Duration

Duration is a measurement, in years, that assesses the interest-rate sensitivity of a bond.

There are two types of bond duration: Macaulay duration and modified duration. Both are measured in years and assess a bond’s interest-rate sensitivity.

Macaulay duration is the weighted average time that it takes for all of a bond’s future cash flows to be received and to cover the true cost of the bond. By future cash flows of the bond, we are considering all payments made by the bond issuers to the investor (including coupon and maturity payments). Macaulay duration will be between zero years up to however many years until the bond’s maturity. It is calculated by first discounting all future cash flows to their present value. Each discounted cash flow is multiplied by the period number in which it is expected to be paid out. The sum of these values will then be divided by the current bond price to determine its Macaulay duration. The longer measure in years for Macaulay duration, the more exposure the bond’s future cash flows will have to changing interest rates.

Modified duration, also measured in years, assesses a bond’s approximate price shift in response to a 1% change in interest rates. Note that a bond’s price has an inverse relationship with interest rates: As interest rates rise, bond prices will decrease. If a bond has a modified duration of 5 years, then we can expect an approximate 5% shift in the bond’s price for every 1% change in interest rates. If interest rates rise by 2%, then the bond price will decrease by roughly 10% (5 years modified duration times 2% change in interest rates).