Börsenlexikon: Duration

Duration is a sensitivity measure that denotes the average period of capital commitment of an investment in a fixed-income security. More precisely and generally speaking, duration is the weighted average of the times at which the investor receives payments from a security. The duration can be used to derive the fluctuation risk of a bond.

The duration was developed in 1938 by Frederick R. Macaulay and is therefore called Macaulay duration. Duration represents that point in time at which total immunization from interest rate risk occurs in terms of terminal value fluctuations. The concept is based on the fact that unforeseen changes in interest rates have two opposite effects on the terminal value of a fixed-income security (e.g. bond): For example, an increase in interest rates leads to a lower present value of the bond; however, because of the reinvestment premise, future payments (coupons) earn higher interest rates. Ultimately, an increase in interest rates leads to a higher terminal value. The reverse is true if interest rates fall. The point in time by which the market value of the bond has at least returned to the expected value in the case of rising interest rates due to the reinvested coupons or by which it has not fallen below the expected value in the case of falling interest rates due to the lower discounting is called duration.

(Macaulay) duration is measured in units of years. However, this greatly complicates its practicality. It would therefore be much more desirable to be able to make a statement about the relative change in the bond price as a function of a change in the market interest rate level. This task is performed by the modified duration. It indicates by what percentage the bond price changes if the market interest rate level changes by one percentage point, i.e. it measures the price effect triggered by a marginal interest rate change and thus represents a kind of elasticity of the bond price from the market interest rate. Since the very restrictive assumptions of the duration concept also apply here, practical applicability is again only given for very small interest rate changes.