In this paper, we compare two risk measures, Value at Risk (VaR) and Expected Shortfall (ES) in their ability to capture risk associated with tail thickness. We test them under both normal and stressed market conditions using historical daily return data for capital-weighted stock indices from major markets around the world. Both log-returns (serially correlated) and ARMA-GARCH residuals (not serially correlated) are tested.We find that expected shortfall is better at capturing tail risk than VaR under all market conditions; the improvement is more dramatic in normal conditions and in serially correlated data. However, in crisis conditions, the stochastic component of returns shows that both risk measures contain very high tail risk. We recommend that practitioners and regulators using VaR consider switching to expected shortfall to be better prepared for extreme negative events.
MSc in Finance - Simon Fraser University
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