Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume:
- each bond is priced at 90 dollars
- each bond has a 4% probability to default within 1 year
- the events of default are independent
- 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?