Q1

Question 1 Consider the following four risk-free government bonds: Bonds A, B, C, and D. All four hnnds have a face value of 100 and pay annual coupons, but the coupon rates are different A has a coupon rate of 6%,B7%,C8%, and D9%. A, B, and C mature in 3 years, and D matures in 4 years. Bonds A and B are currently trading at 105.44 and 108.20, respectively. a) Calculate the 3 -year spot rate. [4 marks] b) Given your answer above, calculate the price of Bond C. [4 marks] c) Are you able to calculate the 1-year and 2-year spot rates based on the above information? Why or why not? What kind of relationship must hold for the 1 -year and 2-year spot rates? [4 marks] d) If you have the price of another 2 -year government bond, what condition must this bond satisfy in order for you to separately derive the one-year and two-year spot rates? [2 marks] e) Suppose that the 4 -year spot rate is 5%, calculate the price of Bond D. [4 marks] f) Suppose that there is a fifth bond, Bond E. It matures in two years and its coupon rate is 5%. It is currently trading at 100.91. Derive the one-year and two-year spot rates. [3 marks] g) What is the shape of the term structure? Which theories of the term structure can explain the shape above? Explain the intuition. [4 marks] Question 1 Consider the following four risk-free government bonds: Bonds A, B, C, and D. All four hnnds have a face value of 100 and pay annual coupons, but the coupon rates are different A has a coupon rate of 6%,B7%,C8%, and D9%. A, B, and C mature in 3 years, and D matures in 4 years. Bonds A and B are currently trading at 105.44 and 108.20, respectively. a) Calculate the 3 -year spot rate. [4 marks] b) Given your answer above, calculate the price of Bond C. [4 marks] c) Are you able to calculate the 1-year and 2-year spot rates based on the above information? Why or why not? What kind of relationship must hold for the 1 -year and 2-year spot rates? [4 marks] d) If you have the price of another 2 -year government bond, what condition must this bond satisfy in order for you to separately derive the one-year and two-year spot rates? [2 marks] e) Suppose that the 4 -year spot rate is 5%, calculate the price of Bond D. [4 marks] f) Suppose that there is a fifth bond, Bond E. It matures in two years and its coupon rate is 5%. It is currently trading at 100.91. Derive the one-year and two-year spot rates. [3 marks] g) What is the shape of the term structure? Which theories of the term structure can explain the shape above? Explain the intuition. [4 marks]