Beyond Duration

This paper addresses the problem of hedging a portfolio of fixed-income cashflows. We first briefly review the traditional duration hedging method, which is heavily used by practitioners. That approach is based on a series of very restrictive and simplistic assumptions, including the assumptions of a small and parallel shift in the yield curve. We know however that large variations can affect the yield-to-maturity curve and that three main factors (level, slope and curvature) have been found to drive the dynamics of the yield curve. This strongly suggests that duration hedging is inefficient in many circumstances. We first show how to relax the assumption of a small shift of the yield-to-maturity curve, by including a convexity component in the Taylor expansion of the value function of the bond. Then, we show how to relax the assumption of a parallel shift of the yield curve in a fairly general framework. In particular, we argue that principal component analysis of interest rates changes allows a portfolio manager to regroup risk in a natural way. We conclude by analyzing the performance of the various hedging techniques in a realistic situation, and we show that satisfying hedging results can be achieved by using a three-factor model for the yield curve.