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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 a 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.
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