Bond Holding Period Return Decomposition

Abstract

The problem of decomposing bond portfolio holding period returns is addressed in this paper. Bond holding period returns are decomposed into four main components, the non-random horizon component, the spread component, the base-rate component, and an interaction component. The horizon component captures the return attributable to the mere passage of time over the holding period horizon based solely on the selected base spot rate curve. The spread component captures the return attributable to any change in the spread over the fitted base spot rate curve. The base-rate component captures movement in the fitted base spot rate curve using the LSC model introduced in this paper. The base-rate component of returns can be further decomposed into three components attributable to modified duration, convexity, and cross-convexity using the Taylor series approximation. Each of these three base-rate components can be further decomposed into three subcomponents tied to movement in level, movement in slope, and movements in a set of curvature components. We illustrate our results with several numerical examples, generic as well as actual U.S. Treasury data.