Fixed Income Securities, 4th Edition

CHAPTER 4DV01, Duration, and Convexity

This chapter, along with Chapters 5 and 6, are about measuring and hedging interest rate risk. Market participants need to understand how fixed income prices change when interest rates change to take a view on the future level or term structure of interest rates, to ensure that a portfolio of assets keeps pace with a portfolio of liabilities, or to hedge one fixed income instrument or portfolio with another. But how exactly should a “change” in rates be defined? Chapters 1 through 3 show that pricing in fixed income markets can be expressed in terms of discount factors, par rates, spot rates, forward rates, yields, and spreads. Which of these quantities should be assumed to change and by how much?

In answering this question, there are two overarching trade‐offs: simplicity versus empirical reality, and robustness versus model dependence. With respect to the first trade‐off, a market maker who is hedging a long position in a 9.75‐year bond with a short position in a 10‐year bond over a short time period might reasonably rely on the simplest of frameworks, namely, that the yields of the two bonds will move up or down by the same number of basis points, that is, in parallel. A swap desk, by contrast, which is managing the risk of a portfolio of long and short swap positions of different terms, has to account for the reality that changes in rates across the term structure do not move perfectly in sync. With respect to robustness versus model ...