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Duration Analysis: An Overview

In: New Issues in Financial and Credit Markets

Author

Listed:
  • Göran Bergendahl
  • Ted Lindblom

Abstract

Duration analysis has long been used in banking, insurance and finance [see Bierwag et al. (1978) and Ingersoll et al. (1978) for historic overviews]. Macaulay (1938) was early to use it for quantifying the length of the payment stream of a bond, defining duration as the weighted average of the time to maturity. Hicks (1939) identified Macaulay’s concept of duration as the bond’s price elasticity. A bond is a fixed-income security whose yield is determined by the interest rate (r) at which the present value of the payment stream equals its price. This makes duration a very suitable measure to calculate the interest-rate sensitivity of a bond’s market value. Following Luenberger (1997, pp. 57–62), suppose that its cash flows (coupons) are received at times t = 1, 2, …, T. As duration (D) is the time-weighted average of the present values of these cash flows {PV(t)}, it is directly related to the volatility (V) of the bond value with respect to interest changes, that is: 1 [ D = ∑ t = 1 T P V ( t ) × t P V = − d P V P V × 1 + r d r = − V × 1 + r d r ]]

Suggested Citation

  • Göran Bergendahl & Ted Lindblom, 2010. "Duration Analysis: An Overview," Palgrave Macmillan Studies in Banking and Financial Institutions, in: Franco Fiordelisi & Philip Molyneux & Daniele Previati (ed.), New Issues in Financial and Credit Markets, chapter 13, pages 171-183, Palgrave Macmillan.
    • Handle: RePEc:pal:pmschp:978-0-230-30218-1_14
    DOI: 10.1057/9780230302181_14
    as

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