You have an equally-weighted bond portfolio contains four bonds. Details of the four bonds are given below: Bond A: 10-year zero coupon government bond, par value $1000, current price 585.43 Bond B: 10-year zero coupon AA rated bond, par value $1000, default risk premium =2.5% Bond C: 5 year 15% coupon, BBB rated bond, par value $1000, annual coupon payments default risk premium =9.5%. The duration of Bond C is 3.855. Bond D: 5 year 15% government coupon bond, par value $1000, annual coupon payments, YTM=7% (a) (3 marks) Find the price of Bond B, C and D, respectively. (b) (3 marks) Find the Macaulay's duration of Bond D. (c) (3 marks) If Bond A's yield increases by 0.5%, what is the price of Bond A based on the duration-with-convexity rule? Assume the convexity of the Bond A is 99.77. (d) (5 marks) Suppose you have a liability with a duration of 8 years, the current value of the liability is $1 million. How many of Bond A and Bond C will you hold in your portfolio to immunize the interest rate risk in your liability? (e) (2 marks) If you forecast that the yield curve will shift upward in the near future, how can you adjust your holdings on Bond A and C to minimize the effect on your portfolio? Briefly explain. (f) (4 marks) The current yield spread between Bond A (Government bond) and Bond B (AA rated bond) is 2.5% due to the credit risk premium. You expect that the bond may tem- porarily increase in credit risk. What investment instrument can you use to minimize the credit risk? Briefly discuss your strategy