Question

A 20-year semi-annual bond has just been issued with its coupon rate set at the current market yield of 6 percent. How much would the price of the bond change (in percentage terms) if the market yield suddenly fell by 50 basis points? How much would the price change if the yield rose by 50 basis points?

Answer 1

Part 1

Change in YTM =-0.5

Bond

K = Nx2

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

k=1

K =20x2

Bond Price =∑ [(6*1000/200)/(1 + 5.5/200)^k]     +   1000/(1 + 5.5/200)^20x2

k=1

Bond Price = 1060.2

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

%age change in price = (1060.2-1000)*100/1000

= 6.02%

Change in YTM =0.5

Bond

K = Nx2

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

k=1

K =20x2

Bond Price =∑ [(6*1000/200)/(1 + 6.5/200)^k]     +   1000/(1 + 6.5/200)^20x2

k=1

Bond Price = 944.48

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

%age change in price = (944.48-1000)*100/1000

= -5.55%