Expected Shortfall is defined as the average of all losses which are greater or equal than VaR, i.e. the average loss in the worst (1-p)% cases, where p is the confidence level. Said differently, it gives the expected value of an investment in the worst q% of the cases. It is important to clarify that CVaR is NOT the worst case scenario – the worst case scenario is always a 100% loss, and in case of many leveraged instruments, a loss exceeding 100% of the initial investment. CVaR is simply an average of losses past arbitrarily selected risk threshold – so for 95% VaR, CVaR will represent the average of outcomes in the worst 5% of the cases. Expected Shortfall is the opposite of Expected Upside.
Distribution of expected portfolio returns with 95% confidence interval and 1 week time horizon – Expected Shortall is the red bars.
Other UCITS related terms