Question: Suppose that each of two investments has a 1.5% chance of $20M (= 20 million) loss and a 98.5% chance of $4M loss in 1

Suppose that each of two investments has a 1.5% chance of $20M (= 20 million) loss and a 98.5% chance of $4M loss in 1 year. The investments are independent of each other.

(a)What is VaR (1 year, 98%) for one of the investments?(1 mark)

(b)What is ES (1 year, 98%) for one of the investments?(2 marks)

(c)What is VaR (1 year, 98%) for the portfolio consisting of the two investments?(3 marks)

(d)What is ES (1 year, 98%) for the portfolio consisting of the two investments?(3 marks)

Show that VaR does not satisfy the sub-additivity condition whereas ES does.(1 mark

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