Bond prices and yields: why prices fall when yields rise

A bond's price and its yield are two ways of stating the same thing. The price is what you pay today; the yield is the annual return that price implies if you collect every promised payment. Because the payments of an ordinary bond are fixed when it is issued, the only way its return can adjust to a change in market interest rates is through the price. When yields across the market rise, existing bonds must get cheaper; when yields fall, they get dearer.

That inverse relationship is the single most important fact in fixed income, and it surprises many new investors, who expect a "safe" government bond fund never to fall. Between July 2020 and September 2026 the 30-year Treasury yield rose from 1.31% to 5.37% in monthly terms, and the price of TLT, an exchange-traded fund holding Treasuries with 20 or more years to maturity, fell by more than half.

This page builds the relationship from the ground up: discounting a single payment, then pricing a whole bond, then reading the yield measures quoted on bonds and how a price drifts toward face value over time. Rate sensitivity in depth (duration and convexity) has its own page, Bond duration and convexity: measuring interest-rate risk, and the broader introduction to fixed income is Bonds and fixed income: how bonds work, pay and lose value.

Present value: the building block

Money promised in the future is worth less than money today, because today's money could be earning interest in the meantime. Compound interest: how growth on growth builds wealth runs that idea forward: $100 invested at 5% a year grows to $105 in one year and $110.25 in two. Present value runs it backward: what is a payment of $110.25 in two years worth today, if 5% a year is what you could earn elsewhere? Exactly $100.

The higher the discount rate, and the farther away the payment, the smaller its present value. A promise of $100 in 10 years is worth $67.56 today at a 4% annual yield but $61.39 at 5%. One percentage point on the discount rate cut the value of that distant payment by about 9%, which is a first hint of why long bonds are so sensitive to rates.

Pricing a whole bond

An ordinary fixed-rate bond is just a bundle of these promises: a coupon payment each period and the face value (also called par or principal, usually quoted per $100) at maturity. Its price is the sum of their present values, each discounted at the same market yield.

Treasury notes and bonds actually pay coupons every six months, so the formula is applied with half the annual coupon and half the annual yield per period. The results differ only slightly: the 10-year, 4% bond below is worth $92.28 with annual payments at a 5% yield, and $92.21 with semiannual payments. The examples here use annual payments to keep the arithmetic readable.

Why prices move opposite to yields

Think about what happens to a bond you already own. Suppose you bought a newly issued 10-year note with a 4% coupon at $100, when the market yield for 10-year money was 4%. Then market yields rise to 5%. New buyers can now get 5% elsewhere. Nobody will pay $100 for your 4% coupon stream, so the price has to fall until the bond also offers 5%: a lower coupon return made up by a gain as the price rises back to $100 at maturity.

The curve shows three things worth memorizing.

1. At a yield equal to the coupon, the bond trades at par. At 4%, the price is exactly $100.00.
2. The relationship is inverse. At 5% the price is $92.28; at 3% it is $108.53. At a 0% yield it would be $140, the plain sum of ten $4 coupons and $100 of principal; at 10% it would be $63.13.
3. The curve bends. A 1-point rise from 4% costs $7.72, but a 1-point fall gains $8.53. Losses from rising yields are a little smaller than gains from falling yields of the same size. That curvature is convexity, and the slope at any point is duration; both are worked through on Bond duration and convexity: measuring interest-rate risk.

The yield measures you will see quoted

"Yield" on a bond can mean several things, and they differ for any bond not priced at par.

Coupon rate. The fixed annual interest as a percentage of face value. A 3% coupon on $100 face pays $3 a year no matter what the bond trades for. It never changes after issue.

Current yield. The annual coupon divided by today's price. It is easy to compute but ignores the gain or loss you will take as the price moves to face value.

Yield to maturity (YTM). The single discount rate that makes the present value of all remaining payments equal the current price. It assumes you hold to maturity, every payment arrives, and coupons can be reinvested at the same rate. When people say a Treasury "yields 5%", they mean its yield to maturity. There is no closed-form solution; YTM is found by trial and error or by a calculator. See Yield to maturity (YTM) for the definition.

For a discount bond, coupon < current yield < YTM. For a premium bond the order flips: coupon > current yield > YTM, because the buyer will lose the premium by maturity.

Premium, discount and pull to par

A bond whose price is above face value is a premium bond: its coupon is higher than the market yield. A bond below face is a discount bond: its coupon is lower. Neither is a bargain or a rip-off by itself. Both are priced to deliver the same market yield.

As maturity approaches, each bond's price converges on face value, because the final $100 payment dominates and there is less time left for the coupon difference to matter. This is called pull to par.

Pull to par is also why a single bond held to maturity returns its original yield regardless of interim price swings, while a bond fund that keeps a constant maturity never reaches par; the comparison is on Bond ETFs vs individual bonds: maturity, risk and cost compared.

Real data: TLT and the 30-year yield

The cleanest real-world demonstration is a fund of very long Treasuries. TLT holds Treasury bonds with 20 or more years to maturity, so its price responds strongly to long-term yields.

The two panes are close to mirror images.

• From July 2020 to September 2026, the 30-year yield rose about 4.1 points and TLT's price fell 54.5%, from $171.00 to $77.78. Most of the damage came by October 2023, when the close was $83.58, down 51.1%.
• Compare August 2002 with September 2026. The 30-year yield was similar, 5.28% then and 5.37% in September 2026, and TLT's price was in the same neighborhood too, $87.08 then and $77.78 now, about 11% lower. Over 24 years of falling and then rising yields, the price made no lasting progress, because yields ended close to where they began.

These are price-only figures. TLT also paid out the interest its bonds earned, which this chart leaves out, so an investor who held through the whole period earned that income on top of the price change. The point of the chart is the mechanism: when the yield on the bonds inside a fund rises, the price of the fund falls, and the longer the bonds, the larger the fall.

Pitfalls and limitations

• YTM is a promise, not a forecast. It assumes every payment is made on time and that coupons are reinvested at the same yield. For Treasuries the first assumption is essentially safe; the second rarely holds exactly.
• Quoted price is not what you pay. Bonds trade at a "clean" price plus accrued interest, the part of the next coupon earned since the last payment date. The total, the "dirty" price, is what changes hands.
• Coupon rate is not return. A high coupon bought at a big premium can yield less than a low coupon bought at a discount. Compare yields to maturity, not coupons.
• A fund is not a bond. A bond fund has no maturity date, so it never pulls to par; its price can stay below its old level for years if yields stay higher.
• Other risks. This page is about rate risk in default-free bonds. Corporate and municipal bonds also carry credit risk, covered in Credit ratings and credit spreads: how bond risk is priced.

Bond yield measures compared

How Finabase does it

Finabase does not show bond-level data (no individual bonds, coupons, durations or yields to maturity) and has no bond calculator. What it does show helps you watch the price-yield link in practice.

• Treasury yields: the Treasury list quotes yields from 1 month to 30 years, and each has a chart, such as the 30-year.
• Bond ETFs on symbol pages: funds such as TLT, IEF, SHY and AGG have full quote and chart pages, so you can put a long-bond fund next to the 30-year yield over the same range, as in the chart above.
• Treasury futures for 2-, 10- and 30-year maturities are in the futures list; their prices move opposite to yields too.

The bond-price curve on this page was calculated by Finabase Research; the TLT and yield history come from Finabase chart data and Federal Reserve data.

Frequently asked questions

Why do bond prices go down when interest rates go up?

Because an existing bond's payments are fixed. When new bonds offer higher yields, the only way an older, lower-coupon bond can offer the same return is to sell for less. Its price falls until its yield to maturity matches the market.

If I hold a Treasury to maturity, do price changes matter?

Not for the final outcome, assuming you don't sell. You receive every coupon and the full face value at maturity, and your return equals the yield to maturity at purchase. Price changes matter if you need to sell early, and they show the opportunity cost of having locked in a lower rate.

What is the difference between a bond's coupon and its yield?

The coupon is the fixed interest rate on face value, set at issue. The yield, usually yield to maturity, is the return implied by today's price. They are equal only when the bond trades at par.

Do bond prices and yields always move by the same amount?

No. Long bonds move far more than short bonds for the same change in yield, and the relationship is curved: a 1-point rise in yield costs a 10-year, 4% bond $7.72 from par, while a 1-point fall gains $8.53. Duration and convexity measure those effects.

Summary

A bond's price is the present value of its fixed coupons and face value, discounted at the market yield, so price and yield move in opposite directions by construction. A 10-year, 4% bond is worth $100 at a 4% yield, $92.28 at 5% and $108.53 at 3%. Yield to maturity is the one rate that ties all of a bond's payments to its price; current yield and coupon rate are partial measures that ignore the pull to par. Real data make the point vividly: as the 30-year Treasury yield rose about 4 points from July 2020 to September 2026, the price of the long-bond fund TLT fell 54.5%, and when yields returned to their 2002 level, so did its price.