Question

Explain how to use duration and convexity of a 100 year bond for interest rate risk management.

Answer 1

Generally bonds with long maturities and low coupon have the longest durations and are more sensitive to changes in interest rates.

Duration risk is the risk associated with the sensitivity of a bond's price to a one percent change in interest rates.

Bond return = - Duration * 1/(1+i) * yield change

However this is just an approximation because convexity defines that bond's price-yield relationship is not linear but convex. But duration replaces the curved relationship to linear.

convexity determines how the duration of a bond changes upon changes in interest rates.

There should be a positive convexity for a 100 year bond i.e. yield falls if bond duration rises