Financial Management · The nature and role of financial markets and institutions

Interest Rates and Yield Curves for ACCA FM

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

Expectations theory says long-term rates reflect expected future short-term rates. Liquidity preference theory adds that investors want a premium for lending long term. So a curve can slope upwards even if rates are not expected to rise.

Q: Why can a yield curve be inverted?

An inverted curve means short-term yields are above long-term yields. Under expectations theory, the market expects short-term rates to fall in future. This is sometimes linked to expected economic slowdown, though it is not certain.

Q: What factors affect the interest rate a company pays?

The main factors are the base rate, the company's default risk, the length of the loan, how easily the debt can be sold, the loan size and expected inflation. Security offered also matters. In the exam, link each factor to the company in the question.

Q: What is market segmentation theory?

It says the market for debt is split by maturity, such as short, medium and long term. Each segment has its own supply and demand, so yields in each part of the curve are set separately. Banks and pension funds are common examples of institutions that prefer different terms.

Updated 11 October 2026 · Fact-checked

An interest rate is the price of borrowing money. It rises with risk, term and lower liquidity. A yield curve plots yield against time to maturity for similar bonds. You explain its shape using expectations theory, liquidity preference and market segmentation. Always link the shape to what the market expects.

Understand Interest Rates and Yield Curves

An interest rate is the price of using someone else's money. Lenders want a return for giving up their cash now. The rate they ask for depends on several things: the base rate set by the central bank, the risk of not being repaid, the length of the loan, how easily the loan can be sold, and expected inflation.

The main components are risk, term and liquidity. Higher default risk means a higher rate, called a credit spread over a risk-free rate such as government bond yields. A longer term usually means a higher rate, because the lender is exposed for longer. A less liquid instrument, one that is hard to sell quickly without losing value, also needs a higher yield. Other factors include the size of the loan, expected inflation, and government borrowing needs and monetary policy.

A yield curve is a graph. The horizontal axis shows time to maturity. The vertical axis shows the yield (redemption yield) on bonds of the same risk class, usually government bonds. It shows the term structure of interest rates. The curve can slope upwards (normal), slope downwards (inverted), or be flat.

There are three main theories. Expectations theory: long-term rates are an average of the expected future short-term rates. A rising curve means the market expects short-term rates to rise. An inverted curve means it expects them to fall. Liquidity preference theory: investors want a premium for tying up money for longer, so long-term rates are higher than expectations alone would give. This explains why curves usually slope upwards. Market segmentation theory: the market is split into separate segments (short, medium and long term) with their own supply and demand, so each part of the curve is set separately. Institutions such as banks prefer short-term and pension funds prefer long-term assets.

The yield curve matters for managers. It guides the choice between short-term and long-term borrowing, helps price bonds and loans, and signals what the market expects about growth and rates.

Key rules to remember

Components of an interest rate: Rate = risk-free rate + risk premium (credit spread) + term (maturity) premium + liquidity premium; A way of remembering the factors. It is not a formula for exam calculations.
Credit spread: Credit spread = yield on risky bond − yield on risk-free bond of similar maturity; Compare bonds with the same term. Government bonds are the usual risk-free benchmark.
Expectations theory (two-year example): (1 + 2-year spot rate)² = (1 + 1-year spot rate) × (1 + forward rate for year 2); Gives the implied forward rate. In FM it is usually tested in words, but you can use this relation to check the shape of the curve.
Shape rules: Upward slope: long yields > short yields. Inverted: long yields < short yields. Flat: roughly equal.; Under pure expectations, upward means rates are expected to rise, and inverted means they are expected to fall.

How to solve Interest Rates and Yield Curves questions

Use this method for any question asking you to explain interest rates or the shape of a yield curve.

1Read the question and identify what is asked: factors affecting a rate, the shape of a curve, or a theory.
2If the question is about one rate, list the factors: base rate, risk, term, liquidity, size of loan, inflation, and government and market conditions.
3Link each factor to the situation in the scenario. For example, a small unlisted company has higher default risk and so pays a higher spread.
4If the question is about a curve, state the shape first: upward, inverted or flat.
5Explain the shape with at least two theories: expectations, liquidity preference and, where useful, market segmentation.
6Say what the shape implies for the company, for example the choice between fixed and floating rates or between short and long borrowing.
7For a numerical question, compare yields for the same maturity and risk, and compute spreads or implied forward rates carefully.
8Finish with a short conclusion that answers the exact question asked.

Quickest way: Shape, theory, implication

When to use it: Use this in Section A and OT case questions where you must choose the right explanation quickly.

Identify the shape of the curve from the data: compare short-term and long-term yields.
Match the theory to the wording: 'expected future rates' means expectations; 'premium for tying up funds' means liquidity preference; 'separate demand and supply for maturities' means market segmentation.
Remember that liquidity preference adds a premium to expectations, so the curve is steeper than expectations alone suggests.
Check the option against the shape: a theory that predicts rising rates cannot explain an inverted curve on its own.
Eliminate options that mix up risk and term, or that confuse credit spread with maturity premium.

Common mistakes in Interest Rates and Yield Curves

Saying an upward-sloping curve always means the market expects rates to rise.
Students apply pure expectations theory and ignore the liquidity premium.
Fix: State that an upward slope may reflect expected rises, a liquidity premium, or both.
Comparing bonds with different risk or maturity when working out a credit spread.
Students take the first two yields in the table.
Fix: Match maturity and use a risk-free benchmark, usually a government bond.
Mixing up liquidity preference with the liquidity of an instrument.
Both phrases use the word liquidity.
Fix: Liquidity preference is about investors wanting a premium for long-term lending. An illiquid instrument needs a higher yield because it is hard to sell.
Giving a list of factors with no link to the scenario.
Students memorise lists and write them out.
Fix: Tie each factor to the company named in the question and say whether it raises or lowers the rate.
Describing an inverted yield curve as a mistake or as an error in the data.
Students expect curves to always rise.
Fix: Explain that it is possible, and under expectations theory shows the market expects short-term rates to fall.

Worked examples

Example 1

The market yields on government bonds are: 1 year 3%, 5 years 4%, 10 years 5%. A company's 10-year bond yields 7.5%. (a) Describe the shape of the curve and give two explanations. (b) Calculate the credit spread on the company's bond.

Show the solution

Part (a): the yields rise as maturity lengthens (3%, 4%, 5%), so the curve slopes upwards. This is a normal curve.
Explanation 1, expectations theory: the market expects short-term rates to rise, so long-term yields, an average of expected short rates, are higher.
Explanation 2, liquidity preference: investors want extra return for tying up funds for longer and bearing more price risk, so long-term yields include a premium.
Part (b): compare with the government bond of the same maturity. The 10-year government yield is 5%.
Credit spread = 7.5% − 5% = 2.5%, or 250 basis points.

Answer: The curve slopes upwards, explained by expected rate rises and a liquidity premium. The credit spread is 2.5%, which compensates investors for the company's default risk (and any lower liquidity).

Example 2

The one-year spot rate is 4% and the two-year spot rate is 5%. Using expectations theory, calculate the implied one-year rate for year 2 (forward rate), to two decimal places, and say what it suggests.

Show the solution

Use (1 + 2-year spot)² = (1 + 1-year spot) × (1 + forward rate).
(1.05)² = 1.1025.
Divide by (1.04): 1.1025 ÷ 1.04 = 1.06010 (to five decimal places).
Forward rate = 1.06010 − 1 = 0.0601, which is 6.01% to two decimal places.
The implied forward rate (6.01%) is higher than the current one-year rate (4%).

Answer: The implied forward rate for year 2 is 6.01%. Under pure expectations theory the market expects short-term rates to rise, which is why the curve slopes upwards.

Exam tips

In Section A questions, match the key phrase to the theory: expected future rates, liquidity premium or separate segments.
In Section C, structure the answer as shape, theories, implication. A clear layout earns marks even if some points are brief.
Always compare yields of the same maturity and risk class. Examiners set traps with mismatched bonds.
Relate your answer to the scenario company: its size, credit standing and borrowing plans.
Do not rely on one theory. Show that real curves reflect expectations, a liquidity premium and market conditions together.

Practice questions from The nature and role of financial markets and institutions

Interest Rates and Yield Curves in other exams

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

Interest Rates and Yield Curves: frequently asked questions

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

Expectations theory says long-term rates reflect expected future short-term rates. Liquidity preference theory adds that investors want a premium for lending long term. So a curve can slope upwards even if rates are not expected to rise.

Why can a yield curve be inverted?

An inverted curve means short-term yields are above long-term yields. Under expectations theory, the market expects short-term rates to fall in future. This is sometimes linked to expected economic slowdown, though it is not certain.

What factors affect the interest rate a company pays?

The main factors are the base rate, the company's default risk, the length of the loan, how easily the debt can be sold, the loan size and expected inflation. Security offered also matters. In the exam, link each factor to the company in the question.

What is market segmentation theory?

It says the market for debt is split by maturity, such as short, medium and long term. Each segment has its own supply and demand, so yields in each part of the curve are set separately. Banks and pension funds are common examples of institutions that prefer different terms.