Factor Inputs

Factor Premiums
%
Annualized risk-free rate (e.g., T-bill yield)
%
E(RM) - Rf, already excess over risk-free
%
Illustrative default ~2-3% (Ken French Data Library)
%
Illustrative default ~3-5% (Ken French Data Library)
%
Profitability factor premium (~3%)
%
Investment factor premium (~2-3%)
Factor Loadings (Betas)
Sensitivity to market excess returns
Positive = small-cap, negative = large-cap
Positive = value, negative = growth
Sensitivity to profitability factor
Sensitivity to investment factor
%
Enter to compute single-period abnormal return
Fama-French Formula
E(Ri) = Rf + βM(RM - Rf) + βSMB·SMB + βHML·HML
Rf = Risk-free rate | βM = Market beta | SMB = Size premium | HML = Value premium
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Expected Return

Expected Return E(Ri) 11.9000% Small-Cap Value
Expected Excess Return 7.9000%
Risk-Free 4.0000%
Market 6.0000%
Size (SMB) 1.0000%
Value (HML) 0.9000%
Profitability (RMW) 0.0000%
Investment (CMA) 0.0000%

Formula Breakdown

E(Ri) = Rf + βM·MRP + βSMB·SMB + βHML·HML
Step-by-step factor contribution breakdown

Factor Profile Interpretation

Factor Positive Loading Negative Loading
Market (βM) Aggressive (high market risk) Defensive (low market risk)
SMB (βSMB) Small-cap tilt Large-cap tilt
HML (βHML) Value tilt Growth tilt
When to Use This Calculator

Use the Fama-French Calculator when you need multi-factor asset pricing that accounts for size and value effects beyond market beta alone.

Use the CAPM Calculator for single-factor (market beta only) expected return estimates.

The Fama-French model explains cross-sectional return differences better than CAPM by capturing size and value premiums (BKM Ch 10.5).

Understanding the Fama-French Model

What is the Fama-French Three-Factor Model?

The Fama-French three-factor model is an asset pricing model developed by Eugene Fama and Kenneth French in 1993. It extends the Capital Asset Pricing Model (CAPM) by adding two factors beyond market risk: a size factor (SMB) capturing the historical outperformance of small-cap stocks, and a value factor (HML) capturing the outperformance of high book-to-market (value) stocks.

Expected Return (Pricing Form)
E(Ri) = Rf + βM(E(RM) - Rf) + βSMB·E(SMB) + βHML·E(HML)
BKM Note: BKM Eq 10.9 presents the realized-return regression form: Ri - Rf = αi + βM(RM - Rf) + βSMB·SMB + βHML·HML + εi. This calculator uses the expected-return pricing form, which sets α = 0 and takes expectations. Both forms share the same factor loadings.

The Three Factors

SMB (Small Minus Big)

Size premium
Return difference between small-cap and large-cap stock portfolios. Small firms historically earn higher returns, possibly due to greater vulnerability to business deterioration and limited capital access.

HML (High Minus Low)

Value premium
Return difference between high book-to-market (value) and low book-to-market (growth) stocks. Value stocks historically outperform, possibly because high B/M signals financial distress risk.

Five-Factor Extension (2015)

The five-factor model adds two more factors:

  • RMW (Robust Minus Weak): Profitability premium. Firms with high operating profitability tend to earn higher returns.
  • CMA (Conservative Minus Aggressive): Investment premium. Firms that invest conservatively (low asset growth) tend to earn higher returns than aggressive investors.

Model Assumptions

  • Factor returns (SMB, HML, RMW, CMA) are exogenous and specified by the user
  • Linear factor model — no interaction effects between factors
  • Factor premiums are assumed constant (user provides point estimates)
  • Does not account for liquidity risk, momentum, or other factors outside the specified model
  • Based on Fama-French empirical factor definitions (portfolio sorts by size and book-to-market)
  • All inputs assumed annualized on the same basis — no mixed-frequency adjustment
  • Default factor premiums are illustrative; actual premiums are time-varying and regime-dependent (source: Ken French Data Library)
  • For educational purposes. Not financial advice. Market conventions simplified.

Related Resources

Frequently Asked Questions

The Fama-French three-factor model is an asset pricing model developed by Eugene Fama and Kenneth French in 1993. It extends the Capital Asset Pricing Model (CAPM) by adding two additional factors beyond market risk: a size factor (SMB, Small Minus Big) and a value factor (HML, High Minus Low book-to-market). The model explains approximately 90% of diversified portfolio return variation, compared to about 70% for CAPM alone.

SMB (Small Minus Big) captures the size premium: the historical tendency of small-cap stocks to outperform large-cap stocks. It is calculated as the return difference between portfolios of small and large stocks. HML (High Minus Low) captures the value premium: the tendency of high book-to-market (value) stocks to outperform low book-to-market (growth) stocks. Both factors are empirical and their premiums are time-varying. Historical factor data is available from the Ken French Data Library at Dartmouth College.

CAPM uses a single factor (market beta) to explain expected returns, while the Fama-French three-factor model adds size (SMB) and value (HML) exposures beyond market beta. This captures cross-sectional return differences that CAPM cannot explain, such as the size and value premiums. The five-factor extension further adds profitability (RMW) and investment (CMA) factors for even broader coverage of return patterns.

The Fama-French five-factor model, introduced in 2015, extends the three-factor model by adding two additional factors: RMW (Robust Minus Weak), which captures the profitability premium — firms with high operating profitability tend to earn higher returns — and CMA (Conservative Minus Aggressive), which captures the investment premium — firms that invest conservatively tend to outperform aggressive investors. The five-factor model provides a more comprehensive explanation of cross-sectional stock returns.

The primary source for Fama-French factor data is the Ken French Data Library, hosted at Dartmouth College. It provides daily, weekly, and monthly factor returns for U.S. and international markets. The data includes the market factor (Mkt-RF), SMB, HML, RMW, CMA, and the risk-free rate. The data is updated regularly and freely available for academic and research purposes.

A negative factor loading indicates inverse sensitivity to that factor. For example, a negative HML beta means the asset behaves like a growth stock (low book-to-market), moving opposite to the value factor. A negative SMB beta indicates large-cap exposure. Negative loadings are common and valid — they reduce the expected return contribution from that factor when the factor premium is positive.
Disclaimer

This calculator is for educational purposes only. Factor premiums are illustrative defaults; actual premiums are time-varying and regime-dependent. The abnormal return shown is a single-period comparison, not a regression-estimated alpha. This tool should not be used for investment decisions without professional consultation.

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Course by Ryan O'Connell, CFA, FRM

Portfolio Analytics & Risk Management Course

Master portfolio theory and risk management from fundamentals to advanced analytics. Covers modern portfolio theory, risk metrics, performance evaluation, and factor models.

  • Sharpe, Sortino, Treynor & Information Ratio deep dives
  • Modern Portfolio Theory and efficient frontier construction
  • Factor models including CAPM and Fama-French
  • Hands-on exercises with real portfolio data
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