FRM Exam Part I · Properties of Interest Rates

Theories of the Term Structure of Interest Rates

Updated 11 October 2026 · Fact-checked

Term structure theories explain why yields differ by maturity. Expectations theory says long rates are averages of expected future short rates. Market segmentation says supply and demand in each maturity bucket set rates. Liquidity preference says long rates include a term premium, so the curve usually slopes upward.

Understand Theories of the Term Structure

The term structure (yield curve) shows yields for different maturities. Three theories try to explain its shape. The exam tests whether you know what each theory assumes and what shape it predicts.

Expectations theory says the long-term rate is an average of the short rates the market expects. Forward rates are unbiased predictions of future spot rates. If investors expect short rates to rise, the curve slopes up. If they expect falls, it slopes down. Under pure expectations, an upward slope means only that rates are expected to rise.

Market segmentation theory says short, medium and long maturities are separate markets. Each has its own borrowers and lenders, such as banks at the short end and pension funds or insurers at the long end. Supply and demand within each segment set the yield. Short and long rates need not be linked, so the curve can take any shape.

Liquidity preference theory says investors want compensation for holding longer bonds, which have more price risk. So forward rates are above expected future spot rates. The gap is a liquidity (term) premium that rises with maturity. This is why the curve is upward sloping most of the time, even when rates are expected to stay flat. Borrowers like to borrow long and lenders prefer to lend short, and banks in particular tend to have short-term liabilities and long-term assets, so the premium is needed to balance this.

A fourth idea, preferred habitat theory, blends the others. Investors prefer certain maturities but will move if the yield pays them enough.

Key formulas to remember

Expectations theory (two periods, annual compounding): (1 + y2)² = (1 + y1) × (1 + E[f]); y1 is the 1-year spot rate, y2 the 2-year spot rate, E[f] the expected 1-year rate one year ahead. Under pure expectations, E[f] equals the forward rate.
Forward rate from spot rates: f(1,2) = (1 + y2)² ÷ (1 + y1) − 1; Annual compounding. This is the rate locked in today for year 2.
Liquidity preference theory: Forward rate = Expected future spot rate + Liquidity premium; The premium is positive and tends to increase with maturity.
Shape summary: Expectations: slope reflects expected rate path; Segmentation: supply and demand by bucket; Liquidity preference: usually upward; Learn the one-line prediction of each theory.

How to solve Theories of the Term Structure questions

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

1Identify which theory the question names or describes. Look for keywords: expected future rates, separate maturity markets, or compensation for risk.
2If numbers are given, convert spot rates to the implied forward rate with (1 + y2)² ÷ (1 + y1) − 1, using the stated compounding.
3Under expectations theory, treat the forward rate as the expected future spot rate.
4Under liquidity preference theory, subtract the liquidity premium from the forward rate to get the expected future spot rate.
5Under market segmentation, do not link maturities. Reason from supply and demand in each bucket.
6Match the predicted curve shape to the theory and check the answer option against it.
7Check units: percent versus decimal, and annual versus semiannual compounding.

Quickest way: Keyword matching and one-line forward check

When to use it: Use it for MCQs where options describe curve shapes or reasons.

Expectations = curve shape equals expected rate path.
Segmentation = separate markets, any shape, no link across maturities.
Liquidity preference = term premium, upward bias, forward above expected spot.
For numbers, compute the forward rate first, then adjust only if a premium is given.
Remove options that contradict the theory named.

Common mistakes in Theories of the Term Structure

Saying liquidity preference theory predicts that forward rates equal expected future spot rates.
It is mixed up with pure expectations theory.
Fix: Remember that liquidity preference adds a positive premium, so forward is greater than expected spot.
Claiming expectations theory always gives an upward-sloping curve.
Students remember that real curves usually slope up.
Fix: Under pure expectations, the curve is flat if short rates are expected to stay flat, and downward if they are expected to fall.
Saying market segmentation links short and long rates through expectations.
It is confused with expectations or preferred habitat.
Fix: Under segmentation, each maturity bucket clears on its own supply and demand.
Reading an upward slope as proof that rates will rise.
Ignoring the term premium.
Fix: With a liquidity premium, part of the slope is compensation for risk, not an expected rate rise.
Forgetting to compound when computing forward rates.
Using a simple subtraction like 2 × y2 − y1.
Fix: Use (1 + y2)² ÷ (1 + y1) − 1 for annual compounding.

Worked examples

Example 1

The 1-year spot rate is 3.0% and the 2-year spot rate is 4.0%, both annually compounded. Under pure expectations theory, what is the expected 1-year rate one year from now?

Show the solution

Forward rate = (1 + y2)² ÷ (1 + y1) − 1.
(1.04)² = 1.0816.
1.0816 ÷ 1.03 = 1.05010.
Subtract 1: 0.05010, about 5.01%.
Under pure expectations, the forward rate equals the expected future spot rate.

Answer: About 5.01%

Example 2

Using the same rates (1-year 3.0%, 2-year 4.0%), the market's liquidity premium for the second year is 0.60%. Under liquidity preference theory, what is the expected 1-year rate one year from now?

Show the solution

Forward rate = 1.0816 ÷ 1.03 − 1 = 5.01%.
Forward = Expected spot + Liquidity premium.
Expected spot = 5.01% − 0.60% = 4.41%.
Compare with pure expectations (5.01%): the expected rise is smaller, so part of the upward slope is a risk premium.

Answer: About 4.41%

Exam tips

Be able to state each theory's prediction in one sentence; many questions are purely conceptual.
Watch for the words 'unbiased predictor of future spot rates', which signal expectations theory.
If a question mentions pension funds, insurers or separate maturity markets, think market segmentation.
A positive premium means forward rates exceed expected spot rates; get the direction right.
Compute forwards with compounding, not by simple subtraction.

Practice questions from Properties of Interest Rates

Theories of the Term Structure in other exams

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

Theories of the Term Structure: 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 longer maturities, so forward rates are above expected spot rates. This lets the curve slope upward even when rates are not expected to rise.

Why is the yield curve usually upward sloping?

The main explanation is liquidity preference: investors demand extra yield for the greater price risk of long bonds. Expected rate rises can add to the slope but are not the only cause.

What does market segmentation theory say about the yield curve?

It says each maturity range is its own market with its own supply and demand. Yields in one segment do not need to be linked to another, so the curve can take any shape.

Is preferred habitat theory part of the FRM syllabus?

It is a useful extension of segmentation and liquidity preference. Know that investors favour certain maturities but will shift for enough extra yield.