Volume 3 — Valuation and Risk Metrics © Copyright 2002, CCRO. All rights reserved. 50 APPENDIX E – DURATION This appendix describes the duration metric commonly used in financial markets and also provides additional detail on the applicability of the duration formula for calculating the tenor of a portfolio, as discussed in Section II-7.0. Duration is a measure of the sensitivity of the value of a series of cash flows to interest rates. The duration calculation is typically used in the construction of fixed-income hedging strategies. Specifically, the desired relationship is defined by analogy to a single cash flow occurring at time t, where the following holds: dPV t PV dy = −  where y denotes the yield to maturity t. The duration of a sequence of cash flows is defined by analogy, namely: 1 DUR= - dPV PV dy . In this case, as the yield can vary by the maturity of each cash flow, the derivative has the implied reference to a constant shift in all yields. Solving for the duration yields: DUR i y ti i i c e− ti PV =  where yi is the yield to maturity ti . NOTE 1: This is the standard definition of duration. Other formulations define the same concept in the context of nominal rates (e.g., annual effective interest rates), but the consequences are insignificant. NOTE 2: The intuition behind this measure is clear for cash flows of the same sign. Namely, the coefficients yti i c e− PV