المدربThe expected shortfall at level is the average loss in the worst of outcomes, ; historically, the average of the largest losses.
أمثلة
Example 21.13 (Two concentrated bonds)
Each of two bonds defaults independently with probability 0.9%, losing 100. Each alone has a 99% VaR of zero; together, the probability of at least one default is 1.79%, so the 99% VaR is 100: diversifying raised VaR. Expected shortfall at 99% is 90 for each bond and 100.8 for the pair, less than their sum of 180.