Consider two defaultable 1-year loans with a principal of $1 million

each. The probability of default on each loan is 2.5%. Assume that if one

loan defaults, the other does not. Assume that in the event of default,

the loan leads to a loss that can take any value between $0 and $1

million with equal probability, i.e., the probability that the loss is higher

than $ million is 1 . If a loan does not default, it yields a profit

equal to $20,000.

a) Compute the 1-year 98% Value at Risk (VaR) and Expected Shortfall

(ES) of a single loan.

b) Compute the 1-year 98% VaR and ES for the portfolio of both loans.

c) Does the VaR and the ES satisfy the subadditivity property in this case?