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Term Structure of Interest Rates

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Core Idea

The term structure of interest rates describes how yields on otherwise equivalent bonds vary with maturity, visualized as the yield curve. Three main theories explain its shape: the pure expectations theory (long rates equal the geometric average of expected future short rates), the liquidity preference theory (investors demand a term premium for longer maturities), and the market segmentation theory (supply and demand in each maturity segment independently determine yields). An inverted yield curve — where short-term rates exceed long-term rates — has historically been a reliable recession predictor. Forward rates, derived from spot rates, represent market expectations of future short-term rates.

How It's Best Learned

Plot the current Treasury yield curve and identify its shape: normal (upward-sloping), flat, or inverted. Study historical inversions before the 2001 and 2008 recessions. Bootstrap forward rates from spot rates to extract implied expectations about future policy rates.

Common Misconceptions

Explainer

You already understand yield-to-maturity: for a single bond, it is the single discount rate that sets the present value of all cash flows equal to the current price. The term structure of interest rates steps back from individual bonds and asks: what pattern of yields do we observe across all maturities at a single point in time? Plot the YTM of risk-free (Treasury) bonds on the vertical axis and time to maturity on the horizontal axis, and you get the yield curve. In normal times it slopes upward — longer maturities yield more than shorter ones. But it can flatten, hump, or invert, and those shapes carry important information about the economy's expected future.

Three competing theories explain why the yield curve has the shape it does at any moment. The pure expectations theory says the long rate is the geometric average of expected future short rates: if 1-year rates are 3% today and expected to be 5% next year, the 2-year rate should be approximately 4%. No term premiums, no preferences — just expectations. The liquidity preference theory modifies this by noting that investors dislike locking up money for long periods and demand compensation for the uncertainty of holding long bonds. This adds a positive term premium to long rates, explaining why the curve usually slopes upward even when short rates are expected to stay flat. The market segmentation theory goes further: different investors (pension funds, banks, money market funds) operate in different maturity segments and do not easily substitute, so supply and demand in each segment independently influence yields.

Forward rates are the key analytical tool derived from spot rates. The 1-year forward rate one year from now is the rate implied by the relationship between the 1-year spot rate and the 2-year spot rate: it is the break-even rate that makes rolling over 1-year bonds equivalent to buying a 2-year bond today. Under pure expectations, forward rates equal expected future spot rates. With term premiums, forward rates exceed expected future short rates. This matters enormously for monetary policy analysis: when the central bank cuts short-term rates, the effect on long rates depends on how much of the long rate reflects expectations versus term premiums — a distinction that inflation and duration knowledge illuminates.

The inverted yield curve — where short-term rates exceed long-term rates — is the most watched shape because of its predictive record. It typically signals that the market expects future short rates to fall substantially, which happens when the market anticipates a recession and subsequent central bank easing. Every U.S. recession since the 1970s has been preceded by a yield curve inversion, often by 12–18 months. The mechanism is partly self-fulfilling: an inverted curve tightens bank lending (banks borrow short and lend long; when the spread inverts, lending becomes unprofitable) and signals economic stress that can dampen investment and consumption.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionSine, Cosine, and Tangent RatiosTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsCenter of MassConservation of Linear MomentumElastic CollisionsInelastic CollisionsCoefficient of RestitutionCollision Analysis and Real-World ApplicationsTwo-Body Collisions in the Center-of-Mass FrameReduced Mass and Two-Body ProblemsKinematics in Two DimensionsProjectile MotionCircular Motion: KinematicsSimple Harmonic MotionIntroduction to Differential EquationsSolow Growth ModelCapital Accumulation and the Golden RuleInvestment Demand and Capital FormationAggregate DemandThe AS-AD ModelBusiness CyclesMonetary Policy ToolsTerm Structure of Interest Rates

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