Expected Shortfall as a Complement to Value at Risk - A study applied to commodities

Abstract: Basel II requires Value at Risk (VaR) as a standardized risk measure for calculating market risk. However, the validity of the risk measure has been questioned since it neglects the losses beyond the VaR level. Expected Shortfall (ES) is a response to this limitation, as it is defined as the average of the losses ignored by VaR. This study applies VaR and ES to three commodities; gold, oil and corn by using the models historical simulation, age-weighted HS, volatility-weighted HS, normal distribution, Student-t distribution, log-normal distribution. Also, conditional volatility, structured as a GARCH(1,1) model, is applied to the three distributions. These nine models are evaluated by backtesting procedures for each commodity. Applying conditional variance improves the models radically and we conclude that the models Volatility-weighted HS and Student-t GARCH(1,1) are the most accurate models regarding the three commodities. Additionally, estimating ES adds value to this study, even though it is almost perfect positively correlated with VaR.