Question 9 (30 marks) Consider the following three zero-coupon bonds with face value 1000 with maturity 1 year. Bond A is default-free. Bonds B and C have positive probability of default: they will either repay the loan in full, or default without paying anything. The probability that bonds B and C repay is as follows: C pays B pays B defaults 0.2 0.25 C defaults 0.45 0.10 Assume that the discount rate for bond A is 5%, for bond B is 10% and for bond C is 15%. (a) What are the expected payoffs of A bond, B bond, and C bond at maturity? (5 marks) (b) What are the standard deviations of A bond, B bond, and C bond payoffs at maturity? (7 marks) (c) What is the correlation between of B and C bonds payoffs? (9 marks) (d) Deciding to diversify, you buy 20% of Abe bond, 50% of B bond and 30% of C bond. What is the expected value and standard deviation of this portfolio payoff? Is the standard deviation of portfolio's payoff bigger or smaller than the standard deviations of individual bonds' payoffs? Why? (9 marks)