Answer: USD 101.8

To determine the price (F3) of the 6% coupon bond by replication, where F1 and F2 are the weight factors in the replicating portfolio for the zero-coupon bond and the 8% coupon bond, respectively, corresponding to the proportions of the zero-coupon bond and the 8% coupon bond to be held, and given a 1-year horizon: The three equations below express the requirement that the cash flows of the replicating portfolio, on each cash flow date (t, in years), be equal to the cash flow of the 6% coupon bond: Time (t=0): 98*F1 + 103*F2 = F3 .. Equation (1) Time (t=0.5): 0*F1 + 4*F2 = 3 .. Equation (2) Time (t=1.0): 100*F1 + 104*F2 = 103 .. Equation (3) From Equation (2), F2 = 3/4 = 0.75 Substituting the value of F2 in Equation (3): 100*F1 + 104*0.75 = 103, giving, F1 = 0.25 Plugging the values of F1 and F2 in Equation (1), we determine F3 = 98*0.25 + 103*0.75 = 101.75 Option A is incorrect. USD 99.25 is the price of the 1-year 6% coupon Treasury bond if the weight factors, F1 and F2, are switched in Equation (1). Option B is incorrect. USD 101.07 is the price of the 1-year 6% coupon Treasury bond if the yield-to-maturity of the 1-year 8% coupon Treasury bond is used in its pricing and the zero-coupon Treasury bond is ignored in the replication. Option D is incorrect. USD 103.91 is the price of the 1-year 6% coupon Treasury bond if the yield-to-maturity of the zero-coupon Treasury bond is used in its pricing and the 1-year 8% coupon Treasury bond is ignored in the replication. The correct answer is C, USD 101.8, which is the price of the 1-year Treasury bond that pays a coupon of 6% semi-annually when using a replication approach with the given weight factors F1 and F2.

Author: LeetQuiz Editorial Team