Back-testing, risk estimation models: a simulation study for two-asset portfolios

The aim of the study is to check the validity of five different risk-estimation models for two-asset portfolios, a topic which is relevant in model selection both for determining the minimum capital requirements for trading book portfolios and for the regulatory monitoring of the performance of internal risk models. Simulations based on a real data set containing the FTSE 100 constituents were carried out, and the risk was gauged by Expected Shortfall, a measure which also captures tail risk. Given that the period studied includes that of the subprime crisis, there is an inherent opportunity to compare and contrast the results produced under disaster conditions with others from less stressful periods. Our empirical analysis has confirmed that using Expected Shortfall instead of Value-at-Risk alone is not enough, and that the risk model has to be carefully selected and back-tested. The general Pareto distribution proved to be a prudent choice for risk models. In fact, among the five models considered, the model when general Pareto marginals were coupled with Clayton copula showed the best performance. It was, however, also revealed that this model is susceptible to being “over-cautious” in estimating loss.