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Theories of the Term Structure

Three theories explain the shape of the yield curve. The expectations theory makes the long rate the average of expected future short rates. The segmented markets theory treats each maturity as its own market with no substitution. The liquidity premium theory combines them, adding a positive term premium that grows with maturity, and it is the only one that fits all three empirical facts.

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Macro· 5:59

The Three Theories of the Yield Curve, expectations, segmented markets and the liquidity premium

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Why it matters

Ask whether rolling short bonds and buying one long bond should leave you equally well off. If investors are indifferent, the long rate is just an average of expected short rates. In reality people prefer the flexibility of short bonds, so a long bond must pay a little extra. That extra, the term premium, is what tilts the curve upward even when no rate change is expected.

Formulas

Expectations theory (n-year rate)
int=it+it+1e++it+(n1)eni_{nt} = \frac{i_t + i^e_{t+1} + \cdots + i^e_{t+(n-1)}}{n}
The n-year rate is the average of today’s short rate and the expected short rates over the life of the bond.
Liquidity premium theory
int=it+it+1e++it+(n1)en+nti_{nt} = \frac{i_t + i^e_{t+1} + \cdots + i^e_{t+(n-1)}}{n} + \ell_{nt}
The same average plus a term premium nt\ell_{nt} that is positive and rises with maturity nn.

Worked examples

Scenario

You can roll two 1-year bonds, the first at 6% and the second expected at 8%, or buy one 2-year bond. Under the expectations theory, what 2-year rate makes you indifferent?

Solution

The 2-year rate equals the average of the two short rates, (6% + 8%) / 2 = 7%. If the 2-year bond actually yields a bit more than 7%, that extra is the term premium that the liquidity premium theory adds.

Common mistakes

  • The expectations theory alone explains the upward slope. It explains why rates move together and why curves invert before recessions, but not the plain fact that curves slope up most of the time, even when no rate rise is expected.
  • The segmented markets theory is enough on its own. It can deliver a usual upward slope but cannot explain why rates of different maturities move together, which is why the liquidity premium synthesis is preferred.
  • A term premium means long bonds are a free lunch. It is compensation for the extra interest-rate risk of tying money up longer, not an arbitrage.

Revision bullets

  • Three theories: expectations, segmented markets, liquidity premium
  • Expectations: long rate equals the average of expected short rates
  • Segmented markets: each maturity priced in its own market
  • Liquidity premium adds a positive term premium that grows with maturity
  • Only the liquidity premium theory fits all three facts

Quick check

Which theory of the term structure is consistent with all three empirical facts, including the usual upward slope?

Connected topics

Sources

  1. Mishkin (2018), Ch. 6
    Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.
    The expectations, segmented-markets, and liquidity-premium (preferred-habitat) theories of the term structure.
How to cite this page
Dr. Phil's Quant Lab. (2026). Theories of the Term Structure. Derivatives Atlas. https://phucnguyenvan.com/concept/mb-term-structure-theories
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