Question

Assume you have a 2-year coupon-paying bond that pays 2% each half a year. Assuming the yield equals to 2% calculate the KRD for 1-year point.

Answer 1

Key rate duration = (P(-) - P(+)) / (2 x 1% x P(0))

P(0) = Original price of the bond=1000*2%/1.01+1000*2%/1.01^2+1000*2%/1.01^3+1000*2%/1.01^4+1000/1.01^4=1039.02

P(-) = Price with 1% decrease in rate=1000*2%/1.005+1000*2%/1.005^2+1000*2%/1.005^3+1000*2%/1.005^4+1000/1.005^4=1059.26

P(+) = Price with 1% increase in rate=1000*2%/1.015+1000*2%/1.015^2+1000*2%/1.015^3+1000*2%/1.015^4+1000/1.015^4=1019.27

Key rate duration =(1059.26-1019.27)/(2*1%*1039.02) =1.92