Question

please explain the relationship between YTM and convexity after controlling the first order risk as clearly as possible.

Answer 1

Convexity and YTM are inversely related.

Convexity is the second order derivative of bond price with respect to YTM.

The first order derivative of bond price with respect to YTM is duration

.................(1)

AP=DAy

$\Delta P$ is the change in bond price, D is the duration and is the change in ytm.

Ay

But the relationship between $\Delta P$ and
Ay
is not linear. Therefore if we calculate $\Delta P$using equation (1), there will be an error.

This correction/error can be explained with convexity

• If a bond's duration increases as yields increase, the bond is said to have negative convexity.
• If a bond's duration rises and yields fall, the bond is said to have positive convexity.