Duration$-$With$-$Convexity Rule

The duration$-$with$-$convexity rule is a way to estimate the change in the price of a bond when the yield to maturity changes. It takes into account both the duration of the bond $($how sensitive its price is to changes in interest rates$)$ and its convexity $($how much the relationship between price and yield curves$).$

Answer

Answer Summary

The bond with higher convexity $($the $30-$year coupon bond$)$ will experience a smaller price change than the bond with lower convexity $($the $12-$year zero$-$coupon bond$)$ when the yield to maturity changes. This is because convexity helps to cushion the price impact of changes in interest rates.

In the scenario where the yield to maturity increases, the zero$-$coupon bond will experience a greater price decline than the coupon bond. Conversely, in the scenario where the yield to maturity decreases, the zero$-$coupon bond will experience a greater price increase than the coupon bond.