Question

Assume a bond has modified duration of 6 and convexity of 200. Its price at yield to maturity of 8% is $98.5 for par value of $100. What will be its new price if interest rate increase by a) 100 bps b) 10 bps c) 1 bps 2. Using duration only adjustment and using both duration and convexity adjustment. What is the significance of convexity adjustment as changes in interest rate decrease?

Answer 1

Using duration only adjustment:
a)
=98.5*(1-6*1%)=92.59
b)
=98.5*(1-6*0.1%)=97.909
c)
=98.5*(1-6*0.01%)=98.4409

Using duration and convexity adjustment:
a)
=98.5*(1-6*1%+0.5*200*(1%)^2)=93.575
b)
=98.5*(1-6*0.1%+0.5*200*(0.1%)^2)=97.91885
c)
=98.5*(1-6*0.01%+0.5*200*(0.01%)^2)=98.4409985

COnvexity adjustment is positve so the actual price rise is more than only using duration