FRM Exam Part I · Interest Rates

Term Structure Theories for FRM Part I Explained

Updated 11 October 2026 · Fact-checked

Term structure theories explain why yields differ by maturity. Expectations theory says long rates reflect expected future short rates. Liquidity preference adds a term premium for long bonds. Market segmentation says supply and demand in each maturity bucket set yields. To solve questions, link the curve shape to the theory's logic.

Understand Term Structure Theories

The term structure of interest rates (the yield curve) shows yields on bonds of similar credit quality across maturities. A curve can slope upward (normal), slope downward (inverted), or be flat. Term structure theories try to explain why.

The pure expectations theory says long-term rates are an average of expected future short-term rates. Forward rates are unbiased predictors of future spot rates. An upward curve means the market expects short rates to rise. An inverted curve means it expects them to fall. Under this theory, investors are indifferent between holding a long bond and rolling over short bonds.

Liquidity preference theory says investors dislike risk from holding long bonds, because long bond prices are more sensitive to rate changes. They demand a term premium that grows with maturity. Forward rate = expected future spot rate + liquidity premium. So the curve tends to slope upward even if rates are expected to stay flat. An inverted curve under this theory needs expected rate falls larger than the premium.

Market segmentation theory says investors and borrowers have fixed maturity preferences. Pension funds and insurers match long liabilities with long bonds. Banks prefer short assets. Each maturity segment has its own supply and demand, and yields are set separately. Expectations of future rates play no direct role. A related idea, preferred habitat theory, lets investors leave their segment if the yield gap is large enough.

For FRM, you need to tell the theories apart, state what each implies for the curve shape, and compute simple forward-rate or premium numbers.

Key formulas to remember

Forward rate from spot rates (annual compounding): (1 + S₂)² = (1 + S₁) × (1 + f₁,₂); General form: (1 + Sₙ)ⁿ = (1 + Sₙ₋₁)ⁿ⁻¹ × (1 + fₙ₋₁,ₙ). Use the same compounding for all rates.
Pure expectations theory: forward rate = expected future spot rate; No risk premium. Long rate is a geometric average of expected short rates.
Liquidity preference theory: forward rate = expected future spot rate + liquidity premium; The premium is positive and rises with maturity, so forwards overstate expected spot rates.
Long rate as average of short rates (approximation): S₂ ≈ (S₁ + E[s₁,₂]) ÷ 2; Exact form is geometric. The average is a quick approximation for small rates.

How to solve Term Structure Theories questions

Use this method for both conceptual and numerical term structure questions.

1Identify which theory the question names or describes: expectations, liquidity preference, market segmentation or preferred habitat.
2Note the shape of the curve given (upward, inverted, flat, humped) and any numbers (spot rates, forwards, premiums).
3If numbers are given, compute the implied forward rate from the spot rates using the same compounding.
4Apply the theory: expectations means forward = expected spot; liquidity preference means expected spot = forward minus premium.
5For segmentation, look for supply and demand in a maturity bucket, not for expected rates.
6Match your conclusion to the answer options and check the direction (higher or lower).

Quickest way: Keyword and premium shortcut

When to use it: Use for conceptual multiple-choice questions where time is short.

Scan for keywords: 'unbiased predictor' or 'indifferent' means pure expectations.
'Term premium', 'compensation for risk' means liquidity preference.
'Maturity preferences', 'separate markets', 'matching liabilities' means market segmentation.
For numbers, forward = spot expectation + premium. Subtract the premium to get the expected rate.
Remember that only segmentation ignores expectations entirely.

Common mistakes in Term Structure Theories

Saying liquidity preference theory always predicts an upward curve.
Students remember the positive premium and forget expectations still matter.
Fix: The curve is the expectations path plus a premium. Strongly expected rate cuts can still invert it.
Treating the forward rate as the expected spot rate under every theory.
Pure expectations is taught first and gets over-generalized.
Fix: Only pure expectations sets forward = expected spot. With a liquidity premium, expected spot = forward − premium.
Saying market segmentation depends on expected future short rates.
Students blend it with expectations theory.
Fix: Segmentation says each maturity has its own supply and demand. Expectations are not the driver.
Mixing compounding conventions when computing forward rates.
Semiannual and annual rates appear together in problems.
Fix: Convert all rates to one compounding basis before using the forward formula.
Claiming an inverted curve proves a recession will occur.
It is a common market heuristic.
Fix: For the exam, say an inverted curve implies expected falling short rates under expectations theory. Do not overstate it as certain.

Worked examples

Example 1

The 1-year spot rate is 3.0% and the 2-year spot rate is 4.0% (annual compounding). Under pure expectations theory, what is the expected 1-year rate one year from now?

Show the solution

Use (1 + S₂)² = (1 + S₁)(1 + f).
(1.04)² = 1.0816.
Divide by (1.03): 1.0816 ÷ 1.03 = 1.05010.
f = 1.05010 − 1 = 5.01%.
Under pure expectations, expected spot = forward.

Answer: About 5.01%

Example 2

Using the same rates, the market believes the one-year liquidity premium for the forward period is 0.50%. Under liquidity preference theory, what is the expected 1-year rate one year from now?

Show the solution

The forward rate from the earlier calculation is 5.01%.
Liquidity preference: forward = expected spot + premium.
Expected spot = 5.01% − 0.50% = 4.51%.
The expected rate is lower than the forward rate because the forward includes compensation for risk.

Answer: About 4.51%

Exam tips

Know the one-line distinguishing feature of each theory; many questions test only that.
Practice the forward rate calculation until it takes under a minute with a financial calculator using the yx key.
Read the direction of the premium carefully: forwards exceed expected spot rates under liquidity preference.
If a question asks which theory cannot explain a normally upward curve without a premium, the answer is pure expectations when rates are expected flat.

Practice questions from Interest Rates

Term Structure Theories in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Term Structure Theories: frequently asked questions

What is the difference between expectations theory and liquidity preference theory?

Expectations theory says forward rates equal expected future spot rates. Liquidity preference adds a positive term premium for holding longer bonds. So under liquidity preference, forwards are higher than expected spot rates.

Why is the yield curve usually upward sloping?

Liquidity preference theory gives one reason: investors demand a premium for the greater price risk of long bonds. Market expectations of rising rates can also produce an upward slope. Segmentation theory points to the relative supply and demand at each maturity.

What does an inverted yield curve mean for the exam?

Short-term yields are above long-term yields. Under expectations theory this signals expected declines in short rates. Under liquidity preference, the expected declines must outweigh the term premium.

How does market segmentation theory differ from preferred habitat theory?

Segmentation says investors stay strictly within their maturity preference. Preferred habitat says they prefer a maturity but will shift if the yield difference is large enough.