Suppose that each of two investments has a 4% chance of loss of $10 million, a 2% chance of loss of $1 million, and a 94% chance of profit of $1 million. They are independent of each other.

a. What is the VaR and CVaR (expected shortfall) at level p = 95% for one of the investments?

b. What is the VaR and CVaR (expected shortfall) at level p = 95% for a portfolio consisting of the two investments?

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