Question 3. 40 marks (split equally between sub-questions) Consider four risky assets. Security A is a two-year default-free bond with a face value of $100, a coupon rate of 5% and a yield to maturity of 5%. Security B is a three-year floating rate (LIBOR 1Y+2% ) bond with face value of $100. Security C is a 3 -year bond. It pays semi-annual coupons of 7%, has a Face value of $1000 and a yield to maturity of 8%. a) Find the Present Value and duration of security A. b) What is the duration of security B? Explain. c) For a regular bond that pays annual coupons, show that when coupon rate = yield to maturity, the bond is traded at par. d) Find Present Value of security C and its duration. e) Explain what happens to the price of C if interest rates rise by 1% using duration approximation and directly. Explain why you got different results when using 2 different approaches. Demonstrate your results on an appropriate graph. Question 3. 40 marks (split equally between sub-questions) Consider four risky assets. Security A is a two-year default-free bond with a face value of $100, a coupon rate of 5% and a yield to maturity of 5%. Security B is a three-year floating rate (LIBOR 1Y+2% ) bond with face value of $100. Security C is a 3 -year bond. It pays semi-annual coupons of 7%, has a Face value of $1000 and a yield to maturity of 8%. a) Find the Present Value and duration of security A. b) What is the duration of security B? Explain. c) For a regular bond that pays annual coupons, show that when coupon rate = yield to maturity, the bond is traded at par. d) Find Present Value of security C and its duration. e) Explain what happens to the price of C if interest rates rise by 1% using duration approximation and directly. Explain why you got different results when using 2 different approaches. Demonstrate your results on an appropriate graph