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CFA Level I · CFA Level I Exam

CAPM, Market Model and Factor-Based Equity Models

The CAPM says an asset's expected return equals the risk-free rate plus beta times the market risk premium. The market model, APT, and Fama-French and Carhart models extend this idea with one or more factors. To solve questions, identify the factor loadings, apply the right formula, and compare the result with the required or actual return.

What this chapter covers

This chapter explains how investors link risk to expected return. It starts with the CAPM, where one factor, market risk measured by beta, drives expected return. It then covers how beta is estimated using the market model, a regression of an asset's returns on market returns.

Next come multifactor models. Arbitrage pricing theory (APT) allows several systematic factors and rests on a no-arbitrage argument. Fama-French and Carhart models are practical versions that add size, value and momentum factors. The chapter ends with how these ideas are used: judging performance with risk-adjusted measures, estimating the cost of equity, and building portfolios.

The chapter links to other parts of the paper. Quantitative Methods supplies the regression logic. Portfolio Construction uses beta, the capital market line and the Sharpe ratio. Equities and Corporate Finance use the cost of equity as a discount rate in valuation. Ethics can also touch it, for example when performance is reported in a misleading way.

Questions here are mostly short and formula-driven, which makes them reliable marks if your basics are firm. The same ideas, required return, beta and risk-adjusted performance, appear again in equity valuation, corporate finance and portfolio management, so time spent here pays off in several topics. All 180 questions carry equal weight and there is no penalty for wrong answers, so you should attempt every question, and a clean grasp of the formulas lets you eliminate two options quickly.

The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models: topics in the order to study them

  1. 1CAPM and the Security Market LineEverything else builds on the one-factor idea, so learn the formula, assumptions and SML first.
  2. 2Beta Estimation and Market ModelOnce you know what beta does, learn how it is estimated from a regression slope and what the intercept and R² mean.
  3. 3Multifactor Models: Arbitrage Pricing TheoryAPT generalises CAPM to several factors, so it reads easily after the single-factor case.
  4. 4Fama-French and Carhart Factor ModelsThese are concrete multifactor models, and you can now interpret their size, value and momentum loadings.
  5. 5Performance Evaluation and Risk-Adjusted Return MeasuresMeasures such as the Sharpe ratio, Treynor ratio and Jensen's alpha use CAPM ideas, so they come after the models.
  6. 6Cost of Equity and Portfolio Construction ApplicationsThis topic applies all the models to real decisions, so it works best as the last topic.

How to prepare The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

Work from the single-factor model outward, and practise with numbers at every stage. The chapter is short on theory and heavy on small calculations.

  1. Write the CAPM formula, E(Ri) = Rf + βi × [E(Rm) − Rf], and solve ten required-return questions until it is automatic.
  2. Learn what each regression output means: slope is beta, intercept is the return not explained by the market, and R² is the share of variance explained.
  3. Compare CAPM and APT side by side: one factor versus several, and what each assumes about investors and arbitrage.
  4. For Fama-French and Carhart, memorise the factor names and what a positive or negative loading says about a portfolio's tilt.
  5. Calculate Sharpe, Treynor and Jensen's alpha on one data set, so you see why each ranks portfolios differently. Use your calculator's memory to avoid re-entering numbers.
  6. Finish with mixed MCQs on cost of equity and portfolio use. For each question, run a quick sense check. A clear grasp of the formulas helps you eliminate options quickly. For example, with a positive market risk premium, a required return below the risk-free rate requires a negative beta, and a required return above the risk-free rate requires a positive beta. Check that the sign of beta matches the question before you accept or reject an option.

Common mistakes in The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

  • Using the market return instead of the market risk premium in the CAPM formula.

    Fix: Always subtract Rf from the market return first, then multiply by beta, then add Rf.

  • Mixing up Sharpe and Treynor ratios.

    Fix: Remember Sharpe divides by standard deviation (total risk) and Treynor by beta (systematic risk).

  • Reading the regression intercept as beta, or the slope as alpha.

    Fix: The slope multiplies the market return and is beta. The intercept is alpha.

  • Saying a stock is overvalued when it plots above the SML.

    Fix: Above the SML means expected return exceeds required return, so the asset is undervalued.

  • Treating APT as telling you which factors to use.

    Fix: APT does not name the factors. Fama-French and Carhart are specific models that do.

  • Assuming a positive alpha always proves skill.

    Fix: Check the model used and the risk factors. Alpha from CAPM may just be exposure to size, value or momentum.

Last-day revision: The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

  • CAPM: E(Ri) = Rf + βi × [E(Rm) − Rf].
  • The security market line plots expected return against beta; the market risk premium is E(Rm) − Rf.
  • Beta measures systematic risk only; CAPM gives no reward for unsystematic risk.
  • A security plotting above the SML is undervalued; below it is overvalued.
  • Market model: Ri = α + βi × Rm + error; beta is the regression slope.
  • APT uses several systematic factors and assumes no arbitrage opportunities persist.
  • Fama-French adds size and value factors to the market factor; Carhart adds momentum.
  • Sharpe ratio = (Rp − Rf) ÷ σp, using total risk.
  • Treynor ratio = (Rp − Rf) ÷ βp, using systematic risk.
  • Jensen's alpha = Rp − [Rf + βp × (Rm − Rf)]; it is an absolute return, not a ratio.
  • Use Sharpe for a standalone or whole portfolio. Use Treynor and Jensen's alpha when the portfolio is one component of a larger diversified portfolio.
  • Cost of equity from CAPM is the required return used to discount equity cash flows.

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

The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models in other exams

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

The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models: frequently asked questions

What is the difference between CAPM and the market model?

CAPM is an equilibrium model that gives the required return from beta and the market risk premium. The market model is a statistical regression of an asset's returns on market returns, used to estimate beta and alpha from past data.

Do I need to memorise the Fama-French factors?

Yes, know the factor names and what they represent: market, size, value, and for Carhart, momentum. You should be able to say what a positive or negative loading on each factor means.

Which risk-adjusted measure should I use?

Use the Sharpe ratio when the portfolio is standalone or is the investor's whole portfolio, since it uses total risk. Use the Treynor ratio or Jensen's alpha when the portfolio is one component of a larger diversified portfolio, since they use beta. Note that Treynor is a ratio, while Jensen's alpha is an absolute return, not a ratio.

How should I use my calculator for this chapter?

The BA II Plus or HP 12C handles the arithmetic well, but the formulas are simple enough to do in steps. Use the memory keys to store Rf and the market premium, then compute each required return in a few presses.