Duration

Duration measures how much a bond's price changes when interest rates move. It is expressed in years but functions as a risk metric: a bond with a duration of 8 years will lose approximately 8% of its value for every 1 percentage point rise in yields.

Two related measures are commonly used:

• Macaulay duration is the weighted-average time to receive a bond's cash flows, where the weights are the present values of each payment. For a par bond with semiannual coupons, Macaulay duration approximates (1 + y/2) / (y/2) x (1 - 1/(1 + y/2)^(2n)), where y is the yield and n is the maturity in years.
• Modified duration adjusts Macaulay duration for the compounding frequency: modified duration = Macaulay / (1 + y/2). This gives the percentage price change per 1% yield change.

Duration increases with maturity and decreases with coupon rate. A 10-year Treasury at par has a modified duration around 8.2 years, while a 30-year bond has roughly 16.4 years.

Portfolio managers use duration to manage interest rate risk. A duration-neutral portfolio is constructed so that gains from one position offset losses from another when rates move. Understanding duration is essential for evaluating how yield curve shifts affect portfolio value.