Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent.
ID: 2819810 • Letter: B
Question
Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent. Both bonds have 13 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?
Bond J: %
Bond K: %
What if rates suddenly fall by 2 percent instead?
Bond J: %
Bond K: %
Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent. Both bonds have 13 years to maturity, make semiannual payments, and have a YTM of 6 percent.
Explanation / Answer
Coupon amount of Bond J = 3% of 1000/2 = $15.
Coupon amount of Bond K = 9% of 1000/2 = $45
YTM = 6%. Thus price of the bond is the present value of all future cash flows. So for J we have n = 13*2 = 26, r = 6%/2 = 3%, pmt = 15 and fv = 1000. Thus using the PV function we get pv = $731.85
For K n = 13*2 = 26, r = 6%/2 = 3%, pmt = 45 and fv = 1000. Thus pv = 1,268.15 (use "pv" function of excel)
Now when interest rate rises by 2% then YTM = 6+2 = 8% and so r = 8%/2
In this case for J n = 13*2 = 26, r = 8%/2 = 4%, pmt = 15 and fv = 1000. Thus using the PV function we get pv = 600.43. Thus % change for Bond J's price = -17.96%
Bond K: n = 13*2 = 26, r = 8%/2 = 4%, pmt = 45 and fv = 1000. Thus using the PV function we get pv = $1,079.91. Thus % change in Bond K's price = -14.84%
Now when the rates fall by 2% then r = (6-2)/2 = 2%
Bond J: n = 13*2 = 26, r = 4%/2 = 2%, pmt = 15 and fv = 1000. Thus using the PV function we get pv = 899.39. Thus % change in J's price = (899.39-731.85)/731.85 = 22.89%
Bond K: n = 13*2 = 26, r = 4%/2 = 2%, pmt = 45 and fv = 1000. Thus using the PV function we get pv = $ 1503.03
% chanhe = (1503.03-1268.15)/1268.15 = 18.52%
Thus when rates rise by 2% then:
When rate falls by 2% then:
%
Bond J -17.96 % Bond K -14.84 %