Macro and rates
Why Bond Prices Fall When Yields Rise: Coupons, Duration and the 10-Year
Why bond prices fall when yields rise, with a worked example, what duration measures, real yields and breakevens, and why the 10-year Treasury matters.
Updated · 3 min read
The coupon is fixed; the price is not
A bond is a promise to pay a fixed coupon each year and the face value at maturity. The coupon never changes. What changes is the price someone will pay today for that fixed stream, and the price is set so that the bond's yield to maturity matches what the market now demands for debt of that maturity and quality.
Take a ten-year bond with a 4% coupon on a face value of 1,000: it pays 40 a year and returns 1,000 at the end. When ten-year yields are 4%, it is worth exactly 1,000. If yields rise to 5%, nobody will pay 1,000 for a stream that yields 4% when new bonds yield 5%, so its price falls until the fixed 40 a year plus the pull to 1,000 at maturity together yield 5%. That price is about 923. If yields fall to 3%, the same bond is worth about 1,085.
Price = Σ Coupon / (1 + y)^t + Face / (1 + y)^n
Yield up, price down; yield down, price up. Nothing about the bond changed; the price of a fixed promise moved to match the new going rate.
Duration
Duration measures how much a bond's price moves for a given change in yield. Modified duration is the percentage change in price for a one-percentage-point change in yield, to a first approximation:
ΔPrice (%) ≈ − Modified duration × Δyield
Duration rises with maturity and falls with the size of the coupon, because a higher coupon returns more of the money sooner. Rough figures for Treasuries at today's yields:
| Instrument | Modified duration | Price move for +1% in yield |
|---|---|---|
| 2-year note | about 1.9 | about −1.9% |
| 5-year note | about 4.5 | about −4.5% |
| 10-year note | about 8 | about −8% |
| 30-year bond | about 16 to 17 | about −16% |
The relation is not a straight line: convexity means prices rise more when yields fall than they drop when yields rise by the same amount, and the effect is larger for long bonds. For moves of a quarter or half a point, duration alone is close enough.
Duration is why a bond fund is not a safe asset in a rising-rate year. A fund holding twenty-year Treasuries lost roughly a third of its value from the start of 2022 to the autumn of 2023 as yields rose, with no default anywhere.
Nominal, real and breakeven
The yield on an ordinary Treasury is a nominal yield. Treasury Inflation-Protected Securities (TIPS) pay a coupon on a principal that rises with the consumer price index, so their yield is a real yield: the return above inflation. The gap between the two for the same maturity is the breakeven inflation rate, the average inflation at which the two bonds would return the same:
Breakeven = Nominal yield − Real yield
A ten-year nominal at 4.3% and a ten-year TIPS at 2.0% imply a breakeven of 2.3%. Real yields are the number that matters most for assets that pay no income, gold above all, and for growth stocks whose earnings are far in the future.
Why the ten-year matters
The ten-year Treasury yield is the benchmark for the price of long-term money in dollars. Thirty-year mortgage rates are priced off it, corporate bonds are quoted as a spread over it, and equity analysts use it as the risk-free rate in the discount factor applied to future earnings. When the ten-year rises, every long-dated asset is marked down at the same time, which is why a sharp rise in yields hits growth stocks, real estate and gold together.
The two-year yield plays the other role: it tracks where the market expects the policy rate to average over the next two years, and it moves most on central bank decisions and the inflation and jobs data that shape them. The relation between the two is the yield curve.
On the desk
The fixed income page carries the live yield indices for the two-, five-, ten- and thirty-year, the day's and the month's changes, the breakevens and the bond ETFs that hold each part of the curve, so a yield move is read in price terms as well as in basis points.
Questions
- Why do bond prices fall when yields rise?
- A bond's coupon is fixed when it is issued. If market yields rise, new bonds pay more, so an existing bond's price must fall until its fixed coupon plus the gain to face value at maturity match the new yield. The price moves because the promise does not.
- What is duration?
- The sensitivity of a bond's price to a change in yield. Modified duration approximates the percentage price change for a one-percentage-point move in yield: a ten-year Treasury with a duration near 8 falls about 8% if its yield rises by one point. Duration rises with maturity and falls with the coupon.
- What is a real yield?
- The yield of an inflation-protected bond, which pays a return above inflation rather than a fixed nominal rate. The ten-year TIPS yield is the standard US real yield. The gap between the nominal and real yield at the same maturity is the breakeven inflation rate.
- Why does the 10-year Treasury yield matter for stocks?
- It is the risk-free rate used to discount future earnings, so when it rises the present value of distant profits falls, which hits growth stocks most. It also sets mortgage rates and corporate borrowing costs, so it feeds through to the real economy.
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