Question

Bond J has a coupon rate of 4 percent. Bond K has a coupon rate of 9 percent. Both bonds have 7 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 Bond J?

-If interest rates suddenly rise by 2 percent, what is the percentage price change of Bond K?

-If interest rates suddenly fall by 2 percent, what is the percentage price change of Bond J?

-If interest rates suddenly fall by 2 percent, what is the percentage price change of Bond K?

Answer 1

Current price

Bond J

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(4*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^7x2

k=1

Bond Price = 887.04

Bond K

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(9*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^7x2

k=1

Bond Price = 1169.44

Part 1

Change in YTM =2

Bond J

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(4*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^7x2

k=1

Bond Price = 788.74

%age change in price =(New price-Old price)*100/old price

%age change in price = (788.74-887.04)*100/887.04

= -11.08%

Bond K

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(9*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^7x2

k=1

Bond Price = 1052.82

%age change in price =(New price-Old price)*100/old price

%age change in price = (1052.82-1169.44)*100/1169.44

= -9.97%

Part 2

Change in YTM =-2

Bond J

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(4*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^7x2

k=1

Bond Price = 1000

%age change in price =(New price-Old price)*100/old price

%age change in price = (1000-887.04)*100/887.04

= 12.73%

Bond K

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(9*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^7x2

k=1

Bond Price = 1302.66

%age change in price =(New price-Old price)*100/old price

%age change in price = (1302.66-1169.44)*100/1169.44

= 11.39%