Fama-French 3-Factor Model Calculator
Run the Fama-French 3-factor model in seconds: expected return from the market, size and value factors - free, with formula, betas and an example.
Also available in German: Fama-French-Dreifaktorenmodell Rechner →
Inputs
Risk-free rate
Also called: Rf
Where to find it: Yield on 10-year government bonds (Bund, US Treasury).
How to derive: Use the current 10-year government bond yield.
Factor beta (market / SMB / HML)
Also called: Factor loading
Where to find it: From a factor regression — or as an assumption.
How to derive: Market beta ≈ 1; SMB (size) >0 = small-cap tilt; HML (value) >0 = value tilt.
Market risk premium
Also called: Equity risk premium
Where to find it: Long-run estimate (Damodaran publishes it yearly).
How to derive: Expected market return − risk-free rate. Typically 4.5–6%.
Factor beta (market / SMB / HML)
Also called: Factor loading
Where to find it: From a factor regression — or as an assumption.
How to derive: Market beta ≈ 1; SMB (size) >0 = small-cap tilt; HML (value) >0 = value tilt.
Factor premium (SMB / HML)
Also called: Factor premium
Where to find it: Long-run research estimates (Fama-French).
How to derive: SMB (size) ~2%, HML (value) ~3% p.a. — extra return of small / cheap stocks.
Factor beta (market / SMB / HML)
Also called: Factor loading
Where to find it: From a factor regression — or as an assumption.
How to derive: Market beta ≈ 1; SMB (size) >0 = small-cap tilt; HML (value) >0 = value tilt.
Factor premium (SMB / HML)
Also called: Factor premium
Where to find it: Long-run research estimates (Fama-French).
How to derive: SMB (size) ~2%, HML (value) ~3% p.a. — extra return of small / cheap stocks.
Result, live
Small value firms historically carry higher expected returns (= more risk = a higher discount rate!). Typical premiums: market 5–6%, SMB ~2%, HML ~3%.
The Fama-French 3-factor model extends the classic CAPM with two extra sources of risk: company size and value. Instead of the market alone, expected return is built from three factors. This calculator shows you the result in seconds.
How the formula works
Three risk premiums are added to the risk-free rate, each weighted by its own beta: the market, the size factor (SMB, small vs. large firms) and the value factor (HML, cheap vs. expensive):
Example: 4% + 1×5.5% + 0.3×2% + 0.2×3% = 10.7%. Plain CAPM would give 9.5% — so size and value add 1.2 points.
How to read the result
The expected return is also the discount rate you would use to bring future cash flows to today. The factor premium versus CAPM reveals the character:
- Clearly positive — strong small/value tilt: higher expected return, but also higher risk.
- Near zero — behaves like the broad market; plain CAPM is enough.
- Negative — large/growth tilt: lower expected return.
What to watch out for
- Premiums are historical averages, not a guarantee — SMB and HML have had multi-year dry spells.
- Betas must be estimated (regression on past data); noisy betas distort the result.
- Higher expected return = higher risk, not a free extra return.
Example portfolios: three factor profiles
Typical factor loadings in practice (illustrative betas; market premium 5%, size premium 2%, value premium 3%):
- Broad market fund: β market ≈ 1.0 · β SMB ≈ 0 · β HML ≈ 0 → expected excess return ≈ 5%. The model collapses to the CAPM.
- Small-value portfolio: β market ≈ 1.0 · β SMB ≈ 0.7 · β HML ≈ 0.6 → ≈ 5% + 1.4% + 1.8% = 8.2%. The extra factors explain why small value stocks historically returned more — with bigger swings.
- Large-growth portfolio: β market ≈ 1.05 · β SMB ≈ −0.2 · β HML ≈ −0.4 → ≈ 5.25% − 0.4% − 1.2% = 3.65%. Negative loadings compress the expected premium of large growth names.
Punch the three profiles into the calculator above and vary the premia — you will instantly see which factor really drives your portfolio.
Where do betas and factor premia come from?
Factor premia: the academic reference is Kenneth French’s freely available Data Library (Dartmouth) with historical monthly returns for market, SMB and HML. Long-run anchors: market 5–6%, size ~2%, value ~3% p.a. — with large swings between decades.
Factor betas: come from regressing portfolio returns on the three factor series. In practice, fund factsheets often report factor exposures directly; for single stocks you can roughly read size and value loadings off market cap and price-to-book (small + cheap = positive SMB/HML loading).
Remember: the model explains portfolio returns far better than single stocks — for the fair value of an individual share, a multi-model approach like our Fair Value Calculator is the better tool.