Financial Management · The valuation of debt and other financial assets

Term Structure of Interest Rates and Yield Curves for ACCA FM

Updated 11 October 2026 · Fact-checked

The term structure of interest rates shows how yields differ with time to maturity for similar bonds. A yield curve plots those yields. To answer questions, name the curve shape, then explain it using expectations, liquidity preference or market segmentation theory, and note any credit spread.

Understand Term Structure of Interest Rates and Yield Curves

A bond pays interest and returns its face value at maturity. Its yield is the return an investor earns if they buy it at today's price and hold it. Two bonds from the same borrower can have different yields simply because one matures in 1 year and the other in 10 years. This link between yield and time to maturity is the term structure of interest rates.

A yield curve is a graph of yield (vertical axis) against time to maturity (horizontal axis). It is normally drawn for bonds with the same credit risk, such as government bonds. The usual shapes are:

Normal (upward sloping): longer maturities have higher yields.
Inverted (downward sloping): short-term yields are higher than long-term yields.
Flat: yields are similar across maturities.
Humped: yields rise, peak at medium maturities, then fall.

Three theories try to explain the shape.

Expectations theory says long-term yields reflect the market's expectation of future short-term rates. If investors expect rates to rise, the curve slopes up. If they expect rates to fall, it slopes down (inverted). A long-term rate is roughly an average of the expected short-term rates over that period.

Liquidity preference theory says investors want a premium for tying up money for longer, because long bonds are more sensitive to rate changes and are harder to turn into cash without loss. So long-term yields include a liquidity premium. This pushes the curve upward even when rates are expected to stay level. It also explains why a normal curve is the most common shape. An inverted curve means expected falls in rates outweigh the premium.

Market segmentation theory says the market is split into separate maturity segments. Each has its own supply and demand. For example, pension funds may prefer long bonds and banks may prefer short ones. Yields at each maturity are set within their own segment, so the curve can take any shape. Investors do not move freely between segments.

The curve is for one risk class. A corporate bond yields more than a government bond of the same maturity. The extra is the credit spread. It compensates for default risk and is wider for lower credit ratings. So a company's cost of debt is roughly the risk-free yield for that maturity plus a spread for its rating.

Key rules to remember

Yield on a corporate bond: Corporate yield = Risk-free yield (same maturity) + Credit spread; The spread rises as the credit rating falls and often differs by maturity.
Expectations theory (two-year bond, annual compounding): (1 + 2-year spot rate)² = (1 + 1-year spot rate) × (1 + forward rate for year 2); Use it to find the implied forward rate: forward = (1 + s₂)² ÷ (1 + s₁) − 1.
Liquidity preference theory: Long-term yield = Expected average short-term rate + Liquidity premium; The premium is normally larger for longer maturities.
Bond price from spot rates: Price = Σ [cash flow in year t ÷ (1 + spot rate for year t)ᵗ]; Each cash flow is discounted at the spot rate for its own maturity.

How to solve Term Structure of Interest Rates and Yield Curves questions

Use this method for both objective questions and written answers on yield curves.

1Identify what is asked: describe a shape, explain it with a theory, calculate a forward rate or a price, or assess a credit spread.
2Read the yields by maturity and decide the shape: upward, downward, flat or humped.
3If a theory is asked for, state it by name and say what it predicts for the shape in the question.
4Link the shape to the scenario: expected rate rises or falls, a premium for liquidity, or separate segments.
5For calculations, use annual compounding with the rates given. Work out forward rates from spot rates, or discount each cash flow at its own spot rate.
6If the bond is not risk-free, add the credit spread for the rating before discounting.
7State the conclusion in one line, such as what the curve implies about expected rates or cost of debt.

Quickest way: Match the shape to the theory

When to use it: Use this for Section A and OT case questions that ask which theory explains a curve or what a shape implies.

Upward curve: expectations (rates expected to rise) or liquidity preference (premium for long term).
Downward curve: only expectations of falling rates can explain it. Liquidity preference alone cannot.
Any odd or humped shape: think market segmentation.
Words like premium, compensation or cash quickly: liquidity preference.
Words like separate demand and supply, pension funds or banks preferring certain maturities: market segmentation.
Words like rate expected next year: expectations.
For forward rates, compute (1 + s₂)² ÷ (1 + s₁) − 1 and check it is above or below s₂.

Common mistakes in Term Structure of Interest Rates and Yield Curves

Saying liquidity preference theory explains an inverted curve on its own.
Students remember the premium but forget it only adds to the expected path.
Fix: Say an inverted curve needs expected falls in short-term rates that outweigh the premium.
Mixing up the three theories.
The names sound similar and notes are memorised without the logic.
Fix: Link each to one idea: expectations = future rates, liquidity = premium, segmentation = separate markets.
Using the 2-year rate instead of the forward rate for year 2 alone.
Students forget the 2-year rate is an average over both years.
Fix: Compute (1 + s₂)² ÷ (1 + s₁) − 1 to isolate year 2.
Comparing yields of bonds with different credit ratings and calling it a yield curve.
The idea of risk class is overlooked.
Fix: A yield curve compares the same risk class. A gap between classes is a credit spread.
Forgetting to add the credit spread when valuing a corporate bond using government yields.
The government curve is given, so students use it directly.
Fix: Add the spread for the rating to the risk-free yield before discounting.

Worked examples

Example 1

The 1-year spot rate is 4% and the 2-year spot rate is 5%. Using expectations theory with annual compounding, find the implied 1-year forward rate for year 2. State what the curve suggests about expected rates.

Show the solution

(1 + s₂)² = (1.05)² = 1.1025.
Divide by (1 + s₁) = 1.04: 1.1025 ÷ 1.04 = 1.06010.
Forward rate = 1.06010 − 1 = 6.01% (to two decimals).
The forward rate of 6.01% is above the 1-year rate of 4%.

Answer: The implied forward rate for year 2 is about 6.01%. The upward curve suggests the market expects short-term rates to rise.

Example 2

A ₹1,000 face-value bond from a government pays no coupon and matures in 2 years. The 2-year government spot yield is 5%. A company issues a similar zero-coupon bond of ₹1,000 with a 2-year maturity and a credit spread of 2%. Find the price of each bond and explain the difference.

Show the solution

Government bond: price = 1,000 ÷ (1.05)² = 1,000 ÷ 1.1025 = ₹907.03.
Company yield = 5% + 2% = 7%.
Company bond: price = 1,000 ÷ (1.07)² = 1,000 ÷ 1.1449 = ₹873.44.
Difference = 907.03 − 873.44 = ₹33.59.
The spread compensates investors for default risk, so the company bond sells at a lower price.

Answer: The government bond is priced at about ₹907.03 and the company bond at about ₹873.44. The lower price reflects the higher yield needed for credit risk.

Exam tips

Always name the theory and say what it predicts. A shape with no explanation earns few marks in a written answer.
In OT questions, remember that an inverted curve can be explained by expectations of falling rates, not by liquidity preference alone.
Show the forward rate formula before substituting. Carry at least four decimals until the final answer.
When a rating or spread is mentioned, link it to the cost of debt and to WACC.
Keep written points short: shape, theory, effect on the company.

Practice questions from The valuation of debt and other financial assets

Term Structure of 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.

Term Structure of Interest Rates and Yield Curves: frequently asked questions

What is the difference between a normal and an inverted yield curve?

A normal curve slopes upward, so long-term yields exceed short-term yields. An inverted curve slopes downward, so short-term yields are higher. Inversion usually signals that the market expects interest rates to fall.

What is liquidity preference theory in FM?

It says investors demand extra yield for holding longer-dated bonds because they are less liquid and more sensitive to rate changes. This liquidity premium makes long-term yields higher than the expected path of short-term rates alone would give.

How do credit ratings affect bond yields?

A lower credit rating means higher default risk, so investors demand a wider credit spread over the risk-free yield. This raises the bond's yield and the issuer's cost of debt.

How does market segmentation theory differ from expectations theory?

Expectations theory says yields reflect expected future short-term rates, with investors moving freely between maturities. Market segmentation says investors stay in preferred maturity segments, so each segment's supply and demand sets its own yield.