Which of the following bonds would have the smallest change in price (in percent
ID: 2665804 • Letter: W
Question
Which of the following bonds would have the smallest change in price (in percentage terms) for a given change in interest rates (that is, in yield to maturity) – that is, if the yield to maturity on a bond increases from 8% to 10%, all else constant, which of the following bond prices will change the least (in percentage terms)?a. A $1000 par value bond with a 10% coupon rate (annual payments) that matures in 2 years.
b. A $1000 par value bond with a 10% coupon rate (semi-annual payments) that matures in 25 years.
c. A $1000 par value bond with a 2% coupon rate (annual payments) that matures in 4 years.
d. A $1000 par value bond with a 2% coupon rate (semi-annual payments) that matures in 30 years.
e. The bond that changes the most (in price percentage terms) cannot be determined from the information given.
Explanation / Answer
Answer d. A $1000 par value bond with a 2% coupon rate (semi-annual payments) that matures in 30 years.
a. A $1000 par value bond with a 10% coupon rate (annual payments) that matures in 2 years.
YTM 8% = $1035.67
YTM 10% = $1000
% change in price = -3.6%
b. A $1000 par value bond with a 10% coupon rate (semi-annual payments) that matures in 25 years.
YTM 8% = $1214.82
YTM 10% = $1000
% change in price = -18%
c. A $1000 par value bond with a 2% coupon rate (annual payments) that matures in 4 years.
YTM 8% = $3378.37
YTM 10% = $3233.26
% change in price = -4.30%
d. A $1000 par value bond with a 2% coupon rate (semi-annual payments) that matures in 30 years.
YTM 8% = $19118.58
YTM 10% = $22849.72
% change in price = -19.52%
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