Duration

Duration is used as a measure of relative interest rate risk between different bonds. Two methods for computing duration are commonly used in the management of bond portfolios. Macaulay duration is a measurement of the average time to receipt of all of the cash flows for a given security weighted by the size of each cash flow. Modified duration is a measure of the estimated change in price in percent for a security given a 100 basis point (1%) change in interest rates.

Macaulay Duration

Macaulay duration is often used to compare the relative risk of two bonds. This volatility measurement can best be understood if all of the cash flows for a given bond could be arranged on a long plank representing the total life of a bond. The Macaulay duration would be the point in the life of the bond where the cash flows were in balance; a wedge could be put under the plank at this point and all of the cash flows would be balanced. For a zero coupon bond, with a single cash flow of face value repaid at maturity, the duration would match the maturity.

To the extent that cash flows take place later in a bond’s life, they lengthen its maturity; to the extent that they take place earlier in a bond’s life, they shorten its maturity. There are a number of general rules of thumb surrounding duration:

• all other things being equal, the longer a bond’s maturity, the greater its duration
• the lower its coupon, the greater its duration
• the less frequent its payments, the greater its duration.

Modified Duration

Modified duration is an attempt to measure the expected change in price of a bond for a given change in yield. This measure is most accurate for small changes in interest rates.