Bond prices and yields: how interest rates affect them

Bond prices and yields describe two sides of the same contract. A bond promises specified cash flows, while the market decides what those cash flows are worth today. When the required yield rises, a fixed payment is discounted more heavily and its price falls. That inverse relationship is fundamental, but it does not make every bond behave alike.

Maturity, coupon, redemption terms, currency, credit quality, liquidity and embedded options all change the result. A government bill held to maturity differs from a thirty-year corporate bond sold after a rate shock. This guide explains the mathematics and the risks without assuming that “fixed income” means a fixed market value.

Bond prices and yields start with the contract

A plain bond has a face value, a coupon schedule and a maturity date. The issuer receives capital and promises interest plus repayment. A 1,000-euro bond with a 3% annual coupon pays 30 each year and normally returns 1,000 at maturity. Those promises are contractual, not guaranteed: default, restructuring or contractual options can alter them.

Market price is separate from face value. An investor may pay 950, 1,000 or 1,050 for the same stream. Buying below par raises the return if repayment occurs at par; buying above par lowers it. Accrued interest and quoting conventions also affect the cash paid at settlement, so a displayed clean price can differ from the invoice price.

Coupon rate, current yield and yield to maturity

Measure	Calculation	What it omits
Coupon rate	Annual coupon divided by face value	Purchase price and capital gain or loss
Current yield	Annual coupon divided by market price	Time value and redemption at par
Yield to maturity	Discount rate equating price with all promised cash flows	Default and realised reinvestment rates
Yield to worst	Lowest yield under specified call outcomes	Scenarios outside the contractual assumptions

If the 3% bond trades at 950, its current yield is 30/950, or 3.16%. That is not its total expected return because maturity also brings a 50 capital gain if the issuer repays 1,000. Yield to maturity incorporates coupons, timing and redemption, but it assumes payments occur as promised and coupons can be reinvested at the calculated yield.

The present-value equation

The price equals the sum of each future cash flow divided by one plus the required yield raised to the appropriate time. For a two-year bond paying a 4 coupon on face value 100, the price at a 5% annual yield is 4/1.05 + 104/(1.05²), approximately 98.14. At a 3% yield it is about 101.91.

The cash flows remain 4 and 104; only the discount rate changes. This is why price and yield move in opposite directions. It also explains why the relationship is curved rather than a straight line: compounding affects distant payments non-linearly. Day-count conventions and payment frequency make professional calculations more detailed, but the economic logic is unchanged.

Why maturity and coupon change sensitivity

A payment due tomorrow is barely affected by a change in ten-year rates. A payment due in twenty years is. Longer maturity generally increases interest-rate sensitivity because more value lies far in the future. A lower coupon also tends to increase sensitivity because less value is returned early, leaving more weight on the final principal payment.

Two bonds with the same maturity can therefore move differently. A ten-year zero-coupon bond has all its cash flow at maturity and is more sensitive than a high-coupon ten-year bond. Time to maturity is a rough descriptor; duration measures the weighted timing of value more precisely.

Duration: useful approximation, not holding period

Macaulay duration is the present-value-weighted average time of cash flows. Modified duration converts it into an approximate percentage price change for a one-percentage-point yield move. If modified duration is 6, a 0.50 percentage-point rise in yield implies roughly a 3% price decline: −6 × 0.005.

The approximation assumes a parallel, small yield move and unchanged cash flows. Duration is not simply “years until the investor gets money back”, nor does it measure credit spread risk on its own. Investor.gov defines duration as a tool for estimating sensitivity; it should be paired with maturity, convexity, credit and option analysis.

Convexity improves the estimate

The price-yield curve bends. For an option-free bond, the price gain from a yield decline is usually larger than the loss from an equal yield rise around the same starting point. Convexity captures this curvature. A common approximation adds one-half times convexity times the squared yield change to the duration estimate.

Suppose modified duration is 6 and convexity is 45. For a one-point rise, duration estimates −6%; the convexity adjustment adds 0.5 × 45 × 0.01², or 0.225%, giving about −5.775%. The estimate is still simplified. Callable bonds can show negative convexity because the issuer is more likely to redeem when rates fall.

Central-bank rates and government yields

Central banks anchor overnight rates, while a five- or ten-year government yield reflects expected future short rates plus a term premium. A policy-rate increase can already be priced before the meeting. Long yields may rise, fall or stay unchanged depending on inflation expectations, growth, credibility, bond supply and demand for duration.

That distinction is developed in the overview of market indices and their construction: a quoted benchmark summarises many underlying prices but does not explain them by itself. For bonds, always identify the exact maturity, issuer and yield convention before comparing a move.

The yield curve is not one rate

A yield curve plots comparable yields across maturities. A parallel shift is convenient for duration exercises, but real curves steepen, flatten and twist. A portfolio concentrated at five years can react differently from one split between two and ten years even if both report similar average duration.

Key-rate duration measures sensitivity at specific maturity points. It is useful when a central-bank surprise moves the front end while long yields respond to growth or inflation. Curve exposure also creates roll-down effects as a bond moves toward shorter maturity, though the realised benefit depends on the curve remaining sufficiently stable.

Credit spread and default risk

A corporate yield can be decomposed roughly into a government benchmark plus a credit and liquidity spread. If the government yield falls by 0.50 points but the corporate spread widens by 1.00 point, the corporate bond’s required yield rises by 0.50 points and its price can fall. “Rates fell” is therefore not enough to predict credit returns.

Spread compensates for expected default loss, uncertainty, liquidity and risk aversion, not just the probability of default. Recovery value matters too. Ratings summarise opinions about creditworthiness but can change and are not guarantees. Investors should inspect leverage, cash flow, covenants, seniority and refinancing needs.

Inflation and real returns

A nominal bond fixes payments in currency units, not purchasing power. If a bond returns 4% while inflation over the period is 3%, the approximate real return is 1%; the exact result is about 0.97%. Unexpected inflation tends to hurt holders of long nominal bonds because the real value of distant fixed payments falls.

Inflation-linked bonds adjust principal or coupons according to a specified index, but they still have real-yield duration, market-price volatility, tax and liquidity considerations. Their breakeven spread versus nominal bonds contains inflation expectations plus risk and liquidity premia. It should not be read as a perfect official forecast.

Reinvestment risk and horizon

Yield to maturity assumes coupons are reinvested at the same yield. If rates fall, a high-coupon bond can deliver less than its quoted yield because interim cash is reinvested more cheaply. A zero-coupon bond has no coupon reinvestment risk before maturity, though its market price can be highly sensitive.

Price risk and reinvestment risk move in opposite directions. Longer duration increases immediate price sensitivity but can lock a yield for longer; short bills show little price movement but must be rolled at unknown future rates. Matching duration to a known liability can reduce horizon risk, provided credit and cash-flow assumptions hold.

Liquidity, taxation and currency

Two bonds with similar cash flows can trade at different yields because one is easier to buy or sell. Bid-ask spreads may widen in stress, and a model price may not be executable. Tax treatment can distinguish coupon income, capital gains and inflation adjustments. Comparisons should therefore use after-cost, after-tax returns appropriate to the investor’s jurisdiction.

A foreign bond adds currency exposure unless hedged. A 5% bond return can become a loss in the investor’s home currency if the bond currency depreciates more than 5%. Hedging has costs and basis risk. Currency movements should not be mistaken for the performance of the fixed-income contract itself.

Individual bonds versus bond funds

An individual bond has a maturity date at which par is scheduled to be repaid. A diversified bond fund continually buys and sells securities and usually has no date when the investor automatically receives a fixed face value. That does not make the fund defective; it means its duration and reinvestment process are ongoing.

A fund can improve portfolio diversification and access but adds fees, tracking and trading effects. Its share price reflects the portfolio’s market value every day. The ETF structure guide explains premiums, discounts and the distinction between the wrapper’s liquidity and the liquidity of the bonds held inside.

Worked comparison: three rate scenarios

Take a bond with modified duration 5 and convexity 30. If yield rises 0.50 points, the approximation is −2.5% plus 0.0375%, or −2.4625%. If yield falls 0.50 points, it is +2.5% plus 0.0375%, or +2.5375%. A two-point move needs a more accurate model because options and curvature become more important.

Now add a credit spread. A 0.40-point fall in the government curve combined with a 0.90-point spread widening is a net 0.50-point yield rise. The price response is close to the first scenario, before coupon income. This shows why duration arithmetic must use the yield that actually prices the bond, not one macro headline.

Common bond mistakes

Calling the coupon the return without considering purchase price and redemption.
Assuming holding to maturity removes default, inflation or opportunity cost.
Comparing yields that use different conventions, currencies or tax treatment.
Using duration for a large or non-parallel move without convexity or key-rate analysis.
Ignoring embedded calls that cap gains when rates fall.
Treating a bond fund as if every investor had a guaranteed maturity value.
Attributing a corporate-bond move to government rates while credit spreads changed.

A bond-analysis checklist

Identify issuer, seniority, currency, face value, coupon and maturity.
Read redemption, call, put and conversion terms.
Confirm whether the quoted yield is current, to maturity, to call or to worst.
Measure duration, convexity and exposure to non-parallel curve moves.
Separate government-rate risk from credit and liquidity spread risk.
Estimate real return, reinvestment assumptions, costs, taxes and currency effects.
Test a default or downgrade scenario rather than relying only on the central case.

Bond prices and yields are mathematically connected, but realised returns remain conditional on cash flows, reinvestment and the investor’s horizon. Fixed income can stabilise a portfolio or create substantial losses depending on duration, credit and valuation. The correct comparison begins with the contract and ends with scenarios, not with the word “bond”.

Economy and markets reading path

To connect monetary policy, bonds, currencies and asset behaviour, continue with the other guides in this cluster:

Sources and further reading

Primary references for the concepts, definitions and market mechanisms discussed in this guide: