CFA Level I Exam · Sources of Equity Returns

Expected Equity Return and Equity Risk Premium Estimation

Updated 7 October 2026

Expected equity return equals a risk-free rate plus an equity risk premium (ERP), the extra return investors require for holding equities. You estimate the ERP from history, from forward-looking models such as Gordon growth or the Ibbotson-Chen supply-side approach, or from surveys. Then you add it to the risk-free rate, adjusting for beta where required.

Understand Expected Return Estimation and Risk Premium

Equity investors take risk, so they expect more than a risk-free asset pays. The extra amount is the equity risk premium (ERP): the expected return on the equity market minus the risk-free rate. Expected equity return is built on top of it.

There are two broad ways to estimate the ERP. Historical estimates take the average past market return minus the average past risk-free return. They are easy to compute and use real data. Their weakness is that they depend on the sample period, the choice of arithmetic or geometric mean, and survivorship bias (markets that survived look better than those that did not). Past returns may also not match future expectations.

Forward-looking estimates use current information. Examples are the Gordon growth model (ERP = dividend yield on the index + expected growth in dividends/earnings − risk-free rate), the supply-side (Ibbotson-Chen) model, and surveys of experts. They adapt to current valuations but depend on assumptions and on the quality of the inputs.

The supply-side model builds expected equity return from what the economy and companies can deliver: inflation, real earnings growth, change in the P/E multiple, and the income (dividend) return. The standard textbook form simply adds these parts, E(R) ≈ i + g_real EPS + g_P/E + Yield. Compounding the growth terms gives the exact form. The model ignores the demand side, meaning investor risk appetite. Analysts usually treat the change in the P/E multiple as zero or small, because the multiple cannot rise indefinitely relative to earnings.

Once you have an ERP, there are two common ways to get a required return on a stock. CAPM uses the market ERP scaled by beta. The build-up approach (used often for private or small firms) starts at the risk-free rate and adds premiums, such as an equity risk premium, a size premium and a specific-company premium. Build-up methods typically do not use beta.

Key formulas to remember

Equity risk premium (basic): ERP = E(R market) − Rf; Expected market return minus the risk-free rate. A historical ERP uses average past returns for both.
Expected return on equity market (building blocks): E(Rm) = Rf + ERP; The risk-free rate should match the horizon of the ERP estimate, e.g. a long-term government bond yield for a long-term view.
Gordon growth ERP (forward-looking): ERP = D1/P + g − Rf; D1/P is the forecast dividend yield of the index and g is the long-run expected growth in dividends or earnings. Sometimes the equation is stated as E(Rm) = D1/P + g.
Supply-side (Ibbotson-Chen) expected return: E(R) ≈ i + g_real EPS + g_P/E + Yield. Exact form: E(R) = [(1 + i)(1 + g_real EPS)(1 + g_P/E) − 1] + Yield; The additive approximation is the standard textbook form; compounding is the exact form. i is expected inflation, g_real EPS is real earnings growth, g_P/E is the change in the P/E multiple and Yield is the income return (dividend yield). Analysts usually set g_P/E to zero or a small value because the multiple cannot rise indefinitely.
Supply-side ERP: ERP = E(R) from supply-side model − Rf; Subtract the risk-free rate from the supply-side equity return.
CAPM required return: E(Ri) = Rf + βi × [E(Rm) − Rf]; βi × ERP is the risk premium of the stock.
Build-up required return: E(R) = Rf + ERP + size premium + specific-company premium; Premiums are added one by one. No beta is needed in the simple form.

How to solve Expected Return Estimation and Risk Premium questions

Use this order for any question on estimating expected equity return or the ERP.

1Identify what is asked: the ERP, the market expected return, or a required return for one stock or firm.
2Identify the method named or implied: historical, Gordon growth, supply-side, survey, CAPM or build-up.
3List the inputs with their labels (Rf, inflation, real growth, P/E change, yield, beta, premiums) and check that each is in the same units and time horizon.
4For the supply-side approach, compute the capital gain part by compounding (1 + i)(1 + g)(1 + P/E change) − 1 unless the question says to add the parts; then add the income return.
5Subtract Rf if you need an ERP; add it back (and scale by beta if CAPM) if you need a required return.
6Check the answer for sense (ERP is normally positive and a few percent) and that you answered the exact question asked (premium, not total return).
7If the question is conceptual, name the weakness of the method: historical gives sample and survivorship bias, forward-looking depends on assumptions.

Quickest way: Three-line shortcut for ERP and required return

When to use it: Use for numeric questions where all inputs are given and the question asks for an ERP or a required return.

Write the model's formula from memory and plug in numbers directly.
Compute the market return first, then subtract Rf to get the ERP.
For a stock, multiply beta by the ERP and add Rf. Check that the answer lies between plausible bounds (beta above 1 gives a premium above ERP).
On the supply-side model, if the options are close, use exact compounding in your calculator and see which option matches. If an option matches only the additive version, that is a hint that the question wants the additive version only when it says so.

Common mistakes in Expected Return Estimation and Risk Premium

Treating the ERP as the total expected return of equities.
The words 'equity return' and 'equity premium' sound alike.
Fix: The ERP is over the risk-free rate. Add Rf to get the total expected return.
Using the supply-side model as if it reflected investor risk aversion.
It gives an ERP number, so it looks like a full model.
Fix: Remember it uses economic and company fundamentals (supply) only, not demand-side investor preferences.
Assuming the historical ERP is a reliable forecast.
It is observed data, so it feels objective.
Fix: State its limits: sample period, arithmetic vs geometric mean, survivorship bias, and the possibility that expected returns have changed.
Including a P/E change as a permanent source of return.
Valuations rose a lot in some past periods.
Fix: Analysts usually treat the P/E change as zero or small, because the multiple cannot rise indefinitely relative to earnings. Use zero unless the question gives a value.
Applying beta in the build-up approach or leaving it out in CAPM.
Both give a required return, so students merge them.
Fix: CAPM scales the ERP by beta; the build-up approach adds premiums to Rf without beta.
Mismatching the risk-free rate horizon, such as a 3-month bill with a long-term ERP.
Any 'risk-free' number seems fine.
Fix: Use a risk-free rate whose maturity is consistent with the investment horizon, usually a long-term government bond for equity valuation.

Worked examples

Example 1

An analyst expects inflation of 2.0%, real earnings growth of 3.0%, no change in the P/E ratio and a dividend yield of 2.5%. The risk-free rate is 3.0%. Using the supply-side (Ibbotson-Chen) approach with compounding of the growth terms, what is the equity risk premium? A) 3.0% B) 4.6% C) 7.6%

Show the solution

Capital gain return = (1.02)(1.03)(1.00) − 1 = 1.0506 − 1 = 5.06%.
Add the income return: 5.06% + 2.5% = 7.56% expected equity return.
ERP = 7.56% − 3.0% = 4.56%, which rounds to 4.6%.
C (7.6%) is the total return, not the premium. A (3.0%) simply equals the risk-free rate, a distractor that is not the premium.

Answer: B) 4.6%

Example 2

The expected dividend yield on an equity index is 2.4%, long-run expected growth in dividends is 4.0% and the risk-free rate is 3.1%. Using the Gordon growth approach for the market return and CAPM, a stock with beta 1.25 has a required return closest to: A) 6.4% B) 7.2% C) 9.7%

Show the solution

Market expected return = D1/P + g = 2.4% + 4.0% = 6.4%.
ERP = 6.4% − 3.1% = 3.3%.
CAPM: 3.1% + 1.25 × 3.3% = 3.1% + 4.125% = 7.225%, about 7.2%.
A (6.4%) is the market return. It ignores beta and the stock's higher risk.
C (9.7%) results from adding the ERP to the market return (6.4% + 3.3%) instead of to the risk-free rate. The premium must be scaled by beta and added to Rf, not to the market return.
Only B matches the CAPM result.

Answer: B) 7.2% (3.1% + 1.25 × 3.3% = 7.225%)

Exam tips

Read whether the question asks for the premium or the total return. Many wrong options are the other one.
Memorize the supply-side components: inflation, real earnings growth, P/E change, income return. Questions often ask which one is unsustainable or ignored.
For conceptual items, link each method to its main weakness: historical (sample and survivorship bias), forward-looking (depends on assumptions), surveys (subjective, may be biased), supply-side (ignores demand-side investor risk appetite).
With three options and no penalty, always answer. Eliminate the option that equals Rf, or the total return when a premium is asked.

Practice questions from Sources of Equity Returns

Expected Return Estimation and Risk Premium: frequently asked questions

What is the difference between a historical and a forward-looking equity risk premium?

A historical ERP averages past market returns minus past risk-free returns. A forward-looking ERP uses current information, such as dividend yield plus expected growth minus the risk-free rate. The first is simple but backward-looking; the second reflects present valuations but relies on assumptions.

What is the Ibbotson-Chen supply-side model?

It estimates expected equity return from fundamentals: inflation, real earnings growth, change in the P/E ratio and the dividend (income) return. The standard textbook form adds these parts, and compounding gives the exact form. You subtract the risk-free rate to get an ERP. It focuses on what companies and the economy can deliver, not on investor demand.

How does the build-up approach differ from CAPM?

CAPM multiplies the equity risk premium by a stock's beta and adds the risk-free rate. The build-up approach starts at the risk-free rate and adds premiums, for example for equity risk, size and company-specific risk, and usually does not use beta. It is common for private or small companies where beta is hard to estimate.

Why do analysts often set the P/E change to zero in the supply-side model?

A P/E ratio cannot rise faster than earnings indefinitely, so analysts usually assume the change is zero or small. Setting it to zero avoids overstating the long-run expected return.