A Simple, Accurate Formula for the Duration of a Portfolio of Bonds Under a Non-Parallel Shift of a Non-Flat Yield Curve

26 Pages Posted: 8 Sep 2004

See all articles by Michael Osborne

Michael Osborne

University of Sussex Business School

Date Written: September 5, 2004

Abstract

It is well known that the various formulas for the duration of a bond give inaccurate results. Their accuracy can be improved by the addition of extra elements, such as convexity or duration vectors. But the results remain inaccurate. A recent paper proposed a new formula for the duration of a portfolio of vanilla bonds. The formula gives a precise, accurate value for any parallel shift in a flat yield curve, without the need for auxiliary concepts. The analysis is performed in the complex plane, and uses all possible interest rates that solve the time value of money equation. In this paper, the analysis is reworked to produce a second, complex formula that is more general. It copes with any non-flat yield curve and any non-parallel shift in the curve, and it is simpler and easier to prove. Some insights and puzzles presented by the new analysis are discussed.

Keywords: Duration, convexity, fixed income, bond, complex plane

JEL Classification: C60, G10, G11, G12

Suggested Citation

Osborne, Michael J., A Simple, Accurate Formula for the Duration of a Portfolio of Bonds Under a Non-Parallel Shift of a Non-Flat Yield Curve (September 5, 2004). Available at SSRN: https://ssrn.com/abstract=587242 or http://dx.doi.org/10.2139/ssrn.587242

Michael J. Osborne (Contact Author)

University of Sussex Business School ( email )

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