Question

A bond's current price and yield are $950 and 2% (compounded continuously), respectively.If the bond's yield was 1.75%, then its price would be $955. What is the bond's duration?

Answer 1

Current Price, P₀ = $ 950; continuously compounded yield, y₀ = 2%

When yield, y₁ = 1.75%; Price, P₁ = $ 955

%change in yield = 2% - 1.75% = 0.25%

%change in price = (P₀ - P₁) / P₀ = (950 - 955) / 950 = -0.5263%

If D is the duration then, %change in bond price / %age change in yield = - Modified duration = - D / (1 + y₀) (in case of annual compounding) = - De^-y₀ in case of continuously compounded yield

Hence, -0.5263% / 0.25% = -2.10526 = -De^-y₀ = -De^-2% = -De^-0.02 = -0.980198673D

Hence, D = 2.10526 / 0.980198673 = 2.147792295 years = 2.15 years