# Question: Suppose that each of two investments has a 4 chance

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 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.

(a) What is the VaR for one of the investments when the confidence level is 95%?

(b) What is the expected shortfall 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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