Question 24: Textbook

You are an investor and consider two investments. Each of them 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. Show all steps, and workings.

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 the 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 case, VaR does not satisfy the subadditivity condition whereas expected shortfall does.