


Duration was originally developed in 1938 by Frederick Macaulay as a means
for comparing the maturities of financial instruments with differing payment
structures (amortizing vs. nonamortizing ). It is essentially a measure of the
sensitivity of market values to small changes in interest rates.
Macaulay’s version of duration is stated as a measure of time. For example, a given instrument has a duration of 2.5 years. This measure is derived by incorporating the instrument’s remaining time to maturity, the level of interest rates, and intermediate cash flows. Duration is calculated by weighting the present value of an instrument’s cash flows by the time to receipt of those cash flows. Macaulay’s measure was later modified to express the price sensitivity of a bond to a given percentage change in interest rates. This came to be known as "modified duration" or "interest rate elasticity". These measures are stated as expected percentage changes to an instrument's present value for a 100 basis point change in interest rates. As an example, if a given instrument has an interest rate elasticity of 1.50, there is an expectation that if interest rates rise by 100 basis points, the instrument’s present value will decline by approximately 1.5%. The use of the negative sign when stating interest rate elasticity reflects the inverse relationship between rate change and a change in an instrument’s present value. Rates up, present value down. Rates down, present value up. Interest rate elasticity basically communicates by how much. Duration (either version) can be used to measure the interest rate exposure of the economic value of a single instrument, a portfolio of instruments, or the bank’s overall economic value of equity. For a given instrument, as indicated above, the duration is derived by weighting the present value of an instrument’s cash flows by the time to receipt of those cash flows. The duration of a portfolio can be determined by simply adding the individual instrument durations and weighting them by their percentage of the total. The duration of the overall economic value of equity, is derived from the duration of all assets, liabilities, and offbalance sheet contracts. Similar to the concept of GAP analysis, the inherent mismatch between the duration of assets, liabilities and offbalance sheet items determines the exposure of the bank’s economic value of equity to changes in interest rates. A bank with longterm assets funded by shortterm liabilities (very typical for many community banks today), will generally have a duration of equity that is positive. The economic value of this bank will decline as interest rates rise. Conversely, a bank with shortterm assets funded by longterm liabilities will generally have a negative duration of equity. The economic value of this bank will increase as interest rates rise.
