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Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other.
a) What is the VaR for one of the investments when the confidence level is 95%?
b) What is the expected shortfall (ES) when the confidence level is 95%?
c) What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%?
d) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 95%?
e) Show that, in this example, VaR does not satisfy the subadditivity condition whereas expected shortfall does.
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