Question

A bond has a coupon rate of 6 percent, 9 years to maturity, semiannual interest payments, and a YTM of 8 percent. If interest rates suddenly rise by 2 percent, what will be the percentage change in the bond price? Group of answer choices -13.9 percent +14.0 percent -12.3 percent -14.0 percent -11.4 percent

Answer 1

Suppose the face value of the bond=$1000
Annual coupon rate=6%
As the interest is paid semiannually, the semiannual coupon rate=6%/2=3%
Coupon payment=(Semiannual coupon rate)*(Face value)=3%*1000=30
Annual yield to maturity (YTM)=8%
Semiannual yield to maturity (YTM)=8%/2=4% or 0.04

When the interest or YTM increases by 2%, the semiannual yield to maturity (YTM) becomes (8%+2%)/2=5% or 0.05

Time period=9 years
As the interest payment is made semiannually, the number of periods=9*2=18 years

We can calculate the prices using excel.

Excel formula used:

Percentage change in the bond price=(Final price after change-Initial price)/Initial price
=(766.21-873.41)/873.41=-0.1227373 or -12.3% (Rounded to one decimal place)

Answer: Correct option is -12.3%