Bond Prices and Yields Explained: Coupons, Current Yield and YTM
Bond prices and yields generally move in opposite directions because a bond’s market price is the present value of its promised future payments, discounted at the return investors currently require. When that required yield rises, a conventional fixed-rate bond becomes less valuable; when it falls, the same bond becomes more valuable. The contractual coupon normally stays unchanged while its price and quoted market yield adjust.
Understanding fixed income pricing requires distinguishing coupon rate, current yield, yield to maturity (YTM) and realised holding-period return. These are related but different measurements. This guide provides transparent numerical examples and explains where common interpretations break down.
Why bond prices fall when yields rise
Imagine a simple security promising £105 in one year. If investors require a 5% annual return, its theoretical price is £105 ÷ 1.05 = £100. If the market now requires 7%, the same cash payment is valued at £105 ÷ 1.07 ≈ £98.13. If investors require 3%, value becomes approximately £101.94. No contractual cash payment changed; only the return required to hold that payment changed.
This is the time value of money applied to bonds. A longer schedule of cash flows is valued by discounting each payment using a rate appropriate to its timing and risk. Coupon bonds usually have multiple interim payments and a redemption amount, so their exact pricing is more complex than the one-year example.
Credit-sensitive bonds can experience changes in both benchmark government rates and credit spreads. A worsening issuer outlook can cause its yield to rise even when government yields are falling. The inverse price–yield relationship still holds for a defined fixed set of cash flows, but the underlying reason for the required yield change matters.
Coupon rate: the contractual interest payment
The coupon rate on a conventional fixed-rate bond is stated relative to face value. For a £1,000 nominal bond with a 5% annual coupon, the annual promised coupon amount is £50. If payments occur twice annually under a simple conventional structure, each coupon is £25. The bond may be quoted above or below its £1,000 nominal value, but that does not change the £50 annual contractual amount.
A coupon is not the same as an investor’s return on purchase price. Paying £1,100 for that bond means £50 annual coupons are only about 4.55% of the price paid. Paying £900 makes the same £50 equal to about 5.56% of the initial price. Future redemption and timing still matter.
Current yield: coupon relative to market price
Current yield = annual coupon amount ÷ current bond price. For the £1,000-face bond paying £50 each year, a market price of £950 produces current yield £50 ÷ £950 ≈ 5.26%. A price of £1,050 gives approximately 4.76%. The calculation ignores capital gain or loss between the purchase price and principal redemption as well as the time value of cash flows.
Current yield may be a quick measure of annual coupon income, but it is not suitable as a complete expected-return measure. For premium and discount bonds, YTM usually gives a more comprehensive single-rate summary, provided its assumptions are understood. For callable debt even YTM can be misleading if redemption happens early.
| Hypothetical £1,000-face bond | Price £900 | Price £1,000 | Price £1,100 |
|---|---|---|---|
| Annual coupon | £50 | £50 | £50 |
| Coupon rate | 5% | 5% | 5% |
| Current yield | 5.56% | 5.00% | 4.55% |
| Principal at ordinary maturity | £1,000 | £1,000 | £1,000 |
Illustrative coupon and current-yield figures, excluding accrued interest, fees, default and early-redemption features.
Yield to maturity: the discount rate implied by all cash flows
Yield to maturity is the annualised rate that equates the discounted value of scheduled contractual payments to the bond’s relevant current price under an assumed compounding convention. For a fixed-rate, non-callable bond, the cash-flow schedule includes coupons and principal at maturity. Quoted YTM is convention-dependent and is not a promise of realised return.
For a three-year, £100-face bond paying £5 annually, theoretical price at a 4% effective annual YTM is approximately £5/1.04 + £5/1.04² + £105/1.04³ = £102.78. At 6%, the same price becomes approximately £97.33. The bond trades above par when its coupon rate exceeds the required yield under those assumptions, and below par when the coupon rate is lower.
Professional quotation conventions can involve semiannual cash flows, different compounding, day-count calculations and settlement dates. The annual-payment illustration should not be applied mechanically to an actual UK gilt or US Treasury without adapting its payment calendar.
Why a discounted bond can offer YTM above current yield
Buying below face value introduces a potential gain if the issuer redeems at par as promised. Suppose a £100 bond with three years remaining pays £4 each year and is bought for £94. Its current yield is £4 ÷ £94 ≈ 4.26%. But a buyer who receives all coupons and £100 at maturity also benefits from £6 of principal accretion, so YTM is higher than 4.26%, under those assumptions.
Conversely, a bond purchased above par produces a capital loss from the premium as it approaches repayment at nominal face value. That does not automatically make the purchase unattractive: its higher coupon payments can compensate. Always examine total cash flows rather than treating the capital movement in isolation.
Bond valuation formula for annual coupon payments
For a conventional fixed-rate bond with annual cash flows, a simplified present-value formula is Price = Σ(C ÷ (1+y)t) + F ÷ (1+y)n, where C is annual coupon, y is yield per annual period, F face value, n periods until redemption and t each coupon period. Each cash flow is discounted by how long it takes to arrive.
For more complex securities, discount factors can vary by date rather than relying on one constant YTM. Cash flows can be uncertain because of calls, amortisation, prepayment or default. That is one reason a single yield number cannot capture every relevant risk.
The US Treasury’s pricing guide explains how Treasury bill, note, bond, TIPS and floating-rate security conventions differ. A Treasury bill’s quoted bank-discount rate is not the same as a coupon bond’s YTM.
Yield to call and yield to worst
Some bonds permit the issuer to redeem before the final maturity date. Their coupon payments can stop earlier if a call is exercised. Yield to call calculates a yield assuming a specified contractual call date and call price. Yield to worst usually reports the lowest of relevant permissible redemption-scenario yields under a defined methodology, excluding default.
A high-coupon bond priced at a premium may be called if the issuer can refinance at a lower rate. Its YTM may appear high because the model assumes coupons continue until a much later maturity, while a call scenario provides a less favourable outcome. Compare actual callable terms and call protection periods.
The SEC’s callable bond explanation identifies the importance of early redemption and reinvestment risk.
The difference between YTM and realised return
A YTM quotation is a mathematical rate based on a payment schedule and price. Actual returns depend on whether payments occur as promised, the holding period, reinvestment opportunities, fees, taxes and any sale price. The common statement that “YTM is the return you are guaranteed if you hold to maturity” is too strong, especially for risky, callable or irregular cash-flow securities.
For a bond held to maturity without default or call, the internal rate of return of the contractual cash flows can equal the quoted YTM when the actual cash flows, dates and conventions match the calculation. However, the realised return on an accumulated investment account can differ when coupons are reinvested at changing rates.
A trader intending to sell in six months should not treat a five-year YTM as a six-month total-return forecast. Price changes may dominate coupon income over such a short holding period.
Clean price, dirty price and accrued interest
Many bonds are quoted at a clean price excluding accrued interest between coupon dates. The dirty price, also called full price, includes accrued interest and is closer to the amount used for settlement before fees. The exact convention varies by market and security. Bond pricing based on present values should use cash-flow timing and the relevant full price consistently.
Suppose the clean price of a bond is £98 per £100 face value and accrued interest is £1.25. The dirty price is £99.25, before costs. A buyer who sees only the clean quote might understate the cash required to settle the trade. See How Bond Markets Work for day-count methods and worked examples.
What is a basis point?
Bond yields are commonly discussed in basis points. One basis point is 0.01 percentage points, or 0.0001 as a decimal. A change from 4.00% to 4.25% is 25 basis points, not 0.25 basis points. The distinction matters when translating market commentary into price risk.
A 50-basis-point yield increase equals 0.50 percentage points or 0.005 in decimal form. For a bond with modified duration of 7, the first-order price change is approximately −7 × 0.005 = −3.5% before convexity and other effects.
Duration and convexity change the response to yields
The price–yield relationship is curved rather than perfectly linear. Duration measures its local slope; convexity describes curvature. A one-year bond generally has less price sensitivity to a given yield move than a similar much longer-term bond, although coupon structure and options matter.
For small yield changes, modified duration can produce a useful approximation. For larger changes, convexity improves the estimate for a conventional option-free bond, but actual spread movements and non-parallel curve shifts still matter. See Bond Duration and Convexity Explained.
Yield curves and the interest-rate environment
A government bond yield depends on the maturity of the debt. Short-dated securities are heavily influenced by the expected path of near-term monetary policy, while longer-term yields incorporate a wider range of future rate expectations, term premia, inflation and supply-demand forces. Consequently, the same day’s central-bank announcement can move a two-year and a thirty-year yield in different directions.
A bond’s YTM may rise because the whole benchmark yield curve moved up, because its own credit spread widened, or because of changes specific to the issue. Professional attribution needs to separate these elements rather than describe all price declines as simply “higher interest rates”.
Learn curve terminology and bull or bear steepening in Yield Curves Explained.
Yield and credit risk: high numbers can signal danger
A corporate bond trading at a deeply discounted price can display a very high quoted YTM. That may reflect concern that the issuer cannot repay all promised amounts. Calculated YTM usually assumes contractual payments occur, and is therefore not a reliable expected realised return when default probability is material.
Suppose a £100-face bond is offered at £70 with £5 coupons and one year remaining. The simple promised cash payment is £105, giving a very high contractual yield if paid. But if the firm is in financial distress, the probability and amount of recovery must be analysed. A high promised yield is not free income.
See Corporate Bond Credit Spreads and Default Risk for recovery, ratings and capital-structure risk.
Worked scenario: two different reasons for a higher corporate yield
| Yield component | Initial market | Later market A | Later market B |
|---|---|---|---|
| Benchmark government yield | 3.0% | 3.5% | 3.0% |
| Corporate spread | 2.0% | 2.0% | 2.8% |
| Illustrative corporate yield | 5.0% | 5.5% | 5.8% |
| Interpretation | Starting condition | Benchmark rates higher | Corporate risk premium wider |
Simplified additive yield decomposition; exact spreads may require matched curves, durations and valuation methods.
In market A, the example corporate yield rises because the government benchmark increases, while its spread remains unchanged. In market B, the benchmark is stable but the credit spread widens. Both can lower the bond’s market price, yet the economic reasons are different. Credit-spread changes may reflect expected default losses, liquidity or risk aversion as well as issuer-specific news.
A practical bond-yield research process
- Identify face value, coupon dates, redemption features and the exact bond.
- Confirm whether the quote is clean, dirty, price-per-100, yield or another convention.
- Calculate current yield and YTM using the actual settlement date and compounding terms.
- Review yield-to-call or yield-to-worst for securities with relevant embedded options.
- Compare an appropriate government or swap benchmark with similar duration.
- Separate changes in benchmark rates from credit-spread and liquidity movements.
- Stress-test duration, convexity and alternative holding periods.
- Check issuer payment capacity before treating promised YTM as likely realised return.
How to compare a zero-coupon bond with a coupon bond
Zero-coupon bonds make no periodic contractual interest payments and provide a maturity cash flow, assuming the issuer performs. Under a simplified effective annual compounding convention, price equals face value ÷ (1 + yield)years. For a £1,000 zero-coupon bond due in five years at a 4% required yield, the theoretical price is approximately £1,000 ÷ 1.04⁵ ≈ £821.93. Its 4% yield does not mean the investor receives £40 annually; the return is embedded in the difference between the price and promised redemption.
Now consider a coupon-paying security with the same final maturity. Because cash flows arrive at earlier dates, the present-value weighting changes the bond’s price sensitivity. Two bonds can have the same stated YTM while providing very different schedules of income, reinvestment needs and duration.
Why the yield convention must be recorded
A quoted yield of 5% may be based on annual, semiannual or another compounding convention. Converting between conventions requires care. For example, 5% nominal yield compounded semiannually corresponds to an effective annual yield of (1 + 0.05/2)² − 1 = 5.0625%, not precisely 5%. Small convention differences can matter when comparing large positions, short-maturity bills or prices near a narrow trading spread.
Accrued interest and settlement dates create another difference. A bond traded between coupon dates may have a clean price quoted on the screen but a higher dirty settlement price. The internal rate of return must be calculated using the appropriate full price and exact payment dates. Using clean price as the full purchase cost can overstate a yield calculation.
Holding-period return: what changes between purchase and sale?
Suppose an investor purchases a hypothetical bond for £98 per £100 face, receives £3 of coupon cash during the holding period, and later sells for £97 clean price, ignoring accrued-interest differences and fees. The simplified return is (£97 − £98 + £3) ÷ £98 ≈ 2.04%. The bond’s price declined, but coupon income more than offset that fall during the period.
If the sale price instead falls to £92, the simple holding-period result is (£92 − £98 + £3) ÷ £98 ≈ −3.06%. The original YTM alone would not predict either interim outcome because market yields, spreads and liquidity can change before maturity. Professional research should state whether it is modelling a promised yield to maturity or a shorter-period total-return scenario.
Frequently asked questions
Why do bond yields rise when bond prices fall?
The promised fixed cash flows are discounted at a higher required return, so their present value declines. A lower market price implies a higher contractual yield under unchanged payment assumptions.
Is coupon rate the same as YTM?
No. The coupon is defined relative to face value. YTM accounts for current price and the timing of scheduled coupon and redemption payments.
Does a high yield guarantee a higher return?
No. Default, calls, changes in sale price, reinvestment, taxes and costs affect the eventual result. Very high yields can indicate distress.
What is the difference between current yield and YTM?
Current yield divides annual coupon cash by price. YTM discounts all contractual future cash flows, including principal, under specified conventions.
What happens when interest rates fall?
For a conventional fixed-rate bond with unchanged payment and credit assumptions, lower required yields generally support higher market prices. The response depends on duration, convexity and other factors.
Key takeaways
Bond coupons are contractual cash payments, while market yields represent the return currently required for those cash flows. Prices and required yields therefore move inversely for ordinary fixed-rate bonds. YTM, current yield, duration, spread and potential calls must be interpreted together rather than treating one quoted percentage as a guaranteed return.
Related Fixed Income Education
Extend the price–yield calculations through duration, convexity and DV01, UK gilts and US Treasuries, and the six-pillar bond analysis framework.
Sources and further reading
- US Treasury — Understanding Pricing and Interest Rates.
- UK DMO — Gilt Pricing and Yield Glossary.
- SEC — Callable Bond Risk.
Important notice: Financial education only, not advice or a security recommendation. Numerical bonds and yields are hypothetical examples, not executable quotations. Credit, interest-rate and liquidity changes can create losses.