25556 Chap.12 Term Structure and Yield Curve Theories
Term Structure and Yield Curve Theories
Topic 6 begins the second bond week by stepping back from single securities to the whole range of maturities. The term structure of interest rates lines up the yields on one class of low-risk, single-payment security from short terms to long ones, and the yield curve is its picture at one point in time.
The workshop calls the yield curve a critical component of financial analysis, because its slope tells you what the market expects for short-term rates and, through them, for the cash rate.
This chapter explains how a clean curve is built, separates spot rates from forward rates and their notation, and shows how implied forward rates are recovered from spot rates with the exact compounding method and the quicker averaging approximation.
Working examples use annual compounding, matching the workshop exercises. It then compares the unbiased expectations hypothesis with the liquidity premium theory and ends with the blended view the lecture adopts, in which forwards reflect expectations that may prove wrong.
What this chapter covers
- 01
Term structure of interest rates and the yield curve
- 02
Normal, inverse and flat curve shapes
- 03
Spot rate and forward rate notation
- 04
Implied forward rates by the exact method
- 05
The approximate averaging method
- 06
Unbiased expectations versus liquidity premium theory
Worked example · free
Decide whether to lock in four years or roll the fourth year against the implied forward rate
- 1Lock in four years: 500,000 times 1.0385 to the fourth power = $581,561.98.
- 1Break-even: three years at 3.70% grow by 1.037 cubed = 1.115158, so the fourth-year rate that matches the lock-in is 1.163124 divided by 1.115158, minus 1, which is the implied forward rate of 4.30%.
- 1Decision at the forecast: rolling gives 500,000 times 1.115158 times 1.045 = $582,669.87, which beats the lock-in by $1,107.89, so the investor's 4.50% view favours rolling.
- 1Risk: if the fourth-year rate is 4.00%, rolling gives 500,000 times 1.115158 times 1.04 = $579,881.98, which is $1,680.00 less than locking in.
Key terms
- Term structure
- The pattern of yields on one class of security across different terms to maturity at a given time.
- Yield curve
- A graph plotting yield against term to maturity for comparable securities at one moment.
- Spot rate
- An interest rate that applies from today for a stated term, written with a zero on the left of its label.
- Forward rate
- An interest rate agreed or implied for a period that begins at a future date.
- Liquidity premium
- Extra yield that investors demand on longer-term securities to compensate for their greater price risk.
Term Structure and Yield Curve Theories FAQ
What does an inverse yield curve tell you?
Long-term yields are below short-term yields, and under the expectations view this means the market expects short-term rates to be lower in future, often because it anticipates cuts to the cash rate. Name the shape first, then state the expectation it reveals and, if asked, a plausible economic reason such as a slowing economy.
How do you calculate an implied forward rate exactly?
Turn each spot rate into a growth factor by compounding it over its term, divide the longer factor by the shorter one, and subtract one. For a one-year forward starting in year two, divide 1 plus the two-year rate squared by 1 plus the one-year rate. The result is the rate that makes both investment routes reach the same value.
When can I use the approximate method?
It works because a multi-year spot rate is close to the average of the one-year rates inside it, so a forward is roughly the longer rate times its years minus the shorter rate times its years. It is quick and good for checking, but use the exact compounding method whenever a question asks for it.
Why does the liquidity premium theory only explain upward curves?
It says longer terms earn a premium for price risk, which on its own always pushes long yields above short ones. A flat or inverse curve therefore needs falling expected rates, which is why the lecture reads short-rate movements through the expectations approach and treats forward rates as forecasts that may turn out wrong.
Are forward rates accurate forecasts of future interest rates?
They are the market's best estimate at the time, but the lecture stresses that expectations will not always be correct. New information, such as an unexpected inflation figure or a change of view about the cash rate, can move actual spot rates well away from what the forwards implied.
Exam move
Draw a quick sketch of each curve shape and write beside it what the market expects for short-term rates, then add one event that could cause it. Practise forward rates from a fresh set of spot rates that you choose yourself, always writing the growth factors before dividing, and check each answer with the approximate method.
Go the other way too, building a multi-year spot rate from a chain of forwards, because the workshop tests both directions. Finish by writing two sentences on why the liquidity premium theory alone cannot explain an inverse curve, and how the blended view used in the lecture resolves that gap. Keep a note of which method each workshop answer uses so you can match the expected form.
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