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?

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