Question

There is a 9%, 23 year note bond which has a ytm of 9%. The ytm alters by one percent down. By how much does the price alter? If the ytm drops by 2%, by how much does the price change? What is the exact percentage change of the bond in the 2 cases?

Answer 1

Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 9%

Change in YTM =-1

Bond

K = Nx2

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

k=1

K =23x2

Bond Price =∑ [(9*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^23x2

k=1

Bond Price = 1104.42

price change = New price-Old price = 1104.42-1000 = 104.42

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

%age change in price = (1104.42-1000)*100/1000

= 10.44%

Change in YTM =-2

Bond

K = Nx2

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

k=1

K =23x2

Bond Price =∑ [(9*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^23x2

k=1

Bond Price = 1227.01

price change = New price-Old price = 1227.01-1000 = 227.01

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

%age change in price = (1227.01-1000)*100/1000

= 22.7%