Question

7.    Consider a one-year coupon bond with face value of $100 and coupon payment equal to $10 paid every 6 months. The market interest rate on similar coupon

       bonds is 12%.

       SHOW ALL STEPS.

       (a) Find the price of the one-year coupon bond.

       (b) Assume a one-year zero coupon bond is priced at $93. Find the bond’s

              yield to maturity.

       (c) The current yield on 6 mo. bonds is 7%.

       (d) Create a synthetic one-year zero-coupon bond from the coupon bond.

       (e) Find the profitable arbitrage possibility. Show carefully why this works by

              filling in the table below to show the cash flows.

ACTION TODAY	Today	In 6 mo.	In one year

Answer 1

(a) Price = PV of cashflows discounted at the market interest rate of 12%

= ($5 / (1 + 0.12) ^ 0.5) + ($105 / (1 + 0.12) ^ 1)

= 4.72 + 93.75

= $98.47

(b) We have to find the interest rate that will make $93 equal to $100 in one years time :

YTM = (100 / 93) - 1 = 0.0752688, or 7.527 %

(c) To create a synthetic coupon bond, we need to replicate the cash flows of the coupon bond and discount the 6-month cash flow at 7% and the one-year cash flow at 12%

($5 / (1 + 0.07) ^ 0.5) + ($105 / (1 + 0.12) ^ 1)

PV = 98.58

A zero-coupon bond priced at $98.58 will replicate the coupon bond