Financial Instruments and Markets: A Casebook

4

Note on Duration and Convexity

When interest rates go up, bond prices fall.

All actors in the financial markets—money managers, traders, arbitrageurs—know this. But how do they compare how much prices will change between various financial instruments, before interest rates actually change? To inform their strategies, traders want to know, for instance, which bond will lose more in price given that interest rates rise 100 basis points: a 6% coupon bond with a 15-year maturity or one with a 30-year maturity—or maybe a 9% coupon bond with a 30-year maturity. To help estimate price sensitivity between bonds of different maturities and coupon rates, two measures are normally used: duration and convexity.

As measures, however, duration and convexity are not just limited to bonds. They apply to all financial instruments, fixed income and equity alike. They also measure price reaction to risk factors other than just interest rates. Therefore, put more generally, duration and convexity take into account any change for any risk factor affecting the price of any financial instrument. Although many examples in this note will center on their use for bonds regarding yield and interest rate changes, this larger application of duration and convexity should not be underrated.

The main difference between the two concepts is that duration focuses on small changes in risk factors, and convexity then builds on duration to adjust for larger changes. For bonds, for instance, the basic price-yield relationship ...