Key Takeaways
Direct answer: A bond's price and its yield are two views of the same contract, and they move in opposite directions by arithmetic necessity. The coupon rate is fixed when the bond is issued; the price is whatever the market will pay for those fixed payments today. When required yields rise, the price of an existing bond falls far enough that a buyer at that lower price earns the new market rate, and vice versa. Yield measures differ in what they include: the coupon rate ignores price entirely, current yield ignores the maturity payment, yield to maturity includes both, and yield to worst adds the issuer's early-repayment options.
- Price and yield are inverse. The relationship is arithmetic, not a market opinion.
- Bonds are quoted as a percentage of par, not in dollars. TreasuryDirect shows a real auction print of 99.429922 for a 7-year note, which is 994.29922 dollars per 1,000 of par.
- Discount, par, and premium describe whether market yield sits above, at, or below the contract's coupon rate. TreasuryDirect states the rule in exactly those terms.
- Four yield numbers answer four different questions. Quoting the wrong one is how bonds get mispriced in an investor's own head.
- On a 5% coupon bond with six years left, buying at 900 dollars produces a 5.56% current yield but a 7.07% yield to maturity. The 1.5-point gap is the pull to par, and current yield hides all of it.
- Yield to maturity assumes you hold to maturity, get paid in full, and reinvest every coupon at the same rate. None of those is guaranteed.
- On a callable bond, yield to worst is the honest number. The gap between it and yield to maturity can exceed two full percentage points.
Why Do Bond Prices and Yields Move in Opposite Directions?
A fixed-rate bond promises a schedule of payments that was set on the day it was issued and never changes. What does change is the return available on newly issued bonds. Those two facts alone force the inverse relationship.
Suppose you hold a bond paying 30 dollars a year on 1,000 of par, and new bonds of similar quality and maturity now pay 40 dollars a year. Nobody rationally pays you 1,000 dollars for a 30 dollar income stream when 1,000 dollars buys a 40 dollar stream elsewhere. Your bond's price has to fall until the combination of its coupons and the gain from the discounted price up to par at maturity matches what the new bond offers. That falling price is the rising yield. They are not two events; they are one event described two ways.
The SEC's investor bulletin on fixed income and interest rates quantifies it with a 1,000 dollar bond carrying a 3% coupon and a 10-year maturity, viewed one year in with nine years remaining:
| Market interest rate | Price | Yield to maturity for a new buyer | Change from par |
|---|---|---|---|
| 2% | about $1,082 | 2% | +8.2% |
| 3% | $1,000 | 3% | 0% |
| 4% | about $925 | 4% | -7.5% |
Two structural details control the magnitude, and the bulletin names both. Longer maturities carry more interest rate risk than shorter ones, because more years of payments have to be repriced. And between two otherwise identical bonds, the one with the lower coupon falls further when rates rise, because more of its value sits in the distant principal repayment rather than in near-term cash. The measure that folds both effects into one comparable number is duration, covered in bond duration explained.
How Are Bond Prices Quoted?
Bond prices are quoted as a percentage of par value rather than as dollar amounts, often to several decimal places. A quote of 98.5 on a 1,000 dollar par bond means 985 dollars. A quote of 101.25 means 1,012.50. Par itself is 100.
The convention is not cosmetic. Par values differ across issues, and percentage-of-par quoting lets a buyer compare two bonds on price without first normalizing for denomination. TreasuryDirect's page on Treasury pricing and interest rates shows a real auction print: a 7-year note that came with a 1.461% high yield and a 1.375% interest rate set at auction priced at 99.429922. That is 994.29922 dollars per 1,000 of par, a small discount, and the reason for the discount is visible in the two rates: the yield buyers demanded exceeded the coupon the security would pay.
Clean price, dirty price, and accrued interest
Quoted prices are normally "clean" prices, which exclude interest that has accumulated since the last coupon date. The buyer pays the clean price plus accrued interest, and the sum is the "dirty" or invoice price. This exists because the next full coupon goes to whoever holds the bond on the payment date, so a mid-period buyer compensates the seller for the days the seller held it.
The practical consequence: the number you see quoted is not the number that leaves your account. Buying a semiannual-pay bond five months after its last coupon means paying roughly five months of interest on top of the quoted price. That amount comes back a month later in the coupon, so it is a timing shift rather than a cost. Mistaking it for a cost is a common source of confusion on a first bond purchase.
The Four Yield Measures and What Each One Answers
"Yield" is not one number. Four different figures circulate under that word, each answering a different question, each leaving something out.
| Measure | Formula or definition | Question it answers | What it ignores |
|---|---|---|---|
| Coupon rate (nominal yield) | Annual coupon divided by par value | What does the contract pay? | The price you actually paid. Useless for comparing purchase decisions. |
| Current yield | Annual coupon divided by current price | What income does this produce per dollar invested right now? | The gain or loss to par at maturity, and the time left to get there. |
| Yield to maturity (YTM) | The discount rate that makes the present value of all remaining coupons plus par equal today's price | What total annualized return does buying at this price imply if everything runs to plan? | Call features, default, and any reinvestment rate other than the YTM itself. |
| Yield to worst (YTW) | The lowest of yield to maturity and the yield to every possible call date | What is the least I could earn across every way this bond can end? | Nothing about the issuer's optionality. This is the conservative figure. |
The step from current yield to yield to maturity is where most of the information lives, because it is the step that recognizes a bond bought below par gains value as it approaches maturity, and a bond bought above par loses value the same way. That pull to par is not a market forecast. It is contractual: the issuer repays par, so on the maturity date the price must be par regardless of what happened in between.
Worked Example: One Bond, Three Prices
This example is hypothetical and constructed to isolate the effect of purchase price. It is not a projection or a quoted market figure. All yields below are calculated with semiannual compounding, the standard convention for a semiannual-pay bond.
Take one bond: 1,000 dollars par, a 5% coupon paid semiannually (25 dollars every six months), six years to maturity. The contract is identical in all three cases. Only the price paid differs.
| Purchase price | Trades at | Current yield | Yield to maturity | Gap between the two |
|---|---|---|---|---|
| $900 | Discount (90.0) | 5.56% | 7.07% | +1.51 points |
| $1,000 | Par (100.0) | 5.00% | 5.00% | 0 |
| $1,100 | Premium (110.0) | 4.55% | 3.16% | -1.39 points |
Three things are worth reading off this table.
- At par, all yield measures agree. Coupon rate, current yield, and yield to maturity are all 5.00%. This is the only case where the three converge, and it is why par-priced examples teach the concepts badly: they hide the differences that matter.
- At a discount, current yield understates the return. The 900 dollar buyer collects 50 dollars a year and also receives 1,000 dollars at maturity for a 900 dollar outlay. That 100 dollar accretion, spread over six years, is the 1.51 points current yield leaves out.
- At a premium, current yield overstates the return. The 1,100 dollar buyer collects the same 50 dollars a year but receives only 1,000 dollars back. The 100 dollar erosion turns a 4.55% income figure into a 3.16% total return. An investor screening on current yield alone would rank this bond above the discount bond on income and be exactly wrong about total return.
Now add a call feature
Keep the premium case, and suppose the bond is callable by the issuer at 102 (1,020 dollars) two years from now. The yield to maturity is still 3.16%. But if the issuer calls, the buyer holds for two years, receives four 25 dollar coupons and 1,020 dollars, against a 1,100 dollar purchase. That path yields about 0.93%. Yield to worst is therefore 0.93%, not 3.16%.
The issuer chooses. And the issuer calls when refinancing is cheap, which is when rates have fallen, which is exactly the environment that pushed the bond to a premium in the first place. The call is most likely in the scenario where it hurts most. That correlation is why yield to worst exists and why quoting yield to maturity on a callable bond is misleading rather than merely optimistic. Investor.gov defines call risk plainly as the possibility that a bond issuer retires a bond before its maturity date.
You can reproduce any of these figures with the bond price and yield to maturity calculator.
What Yield to Maturity Assumes, and Why That Matters
Yield to maturity is the most useful single number in fixed income, and it is routinely read as a promise. It is not one. It is a discount rate, and it rests on three assumptions that are stated nowhere on the quote screen.
- You hold to maturity. Sell early and par is replaced by whatever the market pays that day. A bond bought at a 7.07% yield to maturity and sold in year two produces a realized return set by the year-two price, not by the original figure.
- The issuer pays in full and on time. Yield to maturity is calculated from contractual cash flows, not probability-weighted ones. A bond priced to yield 11% is not offering an 11% expected return; it is offering 11% if it pays, and its price is low precisely because the market doubts that. High quoted yield and high expected return are different statements. See bond credit risk and ratings.
- Every coupon is reinvested at the yield to maturity. This one is the least visible and the most reliably violated. The calculation implicitly compounds each coupon at the same rate. In practice coupons get reinvested at whatever rate exists on the day they arrive. If rates fall, realized return lands below the quoted yield even though the issuer paid every dollar. This is reinvestment risk, and it is the reason a falling-rate environment is not unambiguously good news for a bond holder.
None of this makes yield to maturity a bad measure. It makes it a conditional one. The practical habit is to read any quoted yield as a shorthand for "the annualized return implied by this price, if the plan holds," and then ask which part of the plan is most likely not to hold for this particular bond.
Discount, Par, and Premium: Reading the Price Tag
Where a bond trades relative to par tells you one specific thing: how today's required yield compares to the coupon the contract already fixed. TreasuryDirect states the rule without ambiguity. When yield to maturity is greater than the interest rate, the price falls below par. When the two are equal, the price equals par value. When yield is less than the coupon rate, the price exceeds par.
| Price relative to par | What it tells you | Return composition | Common misreading |
|---|---|---|---|
| Discount (below 100) | Market yield is above the coupon rate | Coupons plus a contractual gain up to par | "It is cheap." It is repriced, not cheap. |
| Par (100) | Market yield equals the coupon rate | Coupons only | Assuming this is the normal or correct state. |
| Premium (above 100) | Market yield is below the coupon rate | Coupons minus a contractual erosion down to par | "I am overpaying." The high coupon is what you bought. |
The important correction here is that neither a discount nor a premium is a mispricing. Both are the arithmetic that makes an old contract competitive with today's market. A discount bond does not offer a free gain, because that gain is exactly offset by its below-market coupon. A premium bond does not represent an overpayment, because the above-market coupon is exactly what the extra price buys. In an efficient market, two bonds of identical credit quality and duration should offer the same yield to maturity whether one is priced at 90 and the other at 110.
Where discount and premium genuinely differ is in taxation and in cash-flow timing, not in gross return. Discount accretion and premium amortization have their own tax treatment, and the two bonds return your capital on very different schedules. Bond and fixed-income taxation covers the treatment; the timing difference matters for anyone matching a bond to a dated spending need.
How the Auction Sets Both the Price and the Rate
For Treasury securities, price and yield are not set by a dealer quoting a market. They come out of an auction, and the mechanism makes the price-yield relationship unusually easy to see.
TreasuryDirect describes the process: the interest rate for a particular security is set at the auction, and the yield to maturity that emerges from bidding determines whether the security prices at par, at a discount, or at a premium. Because both numbers are published for every auction, the discount or premium is fully explained by two figures sitting side by side. In the 7-year note example above, a 1.461% high yield against a 1.375% coupon produced a price of 99.429922. The yield exceeded the coupon, so the price sat below par. No other input is needed.
Treasury bills work differently and are simpler still. They pay no coupon at all. TreasuryDirect describes bills as sold at a discount or at par, with the investor paid face value at maturity, so the entire return is the difference between the purchase price and the face amount received. There is no coupon rate to compare against, which is why bills are quoted on a discount basis rather than as a percentage of par with a coupon attached.
The full set of Treasury security terms, including notes, bonds, TIPS, and floating rate notes, is covered in Treasury securities. For the short end used as a cash holding, see Treasury bills as cash equivalents.
Common Mistakes and Misconceptions
- Comparing bonds on current yield. Current yield ranks a premium bond above a discount bond on income while getting total return backwards. Any comparison of purchase decisions needs yield to maturity or yield to worst.
- Reading yield to maturity as a guaranteed return. It is a conditional figure resting on hold-to-maturity, full payment, and reinvestment at the same rate. Treat it as an implied return, not a promised one.
- Quoting yield to maturity on a callable bond. The issuer holds the option and will use it when it suits the issuer. Yield to worst is the number that survives contact with that fact.
- Treating a discount as a bargain. The discount is compensation for a below-market coupon, not a discovered inefficiency. If a bond trades far below comparable issues, the explanation is usually credit or liquidity, not a pricing error.
- Forgetting accrued interest. The quoted price is a clean price. The invoice includes interest accumulated since the last coupon date, so the cash leaving your account exceeds the quote.
- Assuming a high yield means a high expected return. Price falls when the market doubts payment. An elevated quoted yield on a distressed issuer is a probability statement about default, not an opportunity.
- Ignoring compounding convention. A yield quoted on a semiannual basis is not directly comparable to one quoted annually. On the 900 dollar example above, the difference between conventions is real enough to change a ranking between close candidates.
Frequently Asked Questions
Why do bond prices fall when interest rates rise?
An existing bond pays a coupon that was fixed when it was issued. If newly issued bonds now pay more, nobody will buy the older bond at its previous price, so its price falls until buying it at that lower price delivers the same total return as a new bond. The SEC illustrates the size of the effect with a 1,000 dollar bond paying a 3% coupon with nine years left: at a 2% market yield it is worth about 1,082 dollars, and at a 4% market yield about 925 dollars.
What is the difference between current yield and yield to maturity?
Current yield divides the annual coupon by the current price and ignores everything else. Yield to maturity discounts every remaining coupon plus the return of par back to today’s price, so it captures the pull toward par as well as the coupons. On a 1,000 dollar par bond with a 5% coupon and six years left, bought at 900 dollars, current yield is 5.56% while yield to maturity is about 7.07%. Current yield is a quick income figure, not a total-return figure.
What does it mean when a bond trades at a discount or a premium?
It means the market’s required yield differs from the coupon the contract already fixed. TreasuryDirect states the rule directly: when yield to maturity is greater than the interest rate the price falls below par, when they are equal the price equals par, and when yield is less than the coupon rate the price rises above par. A discount is not a bargain and a premium is not an overpayment. Both are the price adjustment that equalizes an old contract with today’s market.
How are bond prices quoted?
As a percentage of par rather than in dollars, carried to several decimal places. A quote of 99.429922 on a 1,000 dollar par bond means 994.29922 dollars. TreasuryDirect shows exactly this in a real auction result: a 7-year note with a 1.461% high yield and a 1.375% interest rate set at auction priced at 99.429922, a discount because the yield exceeded the coupon. Quoted prices also usually exclude accrued interest, which the buyer pays on top.
What is yield to worst and when should I use it?
Yield to worst is the lowest yield you could receive across every way the bond can end, including every date the issuer may call it. Use it whenever a bond is callable. A 5% coupon bond with six years left bought at 1,100 dollars shows a yield to maturity of about 3.16%, but if the issuer can call it at 102 in two years, the yield in that scenario is about 0.93%. Quoting yield to maturity on a callable bond overstates the realistic return.
Does yield to maturity guarantee my return?
No. Yield to maturity is a discount rate, and it carries three built-in assumptions: that you hold the bond to maturity, that the issuer makes every payment in full and on time, and that you reinvest every coupon at the same yield to maturity. All three can fail. Selling early substitutes the market price for par, a default breaks the payment stream, and coupons reinvested at lower rates leave the realized return below the quoted yield.
What is a basis point, and why do bond markets quote in them?
A basis point is one hundredth of a percentage point, so 100 basis points equals 1 percent. Bond markets use the unit because the differences that matter are small and because saying that a yield rose 25 basis points removes the ambiguity in phrases like a 25 percent increase in a yield. It also makes spreads readable: describing a corporate bond as trading 140 basis points over a comparable Treasury states the credit compensation precisely without restating both yields.
Why do two bonds with the same maturity trade at different yields?
Maturity is only one of the inputs a buyer prices. Two bonds maturing on the same date can differ in credit quality, seniority in a bankruptcy, whether the issuer can call them early, how easily they can be resold, and how their interest is taxed. Each of those differences is compensated in the yield. That is why comparing a corporate bond to a government bond of the same maturity produces a spread rather than a discrepancy, and why a callable bond can offer a higher stated yield than a comparable non-callable one from the same issuer.
What does a bond's yield spread measure?
A yield spread is the difference between a bond's yield and the yield of a reference security of similar maturity, usually a government bond. It isolates the compensation an investor receives for everything the reference does not carry, primarily credit risk and liquidity risk. Because the reference moves with the general level of interest rates, watching the spread separates a change in a bond's own risk profile from a change in market rates that moved every bond at once. A yield that rose while its spread narrowed is telling a different story from one where both widened.
References
This guide is based on U.S. regulator and government publications, each retrieved and verified on 22 August 2026:
- SEC Office of Investor Education and Advocacy: Investor Bulletin, Fixed Income Investments, When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall: the 1,000 dollar, 3% coupon, nine-years-remaining price table reproduced above, and the stated effects of maturity and coupon rate on price sensitivity.
- TreasuryDirect: Understanding Pricing and Interest Rates: the discount, par, and premium rule, and the 7-year note auction print of 99.429922 at a 1.461% high yield against a 1.375% interest rate.
- TreasuryDirect: Treasury Bills: bills sold at a discount or at par, paid at face value at maturity, with no coupon.
- Investor.gov: Bonds FAQs: par value as the amount repaid at maturity, and call risk as the possibility that an issuer retires a bond before its maturity date.
- FINRA: Bonds: duration as an indicator of how much a bond's price is likely to move when interest rates change.
The three-price table and the callable-bond illustration are original, hypothetical calculations produced with standard semiannual discounting on the stated inputs. They are not market quotes, projections, or recommendations. This is educational content, not personalized investment or tax advice.