARCH model and, subsequently, exploit the regular vine copulas to model the joint dependence among the transformed residuals. The tree structure in the regular vines is accomplished using Kendall’s tau. The dependence structure so obtained is used to simulate scenarios for the returns of assets. The simulated data is used to obtain optimal portfolios in the worst-case Copula Omega ratio model. Empirical evidence shows the aptness of the proposed filtering strategy and analyzes the performance of the worst-case copula Omega portfolios on several datasets using a rolling window approach. The optimal portfolios from the worst-case copula Omega model are found to outperform the portfolios from the Gaussian copula Omega ratio model by having a higher information ratio, Value-at-risk ratio, and Rachev ratio.