Duration Hiding in a Taylor Series

Duration has been touted as a tool for measuring the sensitivity of the price, or value, of an asset, or liability, whose cash flows are fairly determinable, to changes in interest rates. This paper seeks to describe the above relationship in a concrete fashion by expressing the value of an asset or liability as a function of the current interest rate. This function is then expanded in a Taylor series to illustrate just where the duration concept fits in. After this presentation is made, the Taylor series is further employed to illustrate that one may obtain a level of immunization as close to complete as desired by essentially matching successive terms in the Taylor series, the second of which reflects duration.