Question

Both Bond Alpha and Bond Beta have 8% coupons, $1,000 face-value, make semi-annual payments and are priced at par value. Bond Alpha has 2 years to maturity, whereas Bond Beta has 15 years to maturity.

1. If interest rates suddenly rise by 2%, what is the percentage change in the price of Bond Alpha relative to the original price?
2. If rates were to suddenly fall by 2%, what would the percentage change in the price of Bond Alpha relative to the original price?
3. If interest rates suddenly rise by 2%, what is the percentage change in the price of Bond Beta relative to the original price?
4. If rates were to suddenly fall by 2%, what would the percentage change in the price of Bond Beta relative to the original price?

Answer 1

a

Part 1

Change in YTM =2

Bond Alpha

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(8*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^2x2

k=1

Bond Price = 964.54

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

%age change in price = (964.54-1000)*100/1000

= -3.55%

b

Bond Beta

K = Nx2

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

k=1

K =15x2

Bond Price =∑ [(8*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^15x2

k=1

Bond Price = 846.28

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

%age change in price = (846.28-1000)*100/1000

= -15.37%

c

Part 2

Change in YTM =-2

Bond Alpha

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(8*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^2x2

k=1

Bond Price = 1037.17

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

%age change in price = (1037.17-1000)*100/1000

= 3.72%

d

Bond Beta

K = Nx2

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

k=1

K =15x2

Bond Price =∑ [(8*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^15x2

k=1

Bond Price = 1196

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

%age change in price = (1196-1000)*100/1000

= 19.6%