Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 15. Duration Estimation for Bonds and Bond Portfolios

FRANK J. FABOZZI, PHD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

Abstract: The major risk faced by participants in the bond market is interest rate risk. An investor or a portfolio manager can measure the exposure to interest rate changes of a position by revaluing that position based on various interest rate scenarios. However, the typical way in which interest rate risk is measured is by approximating the impact of a change in interest rates on a bond or a bond portfolio. The first approximation is referred to as duration. To improve upon this approximation, a second measure is estimated and is referred to as convexity. There are different types of duration measures: duration, dollar duration, modified duration, Macaulay duration, effective duration, option-adjusted duration, portfolio duration, contribution to portfolio duration, spread duration, and index duration. The duration estimate require a good valuation model.

Keywords: duration, dollar duration, price value of a basis point, dollar value of a basis point, modified duration, Macaulay duration, effective duration, positive convexity, negative convexity, option-adjusted duration, portfolio duration, contribution to portfolio duration, spread duration, index duration

The two characteristics of a bond that affect its interest rate risk are well known: coupon rate and maturity. Specifically, for a given change in interest rates: (1) the ...