Duration and Convexity of Inverse Floating Rate Bonds
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1999
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Morse, Joel N.; Nawalkha, Sanjay K.; Zhang, Jun; Lacey, Nelson J. “Duration and Convexity of Inverse Floating Rate Notes,” Journal of Research in Finance, Vol.2, No. 2, Winter, 1999, pp. 169-190
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Abstract
Inverse floating rate bonds introduce unusual patterns of interest rate risk into a portfolio. To help assess and manage that risk, this paper presents duration and convexity measures for inverse floating rate bonds. Both the duration and the convexity of the inverse floater are shown to be weighted averages of the duration and convexity of an associated portfolio of fixed rate bonds and floating rate bonds. This portfolio of bonds mimics the inverse floater, and the weights are determined by the relative prices and the leverage ratio of the mimicking portfolio. The duration of inverse floating rate bond is greater than the duration of the associated fixed rate bond, and the convexity of inverse floating rate bond is greater than the convexity of the associated fixed rate bond. The time decay patterns of duration and convexity of inverse floating rate bond are shown to be dependent on the time decay patterns of the duration and convexity of the associated fixed rate bond and floating rate bond, as well as on the relative prices of the bonds and the leverage ratio. Finally both the duration and the convexity of the inverse floating rate bond are shown to increase dramatically with the leverage ratio.