2. ABC is also interested in buying some corporate bonds for its investment acco
ID: 2695565 • Letter: 2
Question
2. ABC is also interested in buying some corporate bonds for its investment account. Suppose these bonds have identical coupon rates of 7.75% but one issue matures in 3 years, one in 8 years, and the third in 13 years. Assume that a coupon payment was made yesterday and they are all issued by the same company. a) The yield to maturity for all three is 6.55%, what is the fair price of each bond? b) Suppose that the yield to maturity for all of these bonds changed instantaneously to 5%. What is the fair price of each bond now? c) Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond? d) Based on the fair prices at the various yields to maturity is interest-rate risk the same, higher, or lower for longer- versus shorter-maturity bonds.Explanation / Answer
a) The yield to maturity for all three is 6.55%, what is the fair price of each bond?
Fair Price of bond (3year left to Maturity) = $1031.75
Fair Price of bond (8yearleft toMaturity) = $1072.92
Fair Price of bond (13yearleft toMaturity) = $1102.90
b) Suppose that the yield to maturity for all of these bonds changed instantaneously to 5%. What is the fair price of each bond now?
Fair Price of bond (3year left to Maturity) = $1074.89
Fair Price of bond (8yearleft toMaturity) = $1177.74
Fair Price of bond (13yearleft toMaturity) = $1258.32
c) Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond?
Fair Price of bond (3year left to Maturity) = $968.36
Fair Price of bond (8yearleft toMaturity) = $930.81
Fair Price of bond (13yearleft toMaturity) = $906.41
d) Based on the fair prices at the various yields to maturity is interest-rate risk the same, higher, or lower for longer- versus shorter-maturity bonds
Than long term bond will fluctuate more than short term bond
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