Bond duration explained: how much a bond's price moves when rates change

When interest rates rise, bond prices fall. Everyone who owns bonds or a bond fund learns that sooner or later. Duration answers the next question: by how much? It turns a bond’s coupon, maturity and yield into one number you can compare across bonds and funds.

Two durations, one idea

Macaulay duration is the average time until you receive the bond’s money, measured in years. Each coupon and the final repayment count in proportion to what they are worth today. Because coupons arrive before maturity, a coupon bond’s duration is always shorter than its maturity; a zero-coupon bond, which pays everything at the end, has a duration equal to its maturity.

Modified duration turns that into price sensitivity. Divide Macaulay duration by (1 + the yield per period) and you get the approximate percentage the price moves for a 1-point change in yields. A modified duration of 8 means a rise in yields from 5% to 6% should cut the price by about 8%, and a fall to 4% should lift it by about 8%. This is the duration bond funds publish on their factsheets.

A worked example

Take a 10-year bond with a $1,000 face value and a 4% coupon paid twice a year. At a 5% market yield it is worth $922.05. On average its cash flows arrive after a little over 8 years, and its modified duration predicts a fall of about 8.05% if yields rise by 1 point.

Pricing it again at 6% gives $851.23: a fall of 7.68%. At 4%, the yield now equals the coupon, so the bond is worth exactly $1,000, a rise of 8.45%. Both moves differ a little from the 8.05% estimate, in the bond’s favour. You can reproduce every figure in the bond price calculator.

What makes duration longer

A longer maturity. With the same 4% coupon and 5% yield, a 2-year bond moves only about 1.9% for a 1-point rise in yields, while a 30-year bond loses about 14.5%. The longer the coupon is locked in, the more a change in rates matters.

A lower coupon. Over 10 years at a 5% yield, modified duration is about 7.2% with an 8% coupon, 8.05% with a 4% coupon and about 9.76% for a zero-coupon bond. The less income arrives early, the more of the value sits in the final repayment, far in the future.

A lower yield. Distant cash flows are discounted less when yields are low, so they weigh more. The same 4% bond has a modified duration of about 8.41% when market yields are 2%, against 8.05% at 5%. That is why bonds bought when rates are very low carry more interest rate risk than they seem to.

Convexity: why duration is only a first estimate

Duration draws a straight line through a relationship that is curved. For an ordinary bond the curve bends in the holder’s favour: when yields rise the price falls a little less than duration says, and when they fall it rises a little more. For small moves the difference is tiny; for moves of several points it adds up, which is why the calculator reprices bonds exactly instead of relying on duration alone.

What duration means for you

If you hold a bond to maturity, price swings along the way do not change what you receive, as long as the issuer pays. Duration matters when you might need to sell early.

For a bond fund, it is the most useful number on the factsheet. A fund with a duration of 6 would lose roughly 6% if rates rose 1 point. Funds keep replacing their bonds, so there is no maturity date when the price is sure to come back; higher yields on the new bonds make up for the loss over time instead, roughly over a period equal to the duration.

Match it to your horizon. Money you need in two years is safer in bonds or funds with a duration of about two years or less. To compare a bond’s price with the yield it offers, use the bond yield calculator, and see current yield vs. yield to maturity for how to read the yields a broker quotes.