BOND MATH: The Theory Behind the Formulas

CHAPTER 6

Duration and Convexity

Duration and convexity are statistics that estimate the sensitivity of the market value of an asset or liability to a change in interest rates. Usually the asset or liability is a fixed-income bond, but as measures of rate sensitivity, they apply to all sorts of securities and derivatives. We can ask meaningfully about the duration and convexity of a floating-rate note, an inflation-indexed bond, or an interest rate swap. That discussion will have to wait until Chapters 7 and 8. This chapter focuses on the risk statistics applicable to a typical fixed-rate or zero-coupon bond.

We start with classic yield duration—the sensitivity of the bond price to a change in its yield to maturity. This leads to the well-known ...