Fama-French Model: Three & Five Factor Models Explained 2026

What Is the Fama-French Model?

The Fama-French model is a multi-factor asset pricing model that extends the Capital Asset Pricing Model (CAPM) by adding size and value factors to the single market factor. Developed by economists Eugene Fama and Kenneth French, it provides a significantly better explanation of why different stocks earn different returns over time. In its original three-factor form, the model captures roughly 90% of the variation in diversified portfolio returns - a substantial improvement over the CAPM's roughly 70%.

The CAPM says that the only thing that matters for a stock's expected return is its sensitivity to the overall market. Fama and French showed this isn't enough. Small companies tend to outperform large ones, and cheap (high book-to-market) stocks tend to outperform expensive (low book-to-market) ones - even after accounting for market risk. Their model formalises these observations into a framework that's become the standard benchmark in academic finance and professional portfolio management.

In 2015, Fama and French expanded the model to five factors, adding profitability and investment patterns. The fama french five factor model is now the default tool for evaluating whether a fund manager generates genuine alpha or is simply harvesting known risk premiums. If you're working in quant finance, studying factor investing, or trying to understand what drives portfolio returns, the Fama-French framework is foundational.

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The Fama-French Three-Factor Model

The fama french three factor model, published in Fama and French's landmark 1993 paper "Common Risk Factors in the Returns on Stocks and Bonds," explains expected stock returns as a function of three systematic risk factors: the market, size, and value.

The model is expressed as:

E(Ri) - Rf = βi(Rm - Rf) + si(SMB) + hi(HML)

Where:

• E(Ri) - Rf is the expected excess return of stock or portfolio i over the risk-free rate
• Rm - Rf is the market risk premium (the excess return of the market portfolio over the risk-free rate)
• SMB (Small Minus Big) is the size factor - the return of small-cap stocks minus the return of large-cap stocks
• HML (High Minus Low) is the value factor - the return of high book-to-market (value) stocks minus the return of low book-to-market (growth) stocks
• βi, si, hi are the factor loadings (sensitivities) of the asset to each factor

The Market Factor (Rm - Rf)

This is the same factor from the CAPM. It captures the broad systematic risk of holding equities versus a risk-free asset like government bonds. A stock with a market beta of 1.2 is expected to move 1.2% for every 1% move in the market. The market factor typically explains the largest portion of a diversified portfolio's return variation.

The Size Factor (SMB)

SMB captures the historical tendency for small-cap stocks to earn higher average returns than large-cap stocks. Fama and French construct SMB by sorting all stocks into size groups based on market capitalisation, forming portfolios of small and large stocks, and computing the difference in their returns each month.

The economic rationale is that smaller companies carry more risk. They have less diversified revenue, thinner balance sheets, lower liquidity, and greater sensitivity to economic downturns. Investors demand a premium for bearing these risks. The historical SMB premium in the US has averaged roughly 2-3% per year, though it's been inconsistent across decades - particularly after adjusting for liquidity constraints in micro-cap stocks.

The Value Factor (HML)

HML captures the value premium - the tendency for stocks with high book-to-market ratios (value stocks) to outperform those with low book-to-market ratios (growth stocks). Fama and French sort stocks by their ratio of book equity to market equity, form portfolios of high and low book-to-market stocks, and take the difference in returns.

Why do cheap stocks outperform? There are two competing explanations. The risk-based view, which Fama favours, argues that value stocks are fundamentally riskier - they tend to be firms in financial distress or facing uncertain futures, and the higher returns compensate investors for that risk. The behavioural view argues that investors systematically overreact to bad news, pushing prices of struggling companies too low and creating a return premium when prices eventually correct.

The historical HML premium in the US has averaged roughly 3-5% annually, though value suffered a well-documented period of underperformance from roughly 2017 to 2020 before recovering.

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The Fama-French Five-Factor Model

In 2015, Fama and French extended their own model by adding two more factors: profitability and investment. The fama french five factor model addresses patterns in returns that the three-factor version couldn't fully explain.

The five-factor model is expressed as:

E(Ri) - Rf = βi(Rm - Rf) + si(SMB) + hi(HML) + ri(RMW) + ci(CMA)

The two new fama french factors are:

The Profitability Factor (RMW)

RMW stands for Robust Minus Weak. It captures the difference in returns between firms with high operating profitability and firms with low operating profitability. Fama and French define operating profitability as revenue minus cost of goods sold, minus selling, general, and administrative expenses, minus interest expense, all divided by book equity.

The finding is intuitive on the surface - profitable companies earn higher stock returns than unprofitable ones - but it's actually puzzling. If markets are efficient, shouldn't the higher profitability already be priced in? The explanation is that investors often underprice consistent, boring profitability, instead chasing speculative turnaround stories and lottery-like payoffs. RMW has historically delivered a premium of roughly 3-4% annually.

The Investment Factor (CMA)

CMA stands for Conservative Minus Aggressive. It captures the difference in returns between firms that invest conservatively (low asset growth) and those that invest aggressively (high asset growth). Companies that grow their asset base rapidly tend to earn lower subsequent stock returns than those that grow slowly.

This connects to a broader finding in corporate finance: firms that invest heavily often do so during periods of overoptimism, funding projects with diminishing returns. Conservative firms, by contrast, tend to be more disciplined capital allocators. The CMA premium has averaged roughly 2-3% per year.

What Happened to Value?

One notable finding from the five-factor model is that HML becomes largely redundant once profitability and investment are included. The value premium is substantially absorbed by RMW and CMA. This makes economic sense: cheap stocks tend to be less profitable and invest less aggressively, so value is partly a proxy for profitability and investment characteristics. This sparked a genuine debate about whether "value" is a standalone phenomenon or a composite of other, more fundamental attributes.

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Where to Get Fama-French Data

Kenneth French maintains a publicly available data library on his website at Dartmouth College (mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). This is the standard source used by academics and practitioners worldwide.

The data library includes:

• Monthly and daily factor returns for the three-factor, five-factor, and momentum models
• Portfolio returns sorted by size, value, profitability, investment, and other characteristics
• US and international data covering developed and emerging markets
• Historical data stretching back to 1926 for US factors

The data is free to download in CSV format. For Python users, the pandas-datareader library can pull Fama-French data directly, and the getFamaFrenchFactors package offers another convenient interface. The data is updated monthly, typically with a one-month lag.

If you're running a fama french regression for academic research or portfolio analysis, this is where your data should come from. Using the official data ensures your results are comparable to the broader literature.

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Running a Fama-French Regression in Python

A fama french regression estimates how sensitive a stock or portfolio's returns are to each of the Fama-French factors. The standard approach is ordinary least squares (OLS) time-series regression. Here's a complete example using Python.

import pandas as pd
import numpy as np
import statsmodels.api as sm
from pandas_datareader import data as pdr
import yfinance as yf

yf.pdr_override()

# Download Fama-French five-factor data
ff_factors = pdr.DataReader(
    "F-F_Research_Data_5_Factors_2x3",
    "famafrench",
    start="2016-01-01",
    end="2025-12-31"
)[0]

# Fama-French returns are in percentage points, convert to decimals
ff_factors = ff_factors / 100

# Download monthly stock returns (example: Apple)
stock = yf.download("AAPL", start="2016-01-01", end="2025-12-31", interval="1mo")
stock["Return"] = stock["Adj Close"].pct_change()
stock = stock.dropna()

# Align dates - Fama-French uses end-of-month dates
stock.index = stock.index.to_period("M")
ff_factors.index = ff_factors.index.to_period("M")

# Merge datasets
merged = stock[["Return"]].join(ff_factors, how="inner")

# Calculate excess returns (stock return minus risk-free rate)
merged["Excess_Return"] = merged["Return"] - merged["RF"]

# Define independent variables (the five factors)
X = merged[["Mkt-RF", "SMB", "HML", "RMW", "CMA"]]
X = sm.add_constant(X)

# Define dependent variable (excess stock return)
y = merged["Excess_Return"]

# Run OLS regression
model = sm.OLS(y, X).fit()

print(model.summary())
print(f"\nAlpha (annualised): {model.params['const'] * 12:.4f}")
print(f"Market Beta: {model.params['Mkt-RF']:.4f}")
print(f"SMB Loading: {model.params['SMB']:.4f}")
print(f"HML Loading: {model.params['HML']:.4f}")
print(f"RMW Loading: {model.params['RMW']:.4f}")
print(f"CMA Loading: {model.params['CMA']:.4f}")
print(f"R-squared: {model.rsquared:.4f}")

This code downloads Fama-French factor data from Kenneth French's data library, pulls monthly stock returns, computes excess returns, and runs a five-factor regression. The output tells you exactly how exposed the stock is to each systematic factor - and whether there's any alpha left over. A solid grounding in statistical methods will help you interpret the regression diagnostics and test for issues like heteroscedasticity and autocorrelation.

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Interpreting Fama-French Regression Results

The output of a fama french regression gives you two types of information: the intercept (alpha) and the factor loadings (betas). Both matter, but they answer different questions.

Alpha (the Intercept)

The intercept represents the average monthly return that isn't explained by the five factors. If alpha is positive and statistically significant (t-statistic above 2.0), the stock or portfolio has generated returns beyond what its factor exposures would predict. This is genuine outperformance - or at least, outperformance relative to these specific factors.

A positive alpha of 0.3% per month means the stock earned roughly 3.6% per year more than you'd expect given its market, size, value, profitability, and investment exposures. In the context of fund evaluation, a statistically significant alpha suggests the manager has skill - they aren't simply loading up on known risk premiums.

Factor Loadings

Each factor loading tells you the direction and magnitude of the stock's exposure to that factor:

For example, a mutual fund with an SMB loading of 0.45 and an HML loading of 0.60 is significantly tilted toward small value stocks. If that fund advertises itself as a "stock picker" but its returns can be fully explained by these factor exposures (alpha near zero), then it's not adding value through selection - it's just harvesting the size and value premiums, which you could replicate cheaply with a factor-based ETF.

R-Squared

The R-squared tells you what proportion of the portfolio's return variation the model explains. For a well-diversified equity portfolio, the five-factor model typically explains 90-95% of return variation. For individual stocks, R-squared is lower - usually 30-60% - because idiosyncratic (stock-specific) risk is a bigger component.

A low R-squared doesn't mean the model has failed. It means the stock has significant firm-specific risk that no systematic factor model can capture. That's normal for individual names.

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Applications of the Fama-French Model

The Fama-French framework has become a workhorse in both academic research and industry practice. Here are the main ways it's used in 2026.

Performance Attribution

The most common application is decomposing portfolio returns into factor-driven and alpha components. When a pension fund evaluates a manager, they run a Fama-French regression on the manager's returns to determine how much of the performance came from market exposure, size tilts, value tilts, profitability exposure, and investment style - and how much, if any, came from genuine stock selection skill.

Portfolio Construction

Quantitative portfolio managers use Fama-French factors as building blocks. If you want a portfolio tilted toward small value stocks with high profitability, you explicitly target positive loadings on SMB, HML, and RMW while controlling your market beta. The factor model provides the language and the mathematics for expressing these preferences precisely.

Risk Decomposition

Understanding where your risk comes from is as important as understanding where your returns come from. A portfolio with a large positive HML loading carries significant value risk - it will underperform when value stocks fall out of favour (as they did from 2017 to 2020). Factor-based risk decomposition helps investors understand and manage these exposures before they materialise as losses.

Alpha Measurement

The Fama-French model defines the bar for what counts as alpha. Before these models existed, any fund that beat the S&P 500 could claim skill. Now, outperformance only counts if it survives regression against the relevant factors. This has fundamentally changed how the industry evaluates investment skill and has contributed to the growth of passive and factor-based investing.

Academic Research

Virtually every empirical study in asset pricing published since the mid-1990s uses the Fama-French model as a control. If you claim to have discovered a new return anomaly, the first question is whether it survives after controlling for the fama french factors. This makes the model a gatekeeper for what counts as a genuine finding in financial economics.

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Fama-French vs CAPM vs APT

The Fama-French model sits between the CAPM and Arbitrage Pricing Theory (APT) in terms of complexity and flexibility. Here's how they compare:

The CAPM is the simplest model but has the worst empirical fit. It can't explain why small stocks outperform large ones, or why value stocks outperform growth stocks. APT provides a general framework that allows any number of factors but doesn't specify which ones to use - a flexibility that's also a weakness.

The Fama-French model occupies the practical sweet spot. It names its factors explicitly, provides free data, and has decades of empirical support. It's specific enough to be useful and general enough to capture the most important dimensions of risk. For most practical applications in quant finance - fund evaluation, portfolio construction, risk management - the Fama-French model is the default choice.

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Criticisms and Limitations

The Fama-French model is the most widely used multi-factor framework, but it's not without problems. Academics and practitioners have raised several legitimate concerns.

Data Mining

The most fundamental criticism is that the factors were discovered by looking at historical data rather than derived from economic theory. Size and value were identified because they worked in past US stock returns - but is that evidence of a genuine risk premium, or did Fama and French find patterns that happened to exist in one particular dataset? This is the data-mining or data-snooping critique.

Fama and French's response is that the factors have been replicated across many countries, time periods, and independent research teams. But the concern hasn't disappeared entirely, particularly as researchers have identified hundreds of additional factors (the "factor zoo"), most of which don't survive out-of-sample testing.

Factor Premiums May Not Persist

Even if the historical premiums were real, they may not continue into the future. Once a factor premium is widely known and capital flows into strategies targeting it, competition can compress or eliminate the premium. The value premium's extended underperformance from 2017 to 2020 raised genuine questions about whether it had been permanently diminished by crowding. In 2026, value has recovered somewhat, but the episode served as a reminder that historical averages are not guarantees.

International Evidence Is Mixed

The Fama-French factors were originally documented using US data. While the size and value premiums have been found in international markets, the magnitudes vary considerably. The size premium is weak or absent in some markets after adjusting for liquidity. The profitability and investment factors from the five-factor model show less consistent patterns outside the US. Using a model calibrated on US data to analyse non-US portfolios requires caution.

No Momentum Factor

A notable omission from both the three-factor and five-factor models is momentum - the tendency for recent winners to keep winning and recent losers to keep losing. Momentum is one of the most well-documented anomalies in finance, yet Fama and French deliberately excluded it. Fama has argued that momentum is a short-lived phenomenon driven by microstructure effects rather than a fundamental risk factor. Many practitioners disagree, and the Carhart four-factor model (discussed below) adds momentum back in.

Theoretical Weakness

Unlike the CAPM (derived from equilibrium theory) or APT (derived from no-arbitrage arguments), the Fama-French model lacks a clean theoretical foundation. The factors were chosen because they explained historical data, not because economic theory predicted they should matter. This makes the model empirically powerful but theoretically unsatisfying. It describes what happened without fully explaining why.

Regime Sensitivity

Factor loadings aren't stable over time. A company that was a small-cap value stock five years ago may now be a mid-cap growth stock after a period of strong performance. The model assumes relatively stable factor sensitivities, but in practice these shift as firms evolve, market conditions change, and sectors rotate. Regular re-estimation is necessary, and backward-looking loadings may not predict future behaviour accurately.

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The Carhart Four-Factor Model

Mark Carhart proposed the four-factor model in his influential 1997 paper on mutual fund performance persistence. He took the Fama-French three-factor model and added a momentum factor (UMD - Up Minus Down, or WML - Winners Minus Losers).

E(Ri) - Rf = βi(Rm - Rf) + si(SMB) + hi(HML) + mi(UMD)

The momentum factor is constructed by going long stocks with the highest returns over the past 12 months (excluding the most recent month to avoid short-term reversal) and going short stocks with the lowest returns over the same period.

Carhart's motivation was practical. He found that mutual fund performance persistence - the tendency for last year's winners to continue outperforming - was almost entirely explained by the momentum factor. Funds that appeared to have skill were simply holding stocks with positive momentum. Once you controlled for momentum exposure, most of the apparent persistence disappeared.

The four-factor model became the standard for evaluating fund performance throughout the 2000s and into the 2010s. It's still widely used alongside the five-factor model. Some practitioners combine both into a six-factor model (the five Fama-French factors plus momentum), though Fama and French themselves have resisted including momentum in their official framework.

The momentum premium has historically been substantial - roughly 6-8% annually on a gross basis - but it comes with severe tail risk. Momentum strategies suffered devastating drawdowns in 2009 when the market reversed sharply and the stocks that momentum portfolios were shorting (beaten-down financials) staged a violent recovery. Managing this crash risk is a central challenge for anyone implementing momentum-based strategies.

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Summary of All Fama-French Factors

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Frequently Asked Questions

What is the Fama-French model in simple terms?

The Fama-French model explains stock returns using multiple risk factors rather than just market risk alone. The three-factor version says that a stock's expected return depends on three things: how it moves with the overall market, whether it's a small or large company, and whether it's cheap or expensive relative to its book value. The five-factor version adds profitability and investment behaviour. It was developed by Eugene Fama and Kenneth French, and it's the standard framework for evaluating investment performance in both academic research and professional finance.

What is the difference between the three-factor and five-factor models?

The three-factor model includes the market, size (SMB), and value (HML) factors. The five-factor model adds profitability (RMW) and investment (CMA). The five-factor version does a better job of explaining the cross-section of stock returns, particularly for portfolios sorted by profitability and asset growth. One important finding is that HML becomes partly redundant in the five-factor model - its explanatory power is largely absorbed by RMW and CMA. In practice, many researchers and practitioners now default to the five-factor model, though the three-factor version is still common in older studies and simpler analyses.

How do I run a Fama-French regression?

Download factor return data from Kenneth French's data library at Dartmouth (it's free). Obtain your portfolio or stock's monthly returns from a data provider. Calculate excess returns by subtracting the risk-free rate. Then run an OLS time-series regression of your excess returns against the Fama-French factors. Python's statsmodels library makes this straightforward - the code example earlier in this article walks through the full process. The key outputs to look at are the intercept (alpha), the factor loadings, their t-statistics, and the R-squared.

Does the Fama-French model work outside the US?

The factors have been documented internationally, but with caveats. The value premium appears in most developed and emerging markets, though its magnitude varies. The size premium is weaker outside the US and often disappears after adjusting for liquidity. The profitability and investment factors show less consistent patterns in non-US data. Kenneth French's data library does include international factor data, and Fama and French published a 2012 paper examining their factors across 23 countries. The broad conclusion is that the framework transfers internationally, but the specific factor premiums aren't identical across markets.

Why don't Fama and French include momentum?

This is a deliberate choice rooted in Fama's views on market efficiency. Fama has argued that momentum is a short-term, transient phenomenon rather than compensation for a fundamental risk factor. He views the size and value premiums as reflecting systematic risks that investors are compensated for bearing, while momentum is harder to reconcile with a risk-based explanation. Practically, momentum also has much higher turnover and transaction costs than the other factors. Many practitioners disagree with this exclusion and use either the Carhart four-factor model or a combined six-factor model that includes momentum alongside the five Fama-French factors.

Is the Fama-French model consistent with the efficient market hypothesis?

It depends on your interpretation. Fama himself is the intellectual father of the efficient market hypothesis (EMH), and he views the factor premiums as compensation for risk - entirely consistent with market efficiency. Under this view, small-cap and value stocks earn higher returns because they're genuinely riskier, not because markets are making mistakes. However, others interpret the same evidence as showing that markets systematically misprice certain types of stocks, which would be a violation of efficiency. The Fama-French model itself is agnostic on this question - it describes the patterns in returns without taking a position on whether they reflect risk or mispricing.