# Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of \$100. Assume:

1. each bond is priced at 90 dollars
2. each bond has a 4% probability to default within 1 year
3. the events of default are independent
4. recovery on default is 30% of face value

Let $$\Pi$$ denote a portfolio consisting of a long position of 100 dollars face value in each bond, i.e. $$\Pi$$ has a value of 2 × 90 = 180.

I am asked to calculate the Expected Shorfall for the portfolio $$\Pi$$ as a function of $$\alpha\in(0,0.5)$$. How can it be done?

• Since there are 2 bonds and 2 outcomes (def or nodef), there are four cases that can occur: def/def, def/nodef, nodef/def, nodef/nodef. Identify the portfolio value in each of these cases and the probability of each case. Obviously if a bond defaults it goes to 30 (profit -60), if if does not default it goes to 100 (profit 10). Arrange the portfolio outcomes from worst to best. – Alex C Feb 2 '19 at 18:36