Comparison of Archimedean copula and mean variance method in estimating VaR an application to different stock portfolios

Value-at-Risk (VaR) is one of the most important tools used in modern financial risk management. The development of VaR estimation techniques is vibrant in recent decades. Traditional methods such as mean-variance method are popular due to its feasibility and relative accuracy. However, recent research has shown that traditional methods are unable to capture the tail dependencies of assets. As seen in the Sub-prime mortgage crisis, well diversified portfolios became highly correlated and VaR is therefore severely underestimated. As a result, many researchers turn to Archimedean Copula models to estimate VaR which shows a better prediction of extreme market conditions. This study seeks to verify the superiority of Archimedean Copula by analyzing market data of four two-stock portfolios with difference in dependencies that are intuitively implied and statistically proven. These portfolios resemble different exposure to cross-market and cross-industry risks. The results have shown that across different stock portfolios, Archimedean copula always works better than the traditional mean-variance method. Furthermore, the effectiveness Archimedean copula improves significantly when the intra-portfolio correlation is low. Fund managers will therefore find it justifiable to use Archimedean for their portfolios that appear to be well-diversified and has low correlations