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CFA Level I Exam · The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

CAPM and the Security Market Line: Required Return and Mispricing

Updated 7 October 2026 · Fact-checked

The Capital Asset Pricing Model says an asset's required return equals the risk-free rate plus beta times the market risk premium. Plot this against beta and you get the security market line. To solve a question, compute the required return, compare it with the expected return, and judge whether the asset is mispriced.

Understand CAPM and the Security Market Line

Investors need a way to decide what return is fair for a risky asset. The Capital Asset Pricing Model (CAPM) answers this. Its key idea: the market pays you only for risk you cannot diversify away.

Total risk splits into two parts. Systematic risk (market risk) comes from economy-wide factors such as interest rates or recessions. It affects all assets and cannot be removed by diversification. Unsystematic risk (firm-specific risk) comes from events at one company, such as a product recall. A well-diversified portfolio largely eliminates it, so the market does not reward it.

Beta measures an asset's sensitivity to the market. A beta of 1 means the asset moves with the market on average. Above 1, it amplifies market moves. Below 1, it dampens them. Beta = Cov(asset, market) ÷ Var(market), which also equals correlation × (asset standard deviation ÷ market standard deviation).

The security market line (SML) plots required return (vertical axis) against beta (horizontal axis). Its intercept is the risk-free rate and its slope is the market risk premium. An asset whose expected return plots above the line is undervalued (offers more than required). Below the line, it is overvalued.

CAPM rests on assumptions: investors are risk-averse, mean-variance optimizers, use a single period, share homogeneous expectations, can borrow and lend at the risk-free rate, and markets are frictionless (no taxes or transaction costs) with all assets marketable. Do not confuse the SML with the capital market line (CML). The CML plots return against total risk (standard deviation) and applies only to efficient portfolios. The SML plots return against beta and applies to any asset or portfolio.

Key formulas to remember

CAPM required return
E(Ri) = Rf + βi × [E(Rm) − Rf]
[E(Rm) − Rf] is the market risk premium. This is the SML equation.
Beta
βi = Cov(Ri, Rm) ÷ Var(Rm) = ρi,m × σi ÷ σm
Beta of the market is 1. Beta of the risk-free asset is 0.
Portfolio beta
βp = Σ wi × βi
Weights are market-value weights and sum to 1 (include the risk-free asset at beta 0).
Capital market line
E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp
Uses total risk σ and applies to efficient portfolios only.
Mispricing test (alpha)
α = E(R) − required return from CAPM
α > 0: undervalued, above the SML. α < 0: overvalued, below the SML.

How to solve CAPM and the Security Market Line questions

Use this method for any CAPM or SML question.

  1. 1Identify the inputs: risk-free rate, expected market return or market risk premium, and beta.
  2. 2Check whether the question gives the market return or the premium. If it gives the market return, subtract Rf to get the premium.
  3. 3If beta is not given, compute it from covariance ÷ market variance, or correlation × σi ÷ σm.
  4. 4Compute required return = Rf + β × premium. Keep percentages as decimals in the calculation.
  5. 5If the question gives an expected (forecast) return, compute alpha = expected − required.
  6. 6Decide: positive alpha means undervalued (buy); negative means overvalued; zero means fairly priced.
  7. 7Match your answer to the three options. Check that the value is sensible: beta above 1 must give required return above the market return.

Quickest way: Premium first, then add Rf

When to use it: Use for any numerical CAPM question when time is short, typically at 90 seconds per item.

  1. Write the premium (Rm − Rf) first. Many stems give Rm, not the premium.
  2. Multiply beta by the premium in your head or on the calculator.
  3. Add Rf last.
  4. For mispricing, compare expected and required returns only. Ignore price levels.
  5. Eliminate options that break logic: for beta > 1 the answer must exceed Rm; for 0 ≤ beta < 1 it must lie between Rf and Rm; for a negative beta it must be below Rf.

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 Rm first. Required return = Rf + β(Rm − Rf).

  • Confusing the SML with the CML.

    Both are lines starting at the risk-free rate.

    Fix: SML: x-axis is beta, applies to any asset. CML: x-axis is standard deviation, applies only to efficient portfolios.

  • Saying total risk is rewarded.

    Students link higher standard deviation with higher return.

    Fix: Only systematic risk is priced. An asset with high unsystematic risk but low beta has a low required return.

  • Reading mispricing backwards.

    Students think a high expected return means the stock is expensive.

    Fix: Expected return above the SML means the price is too low (undervalued). Below the line means overvalued.

  • Using percentages inconsistently, such as entering 6 for the premium and 0.03 for Rf.

    Mixing formats under time pressure.

    Fix: Convert everything to decimals or everything to percent before calculating.

Worked examples

Example 1

The risk-free rate is 3%, the expected market return is 9%, and a stock has a beta of 1.4. What is the stock's required return under CAPM? Options: (A) 10.4%; (B) 11.4%; (C) 12.6%.

Show the solution
  1. Market risk premium = 9% − 3% = 6%.
  2. Required return = 3% + 1.4 × 6% = 3% + 8.4% = 11.4%.
  3. Check with logic: beta is above 1, so the answer must exceed the 9% market return. 11.4% does.
  4. Option (C), 12.6%, comes from 1.4 × 9%, which multiplies beta by the market return instead of the premium.

Answer: (B) 11.4%.

Example 2

A stock has a correlation of 0.60 with the market. The stock's standard deviation is 30% and the market's is 20%. The risk-free rate is 2% and the market risk premium is 5%. What is the stock's required return? Options: (A) 6.5%; (B) 6.7%; (C) 11.0%.

Show the solution
  1. Beta = ρ × σi ÷ σm = 0.60 × 30% ÷ 20% = 0.60 × 1.5 = 0.90.
  2. Required return = Rf + β × premium = 2% + 0.90 × 5%.
  3. 0.90 × 5% = 4.5%.
  4. Required return = 2% + 4.5% = 6.5%.

Answer: (A) 6.5%. Beta = 0.90.

Exam tips

  • Questions often hide beta inside correlation and standard deviations. Compute beta first.
  • Know the CAPM assumptions as a list, and expect a question asking which assumption is unrealistic or what happens if it is relaxed.
  • For mispricing items, compare expected and required returns only. Do not worry about the price level.
  • Use logic to eliminate: for 0 ≤ beta < 1 the required return lies between Rf and the market return; beta of 0 means required return equals Rf; a negative beta means required return below Rf.
  • For SML versus CML items, check the axis: beta means SML, standard deviation means CML.

Practice questions from The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

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 is the difference between the CML and the SML?

The CML plots expected return against total risk (standard deviation) and applies only to efficient portfolios. The SML plots required return against beta and applies to any asset or portfolio. Both start at the risk-free rate.

Why is unsystematic risk not rewarded in CAPM?

Investors can remove it by diversifying. Since it is avoidable, the market does not pay extra return for bearing it. Only systematic risk, measured by beta, earns a premium.

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

Compute the required return with CAPM and compare it with the expected return. If expected is higher, the security plots above the SML and is undervalued. If lower, it is overvalued.

Can beta be negative?

Yes. A negative beta means the asset tends to move opposite to the market. Under CAPM its required return would be below the risk-free rate, because it reduces portfolio risk.