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Yield-Based Bond Duration Measures and Properties

2025 Curriculum CFA® Program Level I Fixed Income

Overview

Prior lessons explored two sources of interest rate risk—reinvestment risk and price risk—and demonstrated how holding a bond for its Macaulay duration balances them. T his lesson and those that follow extend that discussion by introducing measures of price risk. Two broad categories of such measures exist: those that assume underlying bond cash flows are certain and measure price sensitivity to changes in a bond’s own yield, which are covered in these lessons, and those that introduce the possibility of a bond default and that measure price sensitivity to changes in a benchmark yield curve, which are covered in later lessons. This lesson will illustrate how the interest rate risk of a bond is a function of its features, including its time-to-maturity, coupon rate, and yield.

Most of the examples and exhibits used throughout the reading can be downloaded as a Microsoft Excel workbook. Each worksheet in the workbook is labeled with the corresponding example or exhibit number in the text.

  • Duration is a quantitative measure of interest rate risk. There are several duration measures, including those that measure a bond’s price sensitivity to changes in its own yield-to-maturity and assume underlying cash flows are certain (yield duration) and those that measure changes in a benchmark yield curve, with less certain underlying cash flows (curve duration).
  • Macaulay duration, modified duration, money duration, and the price value of a basis point (PVBP) are yield duration measures.
  • Modified duration is the slope or first derivative of the price of a bond with respect to its yield-to-maturity, measuring the sensitivity of a bond’s price to changes in its yield-to-maturity. Modified duration can be calculated using a bond’s Macaulay duration and yield or through approximation. 
  • Money duration is an extension of modified duration and incorporates the size of the bond position in currency terms. Related to this measure is the price value of a basis point, which is an estimate of the change in the price of a bond for a 1 bp change in the bond’s yield.
  • Duration can be used to estimate the change in the price of a bond in response to a change in yield, but it assumes a linear relationship between price and yield even though, in fact, the relationship is nonlinear. This is most evident when estimating price changes for large changes in yield and for bonds with certain features. 
  • A bond’s features, including its time-to-maturity, coupon rate, and yield-to-maturity, determine its duration. Duration, for a given bond, is not static and decreases as the bond approaches maturity. 
  • All else equal, a longer (shorter) time-to-maturity, a lower (higher) coupon rate, or a lower (higher) yield-to-maturity results in higher (lower) duration or higher (lower) interest rate risk.

     

Learning outcomes

The candidate should be able to:

  • define, calculate, and interpret modified duration, money duration, and the price value of a basis point (PVBP);
  • explain how a bond’s maturity, coupon, and yield level affect its interest rate risk.

1 PL Credit

If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.