FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

CAPM and the Security Market Line for FRM Part I

Updated 11 October 2026 · Fact-checked

CAPM says an asset's required return equals the risk-free rate plus beta times the market risk premium: E(Ri) = Rf + βi × [E(Rm) − Rf]. The security market line plots this against beta. Compare the expected return you are given with the required return. Higher means undervalued, lower means overvalued.

Understand CAPM and the Security Market Line

Investors want compensation for two things: waiting and bearing risk. The risk-free rate pays for waiting. The extra return pays for risk. CAPM says only systematic risk, the part you cannot diversify away, earns that extra return.

Why only systematic risk? Idiosyncratic risk (firm-specific risk) can be removed by holding many assets, so the market does not pay for it. What remains is how much an asset moves with the market portfolio. That sensitivity is beta: β = Cov(Ri, Rm) ÷ Var(Rm) = ρ(i,m) × σi ÷ σm. The market has β = 1. The risk-free asset has β = 0.

The security market line (SML) graphs expected return against beta. Its intercept is Rf and its slope is the market risk premium, E(Rm) − Rf. Any asset priced fairly sits on the line. The SML uses beta on the x-axis. Do not confuse it with the capital market line, which uses standard deviation and applies only to efficient portfolios.

To judge mispricing, compare the expected return you forecast with the CAPM required return. The gap is alpha: α = E(Ri) − [Rf + βi(E(Rm) − Rf)]. Positive alpha plots above the SML, so the asset is undervalued: its price is too low for its risk and it should be bought. Negative alpha plots below the line, so it is overvalued.

CAPM rests on assumptions: investors are rational mean-variance optimisers, have the same single-period horizon and homogeneous expectations, can borrow and lend unlimited amounts at the risk-free rate, are price takers, and face no taxes or transaction costs. All assets are marketable and the market portfolio contains all risky assets. The model is a simplification, and the exam tests the mechanics more than the realism.

Key formulas to remember

CAPM / SML equation: E(Ri) = Rf + βi × [E(Rm) − Rf]; E(Rm) − Rf is the market risk premium. Use the same time basis (annual) for all inputs.
Beta (covariance form): βi = Cov(Ri, Rm) ÷ Var(Rm); Use variance, not standard deviation, in the denominator.
Beta (correlation form): βi = ρ(i,m) × σi ÷ σm; Handy when you are given correlation and volatilities.
Alpha (Jensen's alpha): αi = E(Ri) − [Rf + βi × (E(Rm) − Rf)]; Positive means above the SML (undervalued); negative means below (overvalued).
Portfolio beta: βp = Σ wi × βi; Beta is a weighted average of betas, with weights summing to 1 including any risk-free holding at β = 0.
Systematic variance: Systematic risk = βi² × σm²; Total variance = βi² × σm² + σ²(ε); Under the single-index view, the residual term is idiosyncratic risk.

How to solve CAPM and the Security Market Line questions

Use this order for almost any CAPM or SML question.

1Write down what is given: Rf, market return or premium, beta (or the pieces to compute it), and any forecast return.
2If beta is not given, compute it: Cov(Ri, Rm) ÷ σm², or ρ × σi ÷ σm. If a regression slope is given, that slope is beta.
3Find the market risk premium. If you are given E(Rm), subtract Rf. If you are given the premium, use it directly.
4Compute the required return: Rf + β × premium.
5Compare with the expected (forecast) return. Alpha = expected − required.
6Conclude: alpha > 0 means undervalued (buy), alpha < 0 means overvalued (sell or avoid), alpha = 0 means fairly priced.
7For portfolios, weight the betas first, then apply the SML. Check the answer is sensible, for example a β above 1 should require more than the market return.

Quickest way: Required return in three lines

When to use it: Use for any multiple-choice question that asks for required return, alpha or a mispricing verdict.

Premium = E(Rm) − Rf. Do this subtraction first.
Required = Rf + β × premium. Estimate roughly first: β above 1 means required return above the market return.
Verdict: if forecast return > required, the asset is undervalued. Eliminate options whose sign of alpha contradicts this.

Common mistakes in CAPM and the Security Market Line

Multiplying beta by the market return instead of the market risk premium.
The formula is remembered as Rf + β × Rm.
Fix: Always subtract Rf from E(Rm) first, then multiply by beta.
Using σm instead of σm² in the beta denominator.
Covariance divided by volatility looks natural.
Fix: Beta = Cov ÷ variance. With correlation, use ρ × σi ÷ σm.
Calling an asset overvalued because its expected return is high.
Confusing return with price. Price and expected return move in opposite directions.
Fix: Above the SML means expected return exceeds required, so price is too low: undervalued.
Mixing up the SML and the capital market line.
Both are lines through Rf and the market portfolio.
Fix: SML: beta on the x-axis, any asset. CML: standard deviation on the x-axis, efficient portfolios only.
Expecting idiosyncratic risk to earn a premium.
Thinking higher total volatility must mean higher return.
Fix: Under CAPM only beta is priced. A volatile asset with low beta has a low required return.
Forgetting the risk-free weight when computing portfolio beta.
Focusing only on the risky holdings.
Fix: Include cash at β = 0. Weights must sum to 1.

Worked examples

Example 1

The risk-free rate is 3%, the expected market return is 9%, and Stock A has a beta of 1.4. Analysts forecast a return of 11% for Stock A. What is its required return, its alpha, and is it under- or overvalued?

Show the solution

Market risk premium = 9% − 3% = 6%.
Required return = 3% + 1.4 × 6% = 3% + 8.4% = 11.4%.
Alpha = forecast − required = 11% − 11.4% = −0.4%.
Alpha is negative, so the stock plots below the SML.

Answer: Required return is 11.4%, alpha is −0.4%, so Stock A is slightly overvalued.

Example 2

Stock B has volatility of 30% and a correlation of 0.6 with the market. The market volatility is 20%, Rf is 2%, and the market risk premium is 5%. Stock B's expected return is 8%. Find beta, required return and the verdict.

Show the solution

Beta = ρ × σi ÷ σm = 0.6 × 30% ÷ 20% = 0.6 × 1.5 = 0.9.
Required return = 2% + 0.9 × 5% = 2% + 4.5% = 6.5%.
Alpha = 8% − 6.5% = +1.5%.
Positive alpha means the stock plots above the SML.

Answer: Beta is 0.9, required return is 6.5%, alpha is +1.5%, so Stock B is undervalued.

Exam tips

Questions often hide beta inside covariance, correlation or a regression output. Identify the slope first.
Check units. Variance of 0.04 means volatility of 20%. Convert before using ρ × σi ÷ σm.
Sign of alpha gives the verdict directly. Do not overthink price levels.
Know the assumptions as a list. Conceptual questions ask which assumption, if relaxed, breaks the model, such as unlimited risk-free borrowing or homogeneous expectations.
For a portfolio mixing a risky asset with cash, scale beta by the risky weight.

Practice questions from Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

CAPM and the Security Market Line in other exams

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

CAPM and the Security Market Line: frequently asked questions

What are the main assumptions of CAPM?

Investors are rational mean-variance optimisers with the same single-period horizon and identical expectations. They can borrow and lend unlimited amounts at the risk-free rate, and markets have no taxes or transaction costs. All investors are price takers and hold the market portfolio of risky assets combined with the risk-free asset.

How do I calculate the beta of a stock?

Divide the covariance of the stock's returns with the market's returns by the market variance. Equivalently, multiply the correlation by the stock volatility and divide by the market volatility. It also equals the slope of a regression of stock returns on market returns.

How do I tell if a stock is undervalued using the SML?

Compute the required return from the SML and compare it with the expected return. If expected return is higher, the stock plots above the line and is undervalued. If lower, it plots below the line and is overvalued.

What is the difference between the SML and the CML?

The SML plots expected return against beta and applies to any asset or portfolio. The capital market line plots expected return against standard deviation and applies only to efficient portfolios combining the market portfolio with the risk-free asset.