Suppose that each of two investments has a 0.9% chance of a loss of $10 million and a 99.1% chance of a loss of $1 million. The investments are independent of each other.

a. What is the VaR for one of the investments when the confidence level is 99%?

b. What is the expected shortfall for one of the investments when the confidence level is 99%?

c. What is the VaR for a portfolio consisting of the two investments when the confidence level is 99%?

d. What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 99%?

e. Show that in this example VaR does not satisfy the subadditivity condition, whereas expected shortfall does.