A yield curve is what happens when the price of borrowing is allowed to have a calendar. Instead of asking, “What is the interest rate?”, it asks a more useful question: “What yield does the market require for this kind of claim when the money is committed for one month, two years, ten years or thirty years?”
The result is a line across maturities. That line can slope upward, flatten, invert, bend or change shape from one day to the next. Each movement contains information. None of it should be read as a single unquestionable forecast.
This article opens Batch 034 of the eduKateSG Finance Authority 400. Batch 033 owns the individual bond contract and the inverse bond price–yield relationship. This page owns the cross-maturity term-structure map: how yields across different maturities fit together, why the curve changes shape and what information can reasonably be extracted from it. The canonical whole-system owner remains How Finance Works.
A yield curve is not one interest rate stretched across time. It is a market map of different prices for different maturities.
Educational boundary: this article explains general fixed-income and term-structure concepts. Yield curves vary by issuer, currency, collateral, tax treatment and construction method. Examples are simplified and are not investment recommendations.
The short answer: what is a yield curve?
A yield curve is a relationship between yields and maturities for debt instruments that are sufficiently comparable in credit and other characteristics.
The US Treasury describes its par yield curve as relating the par yield on a security to its time to maturity, derived from market quotations on Treasury securities. The Monetary Authority of Singapore similarly publishes prices and yields for Singapore Government Securities across a range of remaining maturities. See the US Treasury interest-rate statistics and MAS SGS Bond Prices and Yields.
The word comparable matters. If a one-year government bill is compared with a ten-year distressed corporate bond, the resulting difference contains both maturity and credit risk. A meaningful government yield curve tries to hold issuer credit quality broadly constant so maturity becomes the main changing dimension.
Why the x-axis is time
The horizontal axis usually represents maturity. The vertical axis represents yield.
A curve can therefore be read as a set of questions:
- What does the market require for three months?
- What does it require for two years?
- What does it require for five years?
- What does it require for ten years?
- What does it require for thirty years?
Those maturities are not interchangeable. A thirty-year lender accepts far more time during which inflation, policy, economic growth and market conditions can change. A three-month lender gets their principal back quickly and can reset the rate soon.
The curve is therefore a map of the time inside finance.
A curve needs one family of claims
Different curves can exist at the same moment.
- A sovereign government curve.
- A swap curve.
- A secured overnight financing curve.
- A corporate issuer curve.
- A bank funding curve.
- A real-yield curve from inflation-linked bonds.
Each curve prices a different family of financial claims. The maturity dimension can be the same while the credit, collateral, liquidity and legal structure differ.
This is why “the yield curve” is sometimes too vague. A careful reader asks: which curve, in which currency, constructed from which instruments, on which date?
Par yields, spot yields and forward yields are different views
A par yield curve asks what coupon rate would make a hypothetical bond at each maturity trade around par under the construction method. The US Treasury publishes daily par yield curve rates.
A spot curve, or zero-coupon curve, assigns a discount rate to a single payment at each maturity. It is the cleaner mathematical object for valuing cash flows because each future payment can be discounted using the spot rate for its date.
A forward curve derives implied future borrowing rates from today’s term structure under the relevant no-arbitrage relationships and conventions.
These curves are related. They are not the same data series. A headline that quotes a ten-year par Treasury yield should not be silently substituted into a calculation requiring a ten-year zero-coupon spot rate.
The normal upward-sloping curve
An upward-sloping curve has higher yields at longer maturities.
One possible interpretation is that investors expect short-term rates to be higher in the future. Another is that investors require a positive term premium for bearing uncertainty over a longer horizon. Inflation expectations, supply, demand and liquidity can also contribute.
Calling the shape “normal” can be convenient but should not imply that every upward curve reflects the same economy. Two curves can have identical slopes for completely different reasons.
A flat curve
A flat curve means yields across some maturity range are similar.
This can occur when higher current short rates are balanced by expectations that rates will later fall, when the term premium compresses, or when different forces offset one another.
A flat curve is therefore not “the market has no opinion.” It can be the equilibrium result of strong opposing opinions embedded in different parts of the term structure.
An inverted curve
An inverted curve occurs when longer-maturity yields fall below shorter-maturity yields across a chosen pair or range.
That can be consistent with markets expecting future short-term rates to decline. But term-premium changes can also contribute. So can safe-haven demand, supply conditions and other market forces.
The companion article Yield-Curve Inversion | What the Shape Can Signal—and What It Cannot Prove owns the recession-signal question. This article keeps the structural definition clean.
A humped or segmented curve
Yield curves do not need to be smooth one-directional lines. The two-year point can be high, the five-year lower, the ten-year stable and the thirty-year higher again.
A hump can emerge when policy expectations dominate the front end while inflation uncertainty, bond supply or term premium dominate the long end. Specific maturity sectors can also have unusual demand from banks, insurers, pension funds or liability-driven investors.
The curve should therefore be read as a structure, not forced into a binary normal-versus-inverted label.
The expectations component
In standard term-structure reasoning, a longer Treasury yield can be decomposed conceptually into expectations of future short-term rates plus a term premium. The Federal Reserve Bank of New York’s ACM term-premium framework describes Treasury yields in these two components. See New York Fed Treasury Term Premia.
If investors expect the central bank to cut short-term rates sharply over the next several years, longer yields can fall even while today’s short rate remains high.
If investors expect persistent inflation and tighter future policy, longer yields can rise.
But expectations are only one component.
The term premium component
The New York Fed defines the term premium as compensation investors require for bearing the risk that interest rates over the life of the bond do not evolve as expected. Crucially, term premium is not directly observable; it is estimated using models.
This means a ten-year yield of 4% cannot simply be read as “the market expects the average future short rate to be 4%.” Some of the yield may represent term premium.
The companion article Credit Spread vs Term Premium will keep term premium separate from the additional spread a corporate borrower pays for credit and liquidity risk.
A simple decomposition example
Suppose, purely as a teaching model, a ten-year government yield is 4.2%. A term-structure model estimates that the expected average path of future short rates contributes 3.4 percentage points and estimated term premium contributes 0.8 percentage points.
Now suppose the ten-year yield rises to 4.8%. There are several possibilities:
- expected future short rates rose by 0.6 percentage points while term premium stayed unchanged;
- term premium rose by 0.6 while expectations stayed unchanged;
- both components moved;
- the model’s estimates changed because the data relationships used for inference changed.
The observed yield movement alone does not identify the decomposition with certainty.
Steepening and flattening
A curve steepens when the yield difference between a longer and shorter maturity increases. It flattens when that difference decreases.
Suppose the two-year yield is 3% and the ten-year is 4%. The 10-year-minus-2-year spread is +1 percentage point. If the two-year rises to 3.8% while the ten-year stays at 4%, the spread falls to +0.2: the curve flattened.
If the two-year falls to 2% while the ten-year remains at 4%, the spread widens to +2: the curve steepened.
The word tells you the change in shape. It does not tell you which yield moved or why.
Bull and bear steepeners
Market language often distinguishes whether yields are falling or rising while the curve changes shape.
- A bull steepener generally describes falling yields led by a larger fall at the short end.
- A bear steepener generally describes rising yields led by a larger rise at the long end.
- A bull flattener generally describes falling yields led by the long end.
- A bear flattener generally describes rising yields led by the short end.
These labels are shorthand. The useful analysis still asks what changed expectations, term premium, inflation, supply or policy assumptions at each maturity.
Parallel shifts versus shape shifts
If every point on a curve rose by exactly one percentage point, the curve would experience a parallel upward shift. Its shape would be unchanged.
Real curves rarely move perfectly in parallel. Short rates may react strongly to monetary policy while long rates react more to long-run inflation, growth and term-premium expectations.
This is why one duration number cannot fully describe a portfolio exposed to several maturity points. The companion Duration article will introduce key-rate thinking for non-parallel moves.
Nominal and real yield curves
A nominal government bond pays fixed nominal currency amounts. An inflation-linked government bond adjusts according to its inflation mechanism. The US Treasury publishes both nominal par yield curves and real par yield curves for TIPS.
The difference between nominal and real yields across comparable maturities is often used to construct market-based inflation compensation measures. That difference is not a pure forecast of inflation because inflation risk premia and liquidity differences can also contribute.
The broader lesson repeats: observed yield differences often contain more than one economic force.
Supply and demand can change the curve without changing the policy rate
Governments issue bonds in different maturity sectors. Pension funds and insurers may prefer long-duration assets. Banks may need particular liquid securities. Central banks can buy or sell securities. Foreign reserve managers can shift demand.
These flows can alter yields at particular maturities even when the central bank’s overnight policy rate is unchanged.
This is one reason long yields are not controlled mechanically by the current short policy rate. The policy rate strongly influences the front of the curve, while the long end reflects a wider market.
Liquidity creates maturity-specific pricing
Some issues trade more actively than others. Newly issued benchmark securities can be more liquid than older “off-the-run” bonds. Dealers may prefer certain maturities. Collateral demand can make one security unusually expensive relative to nearby maturities.
A yield-curve model often smooths across those individual-security effects to estimate a term structure. That modelling choice should be remembered when a curve is treated as though every point were a directly observed standalone bond.
Singapore SGS: seeing the maturity map locally
MAS publishes issue code, coupon, maturity, price and yield data for Singapore Government Securities and allows issues to be sorted by remaining maturity. This provides a local, observable fixed-income map. See SGS Bond Prices and Yields.
The correct reading is not to compare coupon rates directly and call the highest coupon the best bond. Older securities have different coupons because they were issued under different market conditions. Their current yields translate those contractual cash flows into today’s market valuation.
The curve is built from current market pricing across maturity, not by lining up historical coupons.
US Treasury: the curve as public infrastructure
The US Treasury publishes daily Treasury par yield curve rates across many maturities, based on closing market bid quotations. It also publishes real yield curve data for TIPS. See Daily Treasury Rates.
These public curves are widely used as reference rates because US Treasury securities are central to global collateral, pricing and risk management. A corporate bond yield can then be discussed as a spread over a Treasury maturity or fitted benchmark, with the caveat that the exact comparison method matters.
A yield curve is not a promise about future spot rates
Suppose today’s five-year yield is 3.5% and ten-year yield is 4%. It is tempting to say that “the market predicts rates will be 4% later.” That is not what the curve directly says.
The longer yield reflects the full future cash-flow horizon, expectations of future short rates and a term premium. The curve can be used to infer forward rates under defined relationships, but those forwards also contain risk-premium effects unless further assumptions are imposed.
A forward rate is therefore an implied market-consistent rate under today’s structure, not a guaranteed future observed policy rate.
A curve can move because the economy changed—or because risk appetite changed
Long yields can fall because investors expect weaker growth and future policy cuts. They can also fall because demand for safe long-duration assets rises. Long yields can rise because expected inflation increases, because real growth expectations improve, because government bond supply expands, or because term premium rises.
Several forces can move in opposite directions and partially cancel.
The curve is therefore an observable output of many unobservable beliefs and constraints. Interpretation should be probabilistic, not theatrical.
Worked curve case: same slope, different worlds
Consider two simplified economies with a two-year yield of 3% and a ten-year yield of 4%, producing a +1 percentage-point slope.
| Economy A | Economy B | |
|---|---|---|
| Expected future short-rate contribution | Rising strongly | Roughly stable |
| Term premium | Low | High |
| Observed 2s10s slope | +1% | +1% |
| Interpretation | Expectations dominate | Risk compensation dominates |
The same curve slope can therefore arise from different internal decompositions. This is why term-premium models are useful even though they are estimates rather than directly observed facts.
Curve mathematics can be internally consistent and economically wrong
A fitted curve can be mathematically smooth and still be a poor guide to the future if the underlying regime changes. Models calibrated to one inflation environment can behave differently in another. Liquidity shocks can break historical relationships. Central-bank interventions can alter maturity-specific demand.
The proper use of a curve model is therefore conditional: describe the method, understand the assumptions, test the result against observable securities and avoid treating model decomposition as directly measured truth.
Failure-first reading: what would make the curve interpretation wrong?
Before saying “the curve predicts X,” ask what else could produce the same shape.
- Could term premium have changed?
- Could one maturity sector have unusual supply or demand?
- Could inflation expectations and real-rate expectations be moving differently?
- Could central-bank asset holdings be affecting long yields?
- Could liquidity or collateral scarcity be distorting a point?
- Could the chosen spread be unrepresentative of the full curve?
If several alternatives remain plausible, the curve should be used as evidence within a wider diagnosis rather than as a standalone verdict.
The yield-curve diagnostic
- Which curve is being used?
- What currency and issuer family does it represent?
- Is it a par, spot or forward curve?
- Which maturities are being compared?
- What is the slope?
- Has the curve steepened or flattened?
- Which individual yields moved?
- What changed in expected future short rates?
- What may have changed in term premium?
- What inflation or real-rate information is relevant?
- Could supply, demand or liquidity explain part of the move?
- Is the observation direct or model-estimated?
- What competing explanation could produce the same shape?
- What real financing decisions change because of the curve?
Observable mastery test
The two-year government yield rises from 3% to 4.5%. The ten-year rises from 4% to 4.3%. A commentator says, “Long rates fell relative to short rates, so investors must expect a recession.”
A careful answer begins with the shape: the 2s10s spread moved from +1 percentage point to −0.2, so that particular segment inverted. But both yields rose in absolute terms. The short end rose much more. That can be consistent with tighter near-term policy expectations, changes in future rate expectations and term-premium effects. The curve may contain recession-relevant information, but the shape alone does not prove a recession will occur.
You understand the yield curve when you can describe both the geometry and the economic uncertainty behind it.
The World Return: how the curve reaches real decisions
Economic expectations / risk preferences → yields across maturities → borrowing and discount rates → mortgage, corporate, government and investment decisions → real spending and financing → new economic outcomes → new yield curve.
The curve does not sit outside the economy merely observing it. Long-term borrowing costs affect projects, housing, refinancing and public finance. Those decisions then change the economy the curve is trying to price.
A useful yield-curve reading therefore returns to the real world: which financing decisions become easier, harder, earlier or later because the maturity structure of rates changed?
Research anchors
The US Treasury interest-rate statistics explain the official Treasury par and real yield curves and their market-data basis. The Monetary Authority of Singapore SGS database provides local bond price, coupon, maturity and yield observations. The Federal Reserve Bank of New York Treasury Term Premia page explains the decomposition of Treasury yields into expected future short rates and estimated term premium, while noting that term premium is not directly observable.
Continue through Batch 034
Continue to Duration | Why Long-Dated Bonds Move More When Rates Change, Credit Spread vs Term Premium | Two Different Reasons Yields Rise Above a Base Rate, and Yield-Curve Inversion | What the Shape Can Signal—and What It Cannot Prove. Return to How Finance Works for the complete Finance map.