Using the Copula Function in ETF Portfolio Optimization Problem Based on CVaR Criteria

The anomalous events of past years like the world financial crisis of 2008-2009 and European banking crisis of 2011 imposed on investors the necessary to reconsider their approach to risk estimation. In this work copula model was applied as the solution of non-normal distribution problem and portfolio optimization was performed with the means of CVaR value, in view of its advantages, such as taking into account the thickness of the tail of the distribution and subadditivity. In the current work, a copula was fitted to the sample of ETFs’ returns among elliptic and archimedean families: Gaussian, Student, Clayton and Gumbel copulas. For including autoregression and volatility clustering effects observed in the market the estimated parameters of the ARMA-GARCH model were used. In the work the following research hypotheses are tested: 1. Copula-based portfolio optimization outperforms alternative methods, such as classical Markowitz optimization and optimization based on CVaR value with the Geometric Brownian Motion approach of generation returns. 2. Copula-based portfolio optimization still gives better results than alternative methods in the condition of restrictions on maximum weight on portfolios of 30% (imposition of a requirement to reduce risk concentration). 3. Dependence between the time interval of modeling the joint distribution of assets’ returns using the copula function and the optimal choice of the optimization parameter (the level of CVAR significance) can be found. The non-normal distribution of assets returns, which limits the applicability of some alternative models. At the same time, in the case of copulas, there are no requirements for the initial distribution of data. Secondly, copulas allow tracking the non-linear relationship of time series, which significantly increases their explanatory power in comparison with linear models.