To answer problems 1-7, consider the following bonds , each with a face value of $100: Type of bond Maturity Coupon Price YTM Zero coupon 96.32 3.82% Zero coupon D P_zero 4.60% W N Zero coupon 89.11 Y al -pay coupon 2 0.05 P_coupon 1. Price and yield. What is the price of the 2-year zero-coupon bond, P_zero? What is the yield to maturity of the 3-year zero coupon bond ? 2. No arbitrage pricing . Which price would be consistent with no arbitrage for the annual-pay coupon bond (i.e., a bond that pays $5 after one year and $105 after two years )? 3. Fixed income arbitrage . . Suppose that the coupon bond trades at a price of $101.00. a. What arbitrage trade would you do ? b. Suppose that you hold this arbitrage position until maturity in two years . What will be your profit in dollars ? What is the annual return as a percentage of the value of the long side of the position? If the margin requirement is 10% for all long and short positions , what is the initial margin requirement in dollars ? What is the annual return as a percentage of this initial margin requirement ? c. Suppose that, after one year, the yield to maturity on all bonds is 5%. What is the profit or loss in dollars at this time? What is the annual return as a percentage of the initial margin requirement ? d. Suppose that the yield to maturity on all bonds becomes 5% already 1 month after you put on the trade . What is the profit or loss in dollars at this time ? What is the annual return as a percentage of the initial margin requirement 4. Forward rates and directional l fixed income trading a. What is the forward rate from time 1 to time 2 implied by the above zero - coupon bond prices ? b. Suppose that you believe that the 1-year interest rate will be 4% in one year from now (based on your views on central bank policy). What trade would you consider as a result of the difference between your view and the forward rate? 5. Yield curve. Plot the zero -coupon yield curve , that is, the yields on zero -coupon bonds as a function of their time to maturity . Include the overnight interest rate of 3.7%. 6. Duration . Compute the duration and modified duration of each of the four bonds . If each bond's yield to maturity immediately increases by 1 percentage point, approximately how many dollars will each price decline ? (For the coupon bond , use the no -arbitrage price computed in 2.) 7. Yield curve trading . What is average of the yields of the 1-year and 3-year zero-coupon bonds ? Suppose that you view the 2-year interest rate as abnormally high relative to this average . Your view that the 2-year rate is too high is supported by information that several pension funds and banks have been forced to sell large positions of 2-year bonds, pushing down the price , hopefully only temporarily