To answer problems 1?3 consider the following bonds, each with a face value of $100: Type of bond Maturity Coupon Price J YTM Zero coupon i c 95.32 1 3.32% Zero coupon 2 D P_zero l 4.60% Zero coupon 3 D 89.11 i '1' Annualpay coupon 2 0.05 P_coupon I 1. 2. Price and yield. Whot is the price of the 2 year zerocoupon bond, P_2ero? What is the yield to maturity of the 3 year zero coupon bond? No arbitrage pricing Vii-Thich price would be consistent with no arbitrage for the annual pay coupon bond (1. e. a bond that pays 55 after one y ear and $105 after mo ye ars} 9 Fixed income arbitrage. Suppose that the coupon bond trades at a price of $101.00. a. Wt arbitrage trade would you do.3 b. Suppose that you hold this arbitrage position until maturity in two years. 1Cit"hat will be your profit in dollars? Wt is the annual return as a percentage of the value of the long side of the position: If the margin requirement is 10"! E: 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.3 c. Suppose iat1 after one year the yield to maturity on all bonds is 5%. 1What is the prot or loss in dollars at this time? 1What 15 the annual return as a percentage of the initial margin requirei'nentr d Suppose that the yield to maturity on all bonds becomes 5% already 1 month after you put on the trade. mat is the profit or loss in dollars at this time? lWhat is the annual return as a percentage of the initial margin requirement? Forward rates and directional xed income trading. a. ill-That is the forward rate from time 1 to time 2 implied by the above zero COIJPOII bond PiliCES? b. Suppose that you beliei- -e that the 1year interest rate 1will be 4% 1n one y ear from HOW (based on your views on central bank policy]. Wt trade would y ou consider as a result of the difference between your viev. and the forward rate? Yield curve. Plot the Zerocoupon yield curve, that is, the yields on zero-coupon bonds as a function of their time to maturity. Include the overnight interest rate 01-33913. Duration. Compute the duration and modied duration of each of die four bonds. If each bond' s yield to maturity immediately increases by 1 percentage point1 approximately how many dollars will each price decline: {For the coupon bond use the no- arbitrage price computed in 2.] Yield curve trading. 1What is average of the yields of the 1-year and 3-year zero-coupon bonds.3 Suppose that you view the 2year interest rate as abnormally high relative to this average. Your View that die 2-year rate is too high is supported by information that several pension funds and banks have been forced to sell large positions of 2year bonds, pushing down the price, hopefully only temporarily