3. Suppose that you have two investments, each of which has a 0.9% chance of a loss of $10 million and a 99.1% chance of a loss of $1 million. These two investments are independent of each other.

(1) What is the VaR for one of the investments at the 99% confidence level?

(2) What is the expected shortfall for one of the investments at the 99% confidence level?

(3) What is the 99% VaR for a portfolio consisting of the two investments?

(4) What is the 99% expected shortfall for a portfolio consisting of the two investments? (5) Verify that VaR does not satisfy the subadditivity condition in this example whereas expected shortfall does.