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?

  • 2
    $\begingroup$ 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. $\endgroup$
    – Alex C
    Feb 2 '19 at 18:36

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