FRM Exam Part II · Factor Theory

Style Factors: Value, Size, Momentum and Others

Updated 11 October 2026 · Fact-checked

Style factors are stock characteristics, such as value, size, momentum, quality and low volatility, that have historically earned returns not explained by market beta. Each is built as a long-short portfolio. To solve exam questions, identify the factor, read the sign of its return, and decide whether the explanation is risk-based or behavioral.

Understand Style Factors: Value, Size, Momentum and Others

The CAPM says one factor, market beta, explains expected returns. Empirical work found that stocks sharing certain characteristics earned average returns the CAPM could not explain. These characteristics are called style factors. The long-short portfolio that captures each one is its factor return.

The main ones are: Value: cheap stocks (high book-to-market) beat expensive ones. Size: small-cap stocks beat large-cap stocks. Momentum: recent winners (usually past 12 months, skipping the latest month) beat recent losers. Quality (profitable, stable firms) and low volatility (low-risk stocks) are other common ones.

In the Fama-French three-factor model, a stock's excess return is explained by market excess return, SMB (small minus big) and HML (high minus low book-to-market). A positive HML loading means the stock behaves like a value stock. A negative HML loading means it behaves like a growth stock. A positive SMB loading means it behaves like a small-cap stock. Adding momentum (often called UMD or WML) gives the four-factor model.

Why do the premiums exist? The risk-based view says the premium is compensation for bearing risk that investors dislike, for example value firms are more exposed to distress or bad economic states. The behavioral view says investors make systematic errors: extrapolating past growth, under-reacting to news, or herding, which creates mispricing. Limits to arbitrage, such as costs and short-sale constraints, let the mispricing persist. A third view is that some premiums are data-mined and may not persist.

Momentum has a distinctive risk: momentum crashes. Momentum has negative skewness. After market declines followed by sharp rebounds, losers (often high-beta stocks) rally hard, so the long-short portfolio suffers large losses. This is why a positive average premium can come with severe tail risk.

Key formulas to remember

Fama-French three-factor model: Rᵢ − R_f = αᵢ + βᵢ(R_m − R_f) + sᵢ·SMB + hᵢ·HML + εᵢ; s and h are loadings on size and value. Alpha is the return left unexplained.
SMB: SMB = return of small-cap portfolio − return of large-cap portfolio; Positive SMB means small caps outperformed large caps in that period.
HML: HML = return of high book-to-market (value) portfolio − return of low book-to-market (growth) portfolio; Positive HML means value beat growth.
Four-factor (Carhart) model: Rᵢ − R_f = αᵢ + βᵢ(R_m − R_f) + sᵢ·SMB + hᵢ·HML + mᵢ·MOM + εᵢ; MOM is the winners-minus-losers return.
Expected excess return from factors: E[Rᵢ] − R_f = βᵢ·λ_m + sᵢ·λ_SMB + hᵢ·λ_HML; λ is the factor premium; multiply each loading by its premium and add.

How to solve Style Factors: Value, Size, Momentum and Others questions

Use this sequence for most style-factor questions, whether numeric or conceptual.

1Identify which factor or factors the question refers to: value, size, momentum, quality or low volatility.
2Recall how the factor is built: long what, short what. This fixes the sign of the loading.
3For a regression question, read each loading: sign tells the tilt, size tells the strength.
4For a numeric question, multiply each loading by its factor premium or return and add them. Include the market term and alpha only if given.
5For an explanation question, classify it: compensation for risk (risk-based) or investor error with limits to arbitrage (behavioral).
6For a risk question, check skewness and crash behavior, especially for momentum.
7Check that the conclusion matches the sign and the wording, such as 'explained' versus 'unexplained' return.

Quickest way: Sign-and-sum shortcut

When to use it: Use for MCQs giving factor loadings and premiums, or asking you to classify an explanation.

Name the factor as 'long minus short' and fix the sign.
Multiply loading × premium for each factor and sum them.
For explanation wording, 'compensation for bearing risk' means risk-based. 'Over-extrapolation, under-reaction, herding' means behavioral.
If momentum is mentioned with losses, think crash after market rebound.

Common mistakes in Style Factors: Value, Size, Momentum and Others

Reading a negative HML loading as 'poor performance'.
Students treat the sign as good or bad.
Fix: A negative loading means growth-like exposure. Performance depends on whether HML was positive or negative in the period.
Confusing SMB direction.
The name 'small minus big' is easy to reverse.
Fix: SMB is small minus big. Positive SMB means small caps beat large caps.
Saying value stocks have high price-to-book.
Mixing up book-to-market and market-to-book.
Fix: Value means high book-to-market, which is low price-to-book.
Claiming the risk-based view proves the premium is risk-free profit or that the behavioral view proves it is arbitrage.
Overstating either theory.
Fix: Risk-based: premium compensates for risk. Behavioral: mispricing persists because arbitrage is limited and costly.
Ignoring momentum crash risk because the average premium is positive.
Focusing on mean return rather than tail behavior.
Fix: Remember negative skewness and losses when markets rebound sharply after declines.
Adding alpha into the expected return from factors.
Treating regression alpha as a premium.
Fix: Expected return from factors uses loadings × premiums. Alpha is the unexplained part.

Worked examples

Example 1

A fund's three-factor regression gives β = 1.10, s = 0.40, h = −0.30. Assume a market premium of 5%, SMB premium of 2% and HML premium of 3% per year, and a risk-free rate of 4%. What is the factor-implied expected return?

Show the solution

Market term: 1.10 × 5% = 5.50%.
Size term: 0.40 × 2% = 0.80%.
Value term: −0.30 × 3% = −0.90%.
Sum of premiums: 5.50 + 0.80 − 0.90 = 5.40%.
Add risk-free rate: 4% + 5.40% = 9.40%.

Answer: 9.40% per year. The fund tilts to small caps and growth, and the growth tilt reduces expected return.

Example 2

A long-short momentum strategy has earned strong average returns for years but lost heavily in the months after a sharp market fall when the market rebounded. Which explanation best fits, and what does this show about momentum?

Show the solution

Momentum goes long past winners and short past losers.
After a market decline, the losers are often high-beta stocks.
In a sharp rebound those losers rise strongly, so the short leg loses a lot.
This produces large negative returns in rare periods, meaning negative skewness.
So the high average return comes with crash risk in the left tail.

Answer: This is a momentum crash: momentum has negative skewness, and its losses concentrate in market rebounds after declines. Average premium alone understates its tail risk.

Exam tips

Memorize the construction of each factor as long minus short so signs are automatic.
Expect questions that ask you to classify an explanation as risk-based or behavioral.
For regression output, interpret the sign of each loading before doing any arithmetic.
Link momentum to tail risk and skewness, not just to average return.
Do not say a premium is guaranteed to persist; evidence is historical.

Practice questions from Factor Theory

Style Factors: Value, Size, Momentum and Others: frequently asked questions

What do HML and SMB mean in the Fama-French model?

HML is the return of high book-to-market (value) stocks minus low book-to-market (growth) stocks. SMB is the return of small-cap stocks minus large-cap stocks. Their loadings show how much a portfolio tilts to value or size.

What is the difference between risk-based and behavioral explanations of factor premiums?

The risk-based view says a premium rewards investors for bearing risk, such as distress or bad economic states. The behavioral view says it comes from investor biases that create mispricing. Limits to arbitrage explain why the mispricing can last.

Why does momentum crash?

Momentum is long recent winners and short recent losers. After a market fall and sharp rebound, the losers often rally strongly, so the strategy loses heavily. This gives momentum negative skewness.

Is momentum part of the Fama-French three-factor model?

No. The three-factor model has market, SMB and HML. Momentum is added in the Carhart four-factor model.