FRM Exam Part II · Factors

Factor Theory and the CAPM for FRM Part II

Updated 11 October 2026 · Fact-checked

Factor theory says asset returns are driven by exposure to a few common sources of risk, not by each asset alone. The CAPM uses one factor, the market. Multifactor models add more factors. Factors earn risk premiums because investors demand compensation for bearing risk they cannot diversify away and that hurts in bad times.

Understand Factor Theory and the CAPM

Start with a simple question: why do some assets earn higher average returns than others? The CAPM gave the first answer. Only systematic risk is rewarded, and it is measured by beta, the sensitivity of an asset to the market portfolio. Risk that is specific to one firm can be diversified away, so the market does not pay you for holding it.

The CAPM says expected excess return equals beta times the market risk premium. All assets sit on one line, the security market line. Alpha is the return left over after you account for market beta. In CAPM terms, a positive alpha means the asset earned more than its beta justified.

Empirical work found patterns the CAPM could not explain. Small firms, cheap (value) stocks and recent winners (momentum) earned more than their market betas implied. This led to multifactor models. Here, returns depend on exposures to several factors, each with its own risk premium. The Fama-French models are the standard example: market, size and value, and later extensions. In the language of factor theory, the CAPM is a special case with one factor.

Why does a factor earn a premium? There are three broad explanations. Risk-based: the factor does badly in bad times, such as recessions, so investors need compensation. Behavioral: investors make systematic errors, and the premium is a mispricing that persists. Structural or institutional: constraints, such as limits on leverage or mandates, stop investors from arbitraging it away. A premium is not guaranteed. A factor can go through long periods of poor returns.

The key link: a factor premium is compensation for exposure to a risk that cannot be diversified away. Diversification removes idiosyncratic risk. It does not remove factor risk.

Key formulas to remember

CAPM expected return: E(Ri) = Rf + βi × [E(Rm) − Rf]; Only market beta is priced. [E(Rm) − Rf] is the market risk premium.
Beta: βi = Cov(Ri, Rm) ÷ Var(Rm) = ρ(i,m) × σi ÷ σm; Measures systematic risk relative to the market.
Jensen's alpha: αi = Ri − [Rf + βi × (Rm − Rf)]; Realized excess return not explained by market beta.
Multifactor model: E(Ri) = Rf + βi1 × λ1 + βi2 × λ2 + … + βik × λk; Each λ is the risk premium of factor k. βik is the exposure to that factor.
Factor return decomposition: Ri − Rf = α + Σ βik × Fk + εi; Fk are factor returns. εi is idiosyncratic and diversifiable.

How to solve Factor Theory and the CAPM questions

Use this approach for calculation and concept questions on factor theory.

1Identify the model in the question: CAPM (one factor) or multifactor.
2List the inputs: risk-free rate, betas or factor exposures, and factor premiums. Check that premiums are excess returns.
3Compute the expected return by multiplying each exposure by its premium, summing, and adding the risk-free rate.
4If realized return is given, subtract the expected return to get alpha.
5Separate systematic risk (factor exposures) from idiosyncratic risk (residual). Only systematic risk earns a premium.
6For why-questions, classify the explanation as risk-based, behavioral or structural.
7Check the answer for sign and size before choosing an option.

Quickest way: Sum of beta times premium

When to use it: Use when a question gives betas and factor premiums and asks for expected return or alpha.

Write Rf first.
Multiply each beta by its premium in percent and add them.
Add Rf to the total to get expected return.
Alpha is actual return minus this number.
Eliminate options that treat idiosyncratic risk as priced.

Common mistakes in Factor Theory and the CAPM

Using total return instead of excess return for factor premiums.
Premiums are often quoted loosely.
Fix: Confirm whether a premium is already net of Rf. Add Rf only once.
Saying the CAPM rewards total volatility.
Students confuse standard deviation with beta.
Fix: Only market beta is priced in the CAPM. Idiosyncratic risk is diversifiable and unpriced.
Calling alpha a risk premium for any factor.
Alpha is defined relative to a model.
Fix: Alpha depends on the model. A CAPM alpha can vanish once size or value factors are added.
Assuming factor premiums are guaranteed.
Long-run averages look stable.
Fix: Premiums can be negative for long periods. Risk-based factors carry bad-time losses.
Treating all premium explanations as risk-based.
Textbook focus on rational models.
Fix: Remember behavioral and structural explanations. Identify which one the question describes.

Worked examples

Example 1

The risk-free rate is 3%. The market risk premium is 6%. A stock has a market beta of 1.2. Using the CAPM, what is its expected return?

Show the solution

E(Ri) = Rf + β × market premium.
= 3% + 1.2 × 6%.
1.2 × 6% = 7.2%.
3% + 7.2% = 10.2%.

Answer: 10.2%

Example 2

Rf = 2%. A fund has exposures of 1.0 to the market, 0.5 to size and 0.3 to value. Factor premiums are 5%, 2% and 4% respectively. The fund earned 10% last year. What is its alpha?

Show the solution

Expected return = 2% + 1.0 × 5% + 0.5 × 2% + 0.3 × 4%.
= 2% + 5% + 1% + 1.2% = 9.2%.
Alpha = actual − expected = 10% − 9.2% = 0.8%.

Answer: Alpha is 0.8%.

Exam tips

Read whether the question asks for a CAPM answer or a multifactor answer. The model changes the alpha.
Expect conceptual questions that ask why a factor earns a premium. Match the story to risk-based, behavioral or structural.
Check that premiums are excess returns before adding the risk-free rate.
Remember that idiosyncratic risk is never priced in either model.

Practice questions from Factors

Factor Theory and the CAPM in other exams

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

Factor Theory and the CAPM: frequently asked questions

What is the difference between the CAPM and multifactor models?

The CAPM has one priced factor, the market, measured by beta. Multifactor models have several priced factors, each with its own exposure and premium. The CAPM is a one-factor special case.

Why do factors earn risk premiums?

Risk-based theory says a factor pays off poorly in bad times, so investors need compensation. Behavioral theory says investors make persistent errors. Structural theory says constraints limit arbitrage.

Does a positive alpha always mean skill?

No. Alpha is measured against a model. If the model omits a factor, the alpha may be a factor premium. Adding the missing factor can remove it.

Is idiosyncratic risk rewarded?

No. Diversification removes it, so the market does not pay for it in either the CAPM or multifactor models.