Measuring Risk with Expected Shortfall

Abstract: In 2012, The Basel Committee on Banking Supervision decided to change the standard risk measure from the well-known Value-at-Risk (VaR) to Expected Shortfal (ES). The committee believes that the new standard risk measure could offer more benefit, aside from just overcoming the major weaknesses of VaR like incoherency and inability to capture tail risk. In this study, best models for VaR and ES are determined and a comparison between the best models of the newly implemented risk measure and the former risk measure is amplified. Four estimation approaches are used to estimate best models for VaR and ES: Historical Simulation, Gaussian distribution, Student t-distribution and Extreme Value Theory (Peak Over Threshold model). From these four approaches, nine models of estimation are developed: HS model, conditional and unconditional N-distribution, conditional and unconditional t-distribution, conditional EVT with ξ=0 and ξ≠0, as well as unconditional EVT with ξ=0 and ξ≠0. The evaluation window for this research consists of three distinctive periods: bad economy period, recovery period and good economy period. These three periods are deliberately chosen to apprehend the impact of different economic situations on the models’ ability to forecasts VaR and ES. The final results of the research indicated that in general the models that work best for VaR are the same models that work best for ES. Amongst all nine models, the unconditional EVT model seems to be the only suitable model for all the three evaluation periods.