Optimal Portfolio Allocation with Elliptical and Mixed Copulas

Abstract

This research aims to investigate the asset allocation performance of three different optimization methods commonly applied in the literature for a portfolio composed of univariate returns generated from Mixed and Elliptic copulas instead of historical data. As a result, returns of five equities traded at the BIST30 index of the Turkish Stock Market were obtained. Dynamics of the univariate return series are modelled with GARCH processes with Student-t distributed innovations. Following the marginal modelling, a five-dimensional dependence structure between the series is modelled with Elliptical and Mixed copulas. From the fitted Mixed and Elliptical copula functions, daily returns of the equities are simulated which are employed by the specified optimization methods in order to find out methodology specific optimal portfolio allocations. Performance of the constructed optimal portfolios are compared according to varying risk and reward to variability ratios yielding results especially in favor of the Mixed and Student t copulas. The main contribution of this research is to be able to fill the gap in the literature on the out-of-sample portfolio allocation performance of copula functions where there are still fewer papers compared to the dependency modelling or the in-sample portfolio allocation performance of copulas.

Keywords

• Portfolio Optimization
• Copula Functions
• GARCH
• Portfolio Performance

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