What happens to bond prices when interest rates rise, and what is duration?
Bond prices fall when rates rise because fixed payments are discounted more. Modified duration measures that sensitivity, so a $1,000 bond with duration 7 falls about 3.5%, to $965, on a half point rise. Longer maturity and lower coupons raise duration.
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Example answer
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Bond prices fall when interest rates rise. They always move in opposite directions. A bond pays fixed coupons, and new bonds now pay more, so nobody will pay full price for an old bond with a lower coupon.
Duration measures how much the price moves. It's basically how long the bond has left until it matures, so longer bonds are more sensitive. So a thirty-year bond gets hurt far more than a two-year note by the same rise in rates.
What holds it back
The direction is right and the new-bond logic is fair, but duration is described as time left to maturity. That misses what it measures, and there's no number to show the size of the move.
Bond prices fall when interest rates rise. A bond pays fixed coupons, so its price is the present value of those fixed payments. If the market yield goes up, I discount the same cash flows at a higher rate and the present value is lower. Another way to see it is that new bonds now pay more, so nobody will pay full price for an old bond with a lower coupon. Duration measures how much the price moves. It's the approximate percentage change in price for a one percentage point change in yield. The rule is that the price change is about minus duration times the change in yield. For example, take a bond with a duration of 7. If yields rise by half a point, the price falls by about 7 times 0.5, which is 3.5%. A longer maturity means a higher duration. So a thirty-year bond gets hurt far more than a two-year note by the same rise in rates.
Bond prices fall when interest rates rise. A bond pays fixed coupons, so its price is the present value of those fixed payments. If the market yield goes up, I discount the same cash flows at a higher rate and the present value is lower. Another way to see it is that new bonds now pay more, so nobody will pay full price for an old bond with a lower coupon. Its price drops until its yield matches the market. Duration measures how much the price moves. Strictly, Macaulay duration is the weighted average time until I receive the bond's cash flows, in years. The useful one here is modified duration, which is the approximate percentage change in price for a one percentage point change in yield. The rule is that the price change is about minus duration times the change in yield. For example, take a bond priced at $1,000 with a duration of 7. If yields rise by half a point, the price falls by about 7 times 0.5, which is 3.5%. That's $35, so the bond is worth about $965. Two things raise duration, a longer maturity and a lower coupon, because more of the value sits in distant payments. So a thirty-year bond gets hurt far more than a two-year note by the same rise in rates. The caveat is that duration is a straight-line estimate of a curved relationship. For a big move I'd add convexity, which for a plain bond means the price falls a little less than duration predicts when yields rise and gains a little more when they fall.
The numbers, step by step
A bond priced at $1,000 with a modified duration of 7, and yields rising by half a percentage point.
- Percentage price change−7 × 0.5 points
- −3.5%
- Dollar price change$1,000 × 3.5%
- $35
- New price$1,000 − $35
- $965
What the interviewer listens for
- Do you get the direction right and explain it with discounting?
- Can you define duration as a price sensitivity and not only as a number of years?
- Can you turn a duration and a yield change into a price change?
- Do you know what makes duration higher or lower?
- Do you know where the approximation breaks down?
Common mistakes
- Saying duration is the bond's maturity.They're equal only for a zero-coupon bond under the Macaulay definition, and a coupon bond's duration is shorter than its maturity.
- Forgetting the minus sign or the units, for example reading a duration of 7 and a half-point rise as a 7% fall and not 3.5%.
- Explaining the price fall only as bonds becoming less attractive, without the discounting logic that the same fixed cash flows are worth less at a higher yield.
- Presenting the duration estimate as exact for a large move in yields and never mentioning convexity.
More finance technicals
- Explain delta, gamma, theta and vega.
- What is put-call parity?
- Pitch me a stock.
- What does an inverted yield curve tell you?
- Walk me through a DCF.
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