Question

"Interest Rate Risk [LO2] Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?"

Answer 1

Hi

Below is the formula and the results if YTM increases and decreases by 2%

	Bond J	Bond K
Coupon Rate	0.03	0.09
Face Value	1000	1000
Semiannual coupon payment	15	45
Number of years	14	14
Number of payments	28	28
YTM	0.06	0.06
Price of Bond	$718.54	$1,281.46
After increasing YTM
YTM	0.08	0.08
Price of Bond	$583.42	$1,083.32
Percentage change in price	-18.80%	-15.46%
After decreasing YTM by 2%
YTM	0.04	0.04
Price of Bond	$893.59	$1,532.03
Percentage change in price	24.36%	19.55%

We can see that for lower coupon bonds interest risk is higher because more payment will be on later years.

Thanks