DP
Debt & Yield Curvesintermediate

Yield Curve Types

The yield curve plots interest rates against maturity for a homogeneous credit such as Australian Government Bonds or US Treasuries. Four canonical shapes appear. A normal curve slopes upward (long yields exceed short yields), an inverted curve slopes downward, a flat curve has roughly equal yields, and a humped curve peaks at intermediate maturities. Three theories explain shape, the pure expectations theory, the liquidity preference theory, and the market segmentation or preferred habitat theory.

Why it matters

The yield curve is a snapshot of how much investors demand to lend at different horizons. Normally lending longer earns more because investors face price volatility and opportunity cost, the term premium. When the curve inverts, short rates exceed long rates, which usually means markets expect the central bank to cut rates ahead of an economic slowdown. The US 10Y minus 3M spread inverted in 2006 to 2007 and 2019, and recessions followed both times. Inversion is a leading indicator, not a guarantee.

Formulas

Pure expectations link
(1+r2)2=(1+r1)(1+f1,2)(1 + r_2)^2 = (1 + r_1)(1 + f_{1,2})
Two-year zero r2r_2 implies the 1-year forward rate f1,2f_{1,2} if no risk premium exists. Under continuous compounding r2×2=r1+f1,2r_2 \times 2 = r_1 + f_{1,2} (Hull §4.7).
Liquidity preference adjustment
rT=rˉexp+λ(T)r_T = \bar{r}_{\text{exp}} + \lambda(T)
λ(T)\lambda(T) is the maturity-dependent term premium, typically positive and increasing in TT, which biases the curve upward.

Worked examples

Scenario

Australian Commonwealth Government Securities yields on a normal date: 1yr $3.0\%,2yr, 2yr 3.5\%,5yr, 5yr 4.0\%,10yr, 10yr 4.5\%$.

Solution

Upward-sloping shape. Combine expectations of stable or rising future short rates with a positive term premium. Long-duration investors such as superannuation funds and life insurers populate the long end while bank treasuries dominate the short end, which fits the preferred habitat story.

Scenario

US Treasury curve in mid-2007 just before the GFC: 3M $4.80\%,2Y, 2Y 4.50\%,10Y, 10Y 4.65\%$, classic inversion at the front end.

Solution

The 10Y minus 3M spread turned negative around February 2007. NY Fed recession-probability models built on this spread (Estrella and Mishkin) signalled an elevated probability of US recession, which materialised in December 2007. The inverted shape reflected market expectation that the Fed would cut sharply, consistent with a slowdown.

Common mistakes

  • ✗An inverted yield curve guarantees a recession. The signal is strong but not deterministic. The 1966 and 1998 inversions did not produce immediate recessions. The NY Fed's reading is that inversion lifts the recession probability, not certainty.
  • ✗The yield curve always uses the 10Y minus 2Y spread. Estrella and Mishkin's original work uses the 10Y minus 3M spread because the 3M T-bill is closer to the policy rate. Both are tracked, and the 2Y version is liquidity-weighted while the 3M version has the strongest econometric record.
  • ✗All theories must be true at once. The three explanations are competing but partly complementary. Empirical evidence supports a hybrid story with a meaningful term premium (rejecting pure expectations) and partial market segmentation that QE exploits (Krishnamurthy and Vissing-Jorgensen 2011).

Revision bullets

  • •Normal curve slopes upward (most common)
  • •Inverted curve slopes downward (recession signal)
  • •Flat curve has roughly equal yields across maturities
  • •Humped curve peaks at intermediate maturities
  • •Theories are expectations, liquidity preference, segmentation
  • •NY Fed flags 10Y minus 3M as recession-probability metric

Quick check

An inverted yield curve, where short-term yields exceed long-term yields, has historically signalled

Under the liquidity preference theory, the yield curve is typically

Connected topics

Zero RatesForward RatesBond Price

In learning paths

Fixed Income & Rates Path

Sources

  1. Hull (2022), §4.7
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Treatment of zero rates, forward rates, and the major theories of the term structure.
  2. NY Fed Yield Curve FAQ
    Federal Reserve Bank of New York. The Yield Curve as a Leading Indicator: Frequently Asked Questions. NY Fed, accessed 2026.
    Definitive reference on the recession-prediction properties of the US yield curve, primarily the 10Y minus 3M spread.
  3. Estrella and Mishkin (1998)
    Estrella, Arturo and Frederic S. Mishkin. Predicting U.S. Recessions: Financial Variables as Leading Indicators. Review of Economics and Statistics, Vol. 80, 1998.
    Seminal paper establishing the yield-curve-slope probit model that anchors NY Fed recession forecasts.
  4. RBA Statistical Table F2
    Reserve Bank of Australia. Statistical Tables F2 Capital Market Yields, Government Bonds. RBA, monthly release.
    Source for daily AGS yields used to construct the Australian sovereign yield curve at standard maturities.
  5. CFA Institute Curriculum
    CFA Institute. The Term Structure and Interest Rate Dynamics. Refresher Reading, 2026.
    Practitioner-oriented summary of the expectations, liquidity preference, segmented markets, and preferred habitat theories.
How to cite this page
Dr. Phil's Quant Lab. (2026). Yield Curve Types. Derivatives Atlas. https://phucnguyenvan.com/concept/yield-curve-types
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