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Question
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.
(1) What is the VaR for one of the investments when the confidence level is 99%?
(2) What is the expected shortfall for one of the investments when the confidence level is 99%?
(3) What is the VaR for a portfolio consisting of the two investments when the confidence level is 99%?
(4) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 99%?
(5) Show that in this example VaR does not satisfy the subadditivity condition, whereas expected shortfall does.
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