Two (default-free) government bonds, A and B, are trading at a current market price of $80 and $88, respectively. Bond A is a zero-coupon bond with 1 year to maturity. Bond B is a 20% coupon bond with 2 years to maturity. Both bonds have a face value of $100. Assume any coupons are paid annually. (a) Determine the 1-year and 2-year spot rates, and the implied forward rate between years 1 and 2. (3 marks) (b) The yield to maturity of Bond B is 28.69%. Using the duration approach, approximate the dollar change in the price of What is the Modified Duration of Bond B? (2 marks) the bond if its yield decreases by 1 percentage point. (2 marks) iii. Would the magnitude of this price change be larger or smaller if Bond B was currently selling at par? Explain without the aid of any calculations. (3 marks) (c) 'An upward sloping term structure implies that the market expects future spot rates to increase'. Discuss this statement in relation to theories of the term structure of interest rates. (5 marks) (d) Consider a default-free coupon bond with market price P. The bond matures in N years' time, has face value F, a constant coupon rate e > 0, and yield to maturity r > 0. Coupons are paid annually, and all rates are expressed assuming annual compounding. i. Show that if a bond sells at a premium to face value, then c>r (8 marks) ii. The 'current yield' of a coupon bond is defined as the annual coupon payment expressed as a fraction of the bond price. Show that the following relationship holds for all premium bonds and provide an intuitive explanation: coupon rate c> current yield > yield to maturity r (7 marks) Two (default-free) government bonds, A and B, are trading at a current market price of $80 and $88, respectively. Bond A is a zero-coupon bond with 1 year to maturity. Bond B is a 20% coupon bond with 2 years to maturity. Both bonds have a face value of $100. Assume any coupons are paid annually. (a) Determine the 1-year and 2-year spot rates, and the implied forward rate between years 1 and 2. (3 marks) (b) The yield to maturity of Bond B is 28.69%. Using the duration approach, approximate the dollar change in the price of What is the Modified Duration of Bond B? (2 marks) the bond if its yield decreases by 1 percentage point. (2 marks) iii. Would the magnitude of this price change be larger or smaller if Bond B was currently selling at par? Explain without the aid of any calculations. (3 marks) (c) 'An upward sloping term structure implies that the market expects future spot rates to increase'. Discuss this statement in relation to theories of the term structure of interest rates. (5 marks) (d) Consider a default-free coupon bond with market price P. The bond matures in N years' time, has face value F, a constant coupon rate e > 0, and yield to maturity r > 0. Coupons are paid annually, and all rates are expressed assuming annual compounding. i. Show that if a bond sells at a premium to face value, then c>r (8 marks) ii. The 'current yield' of a coupon bond is defined as the annual coupon payment expressed as a fraction of the bond price. Show that the following relationship holds for all premium bonds and provide an intuitive explanation: coupon rate c> current yield > yield to maturity r (7 marks)
