FINM7008 Chap.12 Fama-French Factors, Momentum and Fund Benchmarks
Fama-French Factors, Momentum and Fund Benchmarks
Factors from anomalies
When the one-factor model left significant alphas, such as on high book-to-market portfolios, Fama and French added size and value factors.
This chapter shows how SMB and HML are built from six sorted portfolios.
Benchmarks and their limits
It then shows how changing the benchmark changes a fund's alpha, introduces momentum and the Carhart four-factor model, and sets out the blind spots of the three-factor model.
Reading factor betas
Each factor beta is the covariance of a return with the factor divided by the factor's variance.
Small firms tend to have positive SMB betas and big firms negative ones; value firms load positively on HML and growth firms negatively; past winners load positively on momentum. A fund's betas therefore describe its style before any alpha is judged.
What this chapter covers
- 01
Cross-section versus time-series prediction
- 02
Alphas as anomalies
- 03
The three-factor model
- 04
Building SMB and HML
- 05
Factor loadings of small, big, value and growth firms
- 06
Benchmarks that change rankings
- 07
Momentum and the Carhart model
- 08
Blind spots of the factors
Worked example · free
Building the size and value factors from six portfolios
- 1SMB: (0.6 + 1.0 + 1.4)/3 − (0.5 + 0.7 + 0.9)/3 = 1.0 − 0.7 = 0.3%.
- 1HML: (1.4 + 0.9)/2 − (0.6 + 0.5)/2 = 1.15 − 0.55 = 0.6%.
Key terms
- Anomaly
- A return pattern that a pricing model fails to explain, showing up as a significant alpha.
- Size Factor
- The return on small-firm portfolios minus the return on big-firm portfolios, written SMB.
- Value Factor
- The return on high book-to-market portfolios minus low book-to-market portfolios, written HML.
- Momentum Factor
- The return on past-winner portfolios minus past-loser portfolios, written MOM.
- Benchmark Model
- The pricing model whose fair returns are used to measure a fund's alpha.
- Book-to-Market Ratio
- A firm's book equity divided by its market value, high for value firms and low for growth firms.
- Carhart Four-Factor Model
- The Fama-French three-factor model extended with a momentum factor, published in 1997.
Fama-French Factors, Momentum and Fund Benchmarks FAQ
Why did Fama and French add size and value factors?
Research in the 1980s found significant CAPM alphas for some portfolios, notably those of high book-to-market stocks. Adding factors for size and value in 1993 explained those alphas, so the three-factor model fitted the data better than the CAPM.
Can a fund look good under the CAPM and poor under three factors?
Yes. If a fund loads heavily on the value or size factor, the CAPM counts the factor's premium as alpha, while the three-factor model prices it as compensation. The same record can then show a positive alpha under one benchmark and a negative alpha under the other.
What are the main weaknesses of the three-factor model?
It lacks an accepted economic explanation of the risks behind SMB and HML, its patterns need not persist, as the poor value returns since the early 2000s show, and it cannot explain momentum or profitability effects.
How is the momentum factor built?
Stocks are sorted on their past returns into winners and losers within small and big firms. MOM is half of the small-winner and big-winner returns minus half of the small-loser and big-loser returns, and Carhart's 1997 model adds it to the three Fama-French factors.
What is the difference between cross-sectional and time-series prediction?
Time-series prediction asks whether the whole market will rise or fall next month. Cross-sectional prediction asks why one stock will outperform another regardless of the market's direction, which is where active managers seek returns and academics test pricing models.
Has the value factor kept working?
Not recently. The lecture notes that the value factor has performed poorly since the early 2000s, with growth funds beating value funds over the past 20 years, which reverses the historical pattern and shows that a factor found in past data need not persist.
Exam move
Draw the two by three sort and build SMB, HML and MOM from made-up returns. Then rank two funds under the CAPM and under three factors, and explain in one sentence why the ranking changes. Then list the three blind spots of the three-factor model in your own words. Keep the dates straight as well: the three-factor model of 1993, the momentum evidence of the 1990s and Carhart's four-factor model of 1997.
Working through Fama-French Factors, Momentum and Fund Benchmarks in FINM7008? Sia is AskSia’s AI Finance tutor — ask any FINM7008 Fama-French Factors, Momentum and Fund Benchmarks question and get a clear, step-by-step explanation grounded in how FINM7008 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
FINM7006 Applied Foundations of Finance · FINM8007 International Finance · STAT7055 Introductory Statistics for Business and Finance
