Analysis of current risk measures and study of model sophistication, via Copulas and Extreme Value Theory, in the estimation of risk within the regulatory framework

The crisis of 2008 has brought to light deficiencies in the risk estimations performed by financial institutions. Despite warnings, the underlying risk of many portfolios has been underestimated. As such, in the view of the regulator and the bank within the current regulatory environment, one may wonder what is the best risk measure and what are the best estimation techniques with regard to the presumed riskiness of a portfolio. We show that, despite its non-elicitability and lack of robustness, the Expected Shortfall (ES) should continue to gain ground over the Value-at-Risk (VaR) as the risk measure reference. Actually, these two features are not even problematic because the non-elicitability does not prevent backtestability and non-robustness to outliers might actually foresee future large losses. We also examine the properties of the risk measure procedure to estimate the VaR/ES, and shade light on the importance of the economical bias that arises in the plug-in estimation of the VaR and ES in the Gaussian framework. Although the bias is small for a 250 days based VaR/ES, the approach remains interesting and we recommend its use. We also show that there is no panacea to estimate the VaR and ES. Depending on the market conditions and the portfolio itself, the best estimation techniques vary. Through Copulas and ExtremeValue Theory, we show that more sophisticated does not necessarily mean better because it may cause risk overestimation. This is shown via simulations of Gaussian log-return(low-risk) versus Johnson distributed log-returns with unforeseeable loss jumps (high risk), and via the VaR and ES estimations of an ETFs portfolio (presumed low-risk) versus a portfolio of cryptocurrencies (presumed high-risk). The EVT is the most conservative method since it produces the least number of violations in the backtesting phase. However, it tends to overestimate the risk if no outliers are found out of sample. It may receive the favor of regulators, or even of prudential risk managers. The Clayton copula is found to be the copula to advocate and its benefit is greater in the context of high risk. They both outperform traditional parametric methods based on the Gaussian assumption, whereas the historical simulation and Monte Carlo jump remain good fit as long as the underlying environment is constant.