Answer-first summary for fast verification
Answer: USD 101.29
C is correct. 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 7% coupon bond, respectively, corresponding to the proportions of the zero-coupon bond and the 7% 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): 97 * F₁ + 102 * F₂ = F₃ ……………………………… Equation (1) Time (t = 0.5): 0 * F₁ + 3.5 * F₂ = 3 ………………………………… Equation (2) Time (t = 1.0): 100 * F₁ + 103.5 * F₂ = 103 ……………………… Equation (3) From Equation (2), F₂ = 3/3.5 = 0.8571 Substituting the value of F₂ in Equation (3): 100 * F₁ + 103.5 * 0.8571 = 103, giving, F₁ = 0.1429 Plugging the values of F₁ and F₂ in Equation (1), we determine F₃ = 97 * 0.1429 + 102 * 0.8571 = 101.2855
Author: LeetQuiz .
Ultimate access to all questions.
An analyst has been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. A 1-year zero-coupon bond is priced at USD 97 and a 1-year 7% coupon bond with semi-annual payments is priced at USD 102. Using a replication approach, what should be the price of a 1-year 6% coupon Treasury bond that pays semi-annually?
A
USD 97.71
B
USD 101.04
C
USD 101.29
D
USD 102.86
No comments yet.