Question

Calculate the duration of a 2-year bond with 8% semiannual coupon selling at par

if interest rate decreases by 1 percentage point,by how much will the price of the bond change, based on the Duration model?

Answer 1

Macaulay duration of a par value bond (semi-annual coupon) = ((1+YTM/2)/YTM)*(1-1/((1+YTM/2)^(2*m)))

YTM = Yield to maturity = 8%

m = Number of years = 2

Macaulay duration of a par value bond (semi-annual coupon) = ((1+0.08/2)/0.08)*(1-1/((1+0.08/2)^(2*2)))

Macaulay duration of a par value bond (semi-annual coupon) = 1.8875455

Modified duration = Macaulay duration/(1+YTM/m)

Modified duration = 1.8875455/(1+0.08/2)

Modified duration = 1.814947596

Percentage change in bond price = -Modified duration *Change in interest rate

Percentage change in bond price = -1.814947596*(-0.01) = 0.0181497

Percentage change in bond price = 1.81497%

Hence, the bond price increases by 1.81497%