Bonds course · Lesson 2 of 7
Duration tells you how far a bond price moves.
Two bonds with the same coupon can react very differently to the same change in rates. Duration is the one figure that tells you how much.
Two kinds of duration
Macaulay duration is the average time until you get your cash, weighted by the value of each payment. For the example bond, it is 8.34 years. That is less than the 10 years to maturity, because the coupons arrive earlier.
Modified duration is the percentage change in price for each 1 point of change in yield. For the example bond, it is 8.18. So a rise of 1 point in the yield lowers the price by about 8.18%.
The estimate against the real price
| Change in yield | Duration estimate | With convexity | Actual change |
|---|---|---|---|
| Up 1 point | -8.18% | -7.78% | -7.79% |
| Down 1 point | +8.18% | +8.57% | +8.58% |
Duration gives a straight line, but the real price follows a curve. The curve is called convexity. Because of it, the real loss is smaller than the estimate, and the real gain is larger. Add the convexity term, and the estimate is almost exact.
Longer bonds move more
| Maturity, 4% coupon | Macaulay duration | Modified duration | Price change, 4% to 5% |
|---|---|---|---|
| 2 years | 1.94 years | 1.90 | -1.88% |
| 5 years | 4.58 years | 4.49 | -4.38% |
| 10 years | 8.34 years | 8.18 | -7.79% |
| 30 years | 17.73 years | 17.38 | -15.45% |
A 2-year bond loses 1.88% when the yield goes from 4% to 5%. A 30-year bond loses 15.45%. A bond with no coupon has a duration equal to its maturity: a 10-year zero coupon bond has a duration of 10.00 years.
How to use it
Most bond funds publish their duration. Multiply it by the change in rates that you want to test. A fund with a duration of 6 loses about 6% if rates rise 1 point. Use this before you buy, not after.
Key points
- Modified duration is the percentage change in price for each 1 point of yield.
- Longer maturities and lower coupons give a longer duration.
- Convexity makes the real loss a little smaller and the real gain a little larger.