APPLICATION OF 4-DIMENSIONAL COPULAS IN CALCULATING VALUE-AT-RISK FOR THE PORTFOLIO OF 4 SP500 COMPANIES

Abstract

Portfolio risk management is a process aimed at maintaining profit streams and reducing uncertainties in investment decisions. Value-at-Risk (VaR) is a widely used metric to quantify the potential loss of profits. Although historical simulations and Gaussian distribution are common methods for estimating VaR, modelling the joint multivariate distribution of portfolio investments can be challenging. Copula models offer a solution to these challenges for joint distributions. In this study, we calculated VaR and Conditional Value-at-Risk (CVaR) for a portfolio consisting of the four least correlated stocks among the 15 largest companies in the SP 500 using historical simulations and copula models. We evaluated portfolio based on equal weighting. The optimal ARIMA-GARCH model was selected using Akaike Information Criteria (AIC) values. Furthermore, the performance of the VaR estimations was compared and analyzed using goodness-of-fit tests.