Duration

The duration of a bond measures the sensitivity of the bond’s full price (including accrued interest) to changes in the bond’s yield to maturity (in the case of yield duration measures) or to changes in benchmark interest rates (in the case of yield-curve or curve duration measures). Duration is among the most important characteristics of a fixed income security. It is often used as a measure of risk in bond investing.

Duration comes in many forms. Yield duration measures, such as modified duration, can be used only for option-free bonds because these measures assume that a bond’s expected cash flows do not change when the yield changes. This assumption is in general false for bonds with embedded options because the values of embedded options are typically contingent on interest rates. Thus, for bonds with embedded options, the only appropriate duration measure is the curve duration measure known as effective (or option-adjusted) duration. Because effective duration works for straight bonds as well as for bonds with embedded options, practitioners tend to use it regardless of the type of bond being analyzed.

Brief History

In 1938, economist Frederick Macaulay suggested duration as a way of determining the price volatility of bonds. ‘Macaulay duration’ is now the most common duration measure.

Until the 1970s, few people paid attention to duration due to the relative stability of interest rates. When interest rates began to rise dramatically, investors became very interested in a tool that would help them assess the price volatility of their fixed income investments. During this period, the concept of ‘modified duration’ was developed, which offered a more precise calculation of the change in bond prices given varying coupon payment schedules.

In the mid-1980s, as interest rates began to drop, several investment banks developed the concept of ‘option-adjusted duration’ (or ‘effective duration’), which allowed for the calculation of price movements given the existence of call features.

Different Duration Measures

While duration comes in many forms, the ones most commonly used by public fund investors include the following:

Macaulay Duration

Developed in 1938 by Frederic Macaulay, this form of duration measures the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future. Thus, it is the only type of duration quoted in “years.” Interest rates are assumed to be continuously compounded.

Modified Duration

This measure expands or modifies Macaulay duration to measure the responsiveness of a bond’s price to interest rate changes. It is defined as the percentage change in price for a 100 basis point change in interest rates. The formula assumes that the cash flows of the bond do not change as interest rates change (which is not the case for most callable bonds).

Effective Duration

Effective duration (sometimes called option-adjusted duration) further refines the modified duration calculation and is particularly useful when a portfolio contains callable securities. Effective duration requires the use of a complex model for pricing bonds that adjusts the price of the bond to reflect changes in the value of the bond’s “embedded options” (e.g., call options or a sinking fund schedule) based on the probability that the option will be exercised. Effective duration incorporates a bond’s yield, coupon, final maturity and call features into one number that indicates how price-sensitive a bond or portfolio is to changes in interest rates.

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