Level III Core · Capital Market Expectations, Part 2: Forecasting Asset Class Returns

Equity Risk Premium Estimation Approaches for CFA Level 3

Updated 8 October 2026 · Fact-checked

The equity risk premium (ERP) is the extra return investors expect from equities over a risk-free rate. You estimate it by the historical method (past averages), forward-looking methods (Gordon growth, supply-side) or surveys. Pick the method, compute using the stated inputs, then state its main weakness.

Understand Equity Risk Premium Estimation Approaches

The equity risk premium is the expected return on equities minus the return on a risk-free asset. It is a core input to capital market expectations. The required return on equity is built as the risk-free rate plus the ERP (plus other premiums if needed). A small error in the ERP changes every equity forecast and every asset allocation built on it.

There are two broad families. Historical estimates take the average past excess return of equities over a bond or bill return. Forward-looking estimates use current market data and expected fundamentals. The Gordon growth and supply-side methods are forward-looking. Survey estimates ask experts or investors what premium they expect.

The historical method is simple but assumes the past repeats. It is sensitive to the sample period, to the choice of risk-free proxy (long bond versus bill), to arithmetic versus geometric averaging, and to survivorship bias in the markets sampled. It also suffers if the premium has changed over time, so past data may not describe today.

The Gordon growth (dividend discount) approach works from today's prices. It uses the expected equity return implied by the market's dividend yield and a growth rate, then subtracts the risk-free rate. The growth rate is the long-run expected dividend growth rate that the question supplies or the analyst justifies. The supply-side approach builds the expected equity return from economic fundamentals: inflation, real earnings growth and income return. It then subtracts the risk-free rate. The valuation-change (P/E) term is often set to zero for long-run estimates when no re-rating is expected, because P/E expansion cannot persist indefinitely. If the question gives a non-zero P/E change, use it.

Surveys are easy to run but can be biased by recent market moves and by who is asked. Many candidates are also tested on how the methods differ. Historical looks backward and needs stable conditions. Forward-looking methods look ahead but depend on the inputs you assume.

Key rules to remember

Equity risk premium: ERP = E(R equity) − Risk-free rate; Use the risk-free rate matching the horizon in the question. Long-horizon questions usually use a long-term government bond yield.
Historical ERP: ERP (historical) = Mean(equity return) − Mean(risk-free return); Check whether the question wants arithmetic or geometric averages. State the sample period and risk-free proxy used.
Gordon growth ERP: ERP = D1 ÷ P0 + g − Risk-free rate; D1 ÷ P0 is the forward dividend yield. g is the long-run expected dividend growth rate, which is supplied or justified by the analyst and may be linked to nominal economic growth.
Supply-side ERP (Ibbotson-Chen style): E(R equity) ≈ (1 + i)(1 + g real EPS)(1 + g P/E) − 1 + Income return; ERP = E(R equity) − Risk-free rate; Here i is expected inflation, g real EPS is real earnings growth per share, g P/E is the percentage change in the P/E, and income return is the dividend yield. Long-run estimates often set the P/E term to zero when no re-rating is expected, but the question may give a non-zero value, and then you must use it. Use the exact form in the question and check which terms are given.
Approximate supply-side form: E(R equity) ≈ i + g real EPS + g P/E + Income return; Use the approximation only when the question allows it. g P/E is the percentage change in the P/E. It is often set to zero for long-run estimates when no re-rating is expected, but use any non-zero value the question gives.

How to solve Equity Risk Premium Estimation Approaches questions

Use this order for any ERP estimation question, whether it asks you to calculate, compare or critique.

1Read the command word. Calculate, compare, explain and recommend each need a different answer shape.
2Identify which method the question names or implies: historical, Gordon growth, supply-side or survey.
3List the inputs given: dividend yield, growth, inflation, real earnings growth, P/E change, risk-free rate.
4Compute the expected equity return first, then subtract the risk-free rate to get the ERP.
5Check that the risk-free rate and growth rate match the horizon and currency (nominal with nominal, real with real).
6Show the calculation lines so a correct number earns full credit.
7If asked for strengths or weaknesses, give the specific limit of that method, not a generic statement.
8If asked for a recommendation, tie it to the client's horizon and to whether current conditions look like the past.

Quickest way: Two-line ERP check

When to use it: Use when an item set gives you the inputs and asks for a number under time pressure.

Write E(R equity) = income + growth (or inflation + real growth + valuation change + income).
Subtract the risk-free rate and check that the answer has a sensible size and the right sign.
If the choices are close, re-check whether you used the forward yield D1 ÷ P0 and not trailing D0 ÷ P0.

Common mistakes in Equity Risk Premium Estimation Approaches

Forgetting to subtract the risk-free rate and giving the expected equity return as the ERP.
The Gordon and supply-side formulas end with an equity return, so the last step feels done.
Fix: Always write ERP = E(R equity) − Rf as the final line.
Mixing real and nominal inputs, such as nominal growth with a real risk-free rate.
Inflation is listed as an input and students add or omit it by habit.
Fix: Label every input nominal or real before combining. Keep the ERP on a consistent basis.
Using the current dividend D0 instead of next year's D1 in the Gordon growth method.
The quoted dividend yield is often trailing.
Fix: If only D0 is given, compute D1 = D0 × (1 + g) and use the forward yield.
Calling the historical method forward-looking, or saying it is unbiased.
Students remember that it uses real data and assume it is objective.
Fix: Say it is backward-looking and sensitive to sample period, risk-free proxy, averaging method and survivorship bias.
Treating a survey result as a precise estimate.
A single number looks authoritative.
Fix: Note that surveys can be affected by recent returns, sample choice and respondents' views, and are best used as a cross-check.
Including a change in the P/E in a long-run supply-side estimate without being told to.
The formula has a term for it, so students fill it in.
Fix: Use the valuation-change term only when it is given or the question expects a re-rating. Otherwise treat it as zero.

Worked examples

Example 1

An analyst uses the Gordon growth approach. The forward dividend yield on a global equity index is 2.4%, the long-run expected growth rate of dividends is 4.1%, and the 10-year government bond yield is 3.2%. Estimate the equity risk premium.

Show the solution

Expected equity return = D1 ÷ P0 + g = 2.4% + 4.1% = 6.5%.
ERP = E(R equity) − Rf = 6.5% − 3.2% = 3.3%.

Answer: The estimated ERP is 3.3%.

Example 2

A supply-side analyst expects inflation of 2.0%, real earnings growth per share of 2.5%, no change in the P/E, and an income return of 2.2%. The government bond yield is 3.0%. Using the approximate additive form, estimate the ERP, then state one reason the analyst might set the P/E change to zero.

Show the solution

E(R equity) ≈ i + g real EPS + g P/E + Income return.
= 2.0% + 2.5% + 0% + 2.2% = 6.7%.
ERP = 6.7% − 3.0% = 3.7%.
A P/E cannot expand without limit relative to earnings, so over the long run a zero change is a reasonable base case.

Answer: The estimated ERP is 3.7%. Setting the P/E change to zero reflects that valuation re-rating cannot keep adding to returns over a long horizon.

Exam tips

Look at the command word first. Calculate needs a number, while justify or discuss needs a reason tied to the method.
Show every line: expected equity return, then the subtraction of the risk-free rate. A correct number on its own earns full credit in essay calculations, but show the working in case you slip.
In item sets, check whether the dividend yield is forward or trailing before you add growth.
When comparing methods, name one specific weakness for each: sample dependence for historical, input sensitivity for Gordon growth, sensitivity to the forecast inputs and to the assumption about the P/E change for supply-side, and bias for surveys.
Only the number of responses asked for is evaluated, in the order given. If asked for two reasons, give exactly two.

Equity Risk Premium Estimation Approaches in other exams

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

Equity Risk Premium Estimation Approaches: frequently asked questions

What is the difference between historical and forward-looking ERP estimates?

A historical estimate averages past equity returns above a risk-free proxy and assumes the future resembles the past. A forward-looking estimate uses current prices and expected fundamentals such as dividend yield, growth and inflation. Forward-looking methods respond to today's valuations but depend on the inputs you choose.

How does the supply-side ERP differ from the historical ERP?

The supply-side method builds expected equity returns from economic fundamentals such as inflation, real earnings growth and income return. It often sets the P/E change to zero for long-run estimates when no re-rating is expected. The historical method averages past returns, so it embeds any valuation re-rating that occurred in the sample period.

How do I use the Gordon growth model to get the ERP?

Add the forward dividend yield to the long-run growth rate to get the expected equity return, then subtract the risk-free rate. Use D1 ÷ P0, not the trailing yield, and keep nominal and real terms consistent.

Which ERP method is best for the exam?

None is best in all cases. Choose the one the question names or the one that fits the inputs given, and be ready to state its main limitation. For recommendations, link the choice to the horizon and to how stable conditions are.