Suppose that each of two investments has a 0.9% chance of a loss of $10 million, a 99.1% 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.

AppendixLO1