Question

There is a par 30 year, 6% bond. What is the % alteration, if the ytm alters by 2%? Do it with duration alone. Then, find the change, if you include convexity also. The convexity is 40.

Answer 1

As the bond is a par bond, coupon rate=ytm=6%
Duration of the bond==DURATION(DATE(2000,1,1),DATE(2030,1,1),6%,6%,1,2)=14.59 years
Modified Duration=14.59/1.06=13.76415094

Using duration alone:
If ytm rises by 2%
% change=-13.76415094*2%=-27.53%
If ytm falls by 2%
% change=-13.76415094*(-2%)=27.53%

Using duration and convexity:
If ytm rises by 2%
% change=-13.76415094*2%+0.5*40*(2%)^2=-26.728%

If ytm falls by 2%
% change=-13.76415094*(-2%)+0.5*40*(-2%)^2=28.328%