Macaulay durations for nonparallel shifts

Macaulay duration is a well-known and widely used interest rate risk measure. It is commonly believed that it only works for parallel shifts of interest rates. We show in this paper that this limitation is largely due to the traditional parametric modelling and the derivative approach; the Macaulay duration works for non-parallel shifts as well when the non-parametric modelling and the equivalent zero coupon bond approach are used. We show that the Macaulay duration provides the best one-number sensitivity information for non-parallel interest rate changes and that a Macaulay duration matched portfolio is least vulnerable to the downside risk caused by non-parallel rate changes under some verifiable conditions.