Question: Question 2 (a) Explain why the utility function of a risk-averse agent is concave. [5 marks] (b) Consider three identical bonds A, B and C.

Question 2 (a) Explain why the utility function of a risk-averse agent is concave. [5 marks] (b) Consider three identical bonds A, B and C. Each bond makes a profit of 10% with a probability of 90% and a loss of 70% with a probability of 10% independently of the others. Let X be an investment of 30,000 in bond A and Y a portfolio investment of 10,000 in each of the three bonds A, B and C. Let Lx and Ly be the loss function of investment X and Y respectively. Find the VaR of Lx and Ly at a level of 95% and comment on your result. [10 marks] (c) Calculate VaRf(L) and CVaRf(L) where L has a Cumulative Distribution Function (CDF) F1(x) = 1 e-for 0
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