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The Yield Curve and Term Structure

The yield curve plots the yield on bonds of the same credit quality against their maturity, giving a picture of the term structure of interest rates. A normal curve slopes upward, rewarding investors for committing money longer. A flat curve shows little difference across maturities, and an inverted curve, where short yields exceed long yields, has often preceded recessions. The expectations hypothesis explains the slope as the market’s forecast of future short-term rates, so a steep curve signals expected rate rises and an inverted curve signals expected cuts. Liquidity and risk premia also shape the curve beyond pure expectations.

Try it yourself

Term Structure & Implied Forward Rates

Shape the spot (zero) curve and watch the no-arbitrage forward rates respond. An upward-sloping curve implies one-year forwards above the spot rates — these are the rates an FRA locks in.

Spot curve s_nImplied 1y forwards f(n−1,n)
0.0%1.2%2.5%3.7%5.0%1y2y3y4y5yMaturity (years)Annualized rate (%)FRA 4.05%
Forward Rate Agreement — pick the period
The 1×3 forward rate f1,3 = 4.05% locks in borrowing or lending over years 1 to 3 (a 2-year period).
FRA f(1,3)
4.05%
Curve shape
Upward
1y spot
3.00%
5y spot
4.00%
1y
3.00%
spot = fwd
3.00%
2y
3.40%
f(1,2)
3.80%
3y
3.70%
f(2,3)
4.30%
4y
3.90%
f(3,4)
4.50%
5y
4.00%
f(4,5)
4.40%

Why it matters

The yield curve is the bond market’s map of time. For one issuer, it asks what you earn for locking your money up for three months versus three years versus thirty years. Usually longer means more, because lending for longer carries more uncertainty, so the curve slopes up. When it inverts, with short rates above long rates, the market is effectively betting that rates will fall, which often happens when investors expect a slowdown. Reading the shape is reading a forecast embedded in prices.

Formulas

Expectations hypothesis (two-period link)
(1+y2)2=(1+y1) (1+f1,2)(1+y_2)^{2} = (1+y_1)\,(1+f_{1,2})
The two-period yield y2y_2 compounds the one-period yield y1y_1 with the forward rate f1,2f_{1,2} expected between periods one and two. An upward slope implies a forward rate above today’s short rate.

Worked examples

Scenario

The one-year yield is four percent and the two-year yield is five percent. Under the expectations hypothesis, what one-year rate does the market expect to prevail a year from now?

Solution

Set (1.05)2=(1.04) (1+f)(1.05)^2=(1.04)\,(1+f), which gives 1.10251.04−1=0.0601\tfrac{1.1025}{1.04}-1=0.0601. The implied forward rate ff is about 6.01 percent. The upward-sloping curve embeds an expectation that the one-year rate will rise from four percent today to roughly six percent next year.

NoteAn upward slope mechanically implies forward rates above current short rates, which the expectations hypothesis reads as anticipated rate increases.

Common mistakes

  • ✗An inverted yield curve means long-term bonds are riskier than short-term ones. Inversion reflects expectations that short rates will fall, usually because of an expected slowdown, not a sudden jump in long-bond risk.
  • ✗The yield curve compares bonds from different issuers. A meaningful curve holds credit quality fixed and varies only maturity, so the shape reflects the term structure rather than differences in default risk.
  • ✗A normal upward slope guarantees that rates will rise. The slope reflects expectations plus risk premia. A term premium can produce an upward slope even when rates are expected to stay flat.
  • ✗The yield curve is fixed and rarely moves. The curve shifts and changes shape continuously as expectations about growth, inflation, and policy evolve.

Revision bullets

  • •The yield curve plots yield against maturity for one credit quality
  • •Normal curves slope up, flat curves are level, inverted curves slope down
  • •Inversion has often preceded recessions
  • •The expectations hypothesis reads the slope as forecast future short rates
  • •Liquidity and term premia shape the curve beyond pure expectations

Quick check

An inverted yield curve, where short-term yields exceed long-term yields, is most often interpreted as a signal that

For the yield curve to convey information about the term structure, the bonds plotted should differ in

Connected topics

Money MarketBond BasicsBond PricingBond YieldDuration

Sources

  1. Brailsford, Heaney & Bilson (2015), Ch. on the term structure
    Brailsford, T., Heaney, R., & Bilson, C. Investments: Concepts and Applications. 5th ed. Cengage Learning Australia, 2015.
    Introduces the yield curve, its shapes, and the expectations theory of the term structure.
  2. Bodie, Kane & Marcus (2021), Ch. 15
    Bodie, Z., Kane, A., & Marcus, A. J. Investments. 12th ed. McGraw-Hill Education, 2021.
    Develops the term structure, forward rates, and the expectations and liquidity-premium theories.
How to cite this page
Dr. Phil's Quant Lab. (2026). The Yield Curve and Term Structure. Derivatives Atlas. https://phucnguyenvan.com/concept/im-yield-curve
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