Building Efficient Frontier by CVaR minimization for Non-normal Asset Returns Using Copula Theory

In the realm of Computational Finance, the performance of the optimal portfolio largely depends upon its composition and its ability to accurately predict the market movements. Recent empirical studies have shown that the underlying assumption of normality of asset returns for risk modeling is seriously flawed, in view of their asymmetric and fat-tailed behavior. This problem is further aggravated when we delve into the functioning of the Financial market and realize that the market parameters have highly non-linear kind of inter-dependence amongst themselves. Any investment portfolio that does not account for these factors and their mutual relationship, will tend to under-perform. This work is a novel attempt, which aims at developing a framework which solves all of these problems in an integrated fashion, without overlooking any of them or pre-assigning lesser importance to any of these issues. The contemporary techniques often neglect one of them, resulting in an incomplete and sometimes even a misleading picture of the market scenario. In this work, copula theory effectively captures the non-linear inter-dependence. The scenarios are generated from a non-elliptical multivariate distribution constructed by a Students $t$-copula assuming marginal   distributions as Gaussian in the center and EVT distributed in the tail. For gauging the market risk we have used CVaR(Conditional Value-at-Risk) as the risk measure. The efficient frontier thus resulted by minimizing the CVaR and maximizing the returns, gives a clear insight into how does the composition of the optimal portfolio changes with respect to change in CVaR of the portfolio. Our aim is to prove that much more reliable conclusions will certainly be drawn if a more realistic representation of data can be done using the concept of Copulas.