Question

1. Duration provides a good approximation of changes in the price of an option-free bond, when the change in yield is relatively small. However, for large changes in yield a convexity adjustment needs to be incorporated.

With the aid of your own fully annotated diagram, discuss the statement above and address why a convexity adjustment is necessary.

Answer 1

Duration is th weighted average of the PV of the coupon and principal repayments and it captures and shows the best estimate only for the small changes in the interest rate.

The rlation between prices and yields is no linear and there are large changes in eitherwith respect to the other if one of them has a increases a lot or decreases a lot. So when there is an unsymmetrical change in the prices of bonds an adjustment is required. Convexity basically refers to the non linear change in the prices of output given a change in the prices or rates of the underlying variable. For larges changes in yield duartion may not give an accurate picture of the price of the bond so a convexity adjustment is done taking into account the curavture of the price yield curve as given in the above diagram.  

Convexity adjustment = Bonds convexity * 100 * ( Changes in Yield )^2