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Suppose that each of two investments has a 4% chance of a loss of $10 million,...

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Basic Math

Suppose that each of two investments has a 4% chanceof a loss of $10 million, a 2% chance of a loss of $1 million, anda 94% chance of a profit of $1 million. They are independent ofeach other.
a. What is the VaR for one of the investments when the confidencelevel is 95%?
b. What is the expected shortfall for one of the investments whenthe confidence level is 95%?
c. What is the VaR for a portfolio consisting of the twoinvestments when the confidence level is 95%?
d. What is the expected shortfall to a portfolio consisting of thetwo investments when the confidence level is 95%?
e. Show that in this example VaR does not satisfy the subadditivitycondition whereas expected shortfall does.

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