This page reviews "Common Risk Factors in the Returns on Stocks and Bonds," a 1993 paper by Eugene Fama and Kenneth French. The researchers identified three factors that explain the majority of differences in stock returns: the overall market, company size (small companies versus large), and value (lower-valuation stocks versus higher-valuation). This three-factor model replaced the single-factor Capital Asset Pricing Model (CAPM) as the standard framework for understanding why some stocks earn higher returns than others.

Published in the Journal of Financial Economics, the paper built on the authors' earlier 1992 work showing that company size and the ratio of book value to market value (a measure of how cheap a stock is) predicted future stock returns better than market risk alone. The 1993 paper formalized these observations into a testable model and extended the analysis to bond returns, creating the foundation for modern factor investing.

Key Findings

The paper's central contribution is demonstrating that a three-factor model captures patterns in stock returns that the single-factor CAPM misses entirely. Where CAPM says only market risk matters, Fama and French showed that two additional characteristics, company size and relative cheapness, explain a large portion of the variation in returns across different stocks.

The Three Factors

Market factor (Rm - Rf): The return of the overall stock market minus the risk-free rate (typically the return on short-term government bonds). This captures the extra return investors earn for holding stocks instead of safe assets. The CAPM used only this factor; Fama and French kept it and added two more.

Size factor (SMB, "Small Minus Big"): The return difference between small-company stocks and large-company stocks. The researchers found that small companies earned higher returns on average than large companies, even after accounting for their market risk. SMB measures this size premium by tracking how much small stocks outperform large stocks in any given period.

Value factor (HML, "High Minus Low"): The return difference between value stocks (high book-to-market ratio, meaning the company's assets are worth a lot relative to its stock price) and growth stocks (low book-to-market ratio). The researchers found that lower-valuation stocks consistently outperformed higher-valuation stocks. HML measures this value premium.

What the Model Explains

The three-factor model explained most of the variation in average returns across portfolios sorted by size and book-to-market ratio. Portfolios of small, cheap stocks earned the highest returns; portfolios of large, expensive stocks earned the lowest. The researchers documented that the three factors explained this spread more effectively than the single-factor CAPM.

The model's explanatory power was substantial. When the researchers tested 25 portfolios formed by sorting stocks into five size groups and five value groups, the three-factor model captured the return differences across these 25 portfolios far better than the market factor alone. The pricing errors (the returns left unexplained by the model) were small and statistically insignificant for most portfolios.

Extending to Bonds

The paper also identified two factors that drive bond returns: the term premium (the extra return from holding long-term bonds instead of short-term bonds) and the default premium (the extra return from holding corporate bonds instead of government bonds). The researchers found that these bond factors also helped explain stock returns, suggesting a connection between the risks in stock and bond markets.

This cross-market analysis was important because it showed that the forces driving investment returns are not isolated to one type of asset. Economic conditions that affect bond returns, such as changes in interest rates or the health of corporate borrowers, also influence which stocks do well and which struggle.

Practical Implications

The Foundation of Factor Investing

The three-factor model provided the intellectual basis for an entire investment industry. Before this paper, a fund manager who outperformed the market could claim skill. After this paper, it became clear that much of what appeared to be skill was actually exposure to the size and value factors. A manager who bought small, cheap stocks would naturally outperform the market on average, not because of stock-picking ability, but because of systematic factor exposure.

This insight led directly to the development of factor-based investment products: index funds and ETFs designed to capture the size premium, the value premium, or both. Today, trillions of dollars are invested in strategies explicitly designed around the factors Fama and French identified.

Changing How We Evaluate Investment Managers

The three-factor model transformed performance evaluation. Under the CAPM, any return above what market risk would predict was considered "alpha," evidence of manager skill. The three-factor model raised the bar: to claim genuine skill, a manager must outperform after accounting for market, size, and value exposures.

This higher standard revealed that many managers previously credited with skill were simply holding small and cheap stocks. Their "alpha" disappeared once the size and value factors were included in the benchmark. The three-factor model became the standard tool for separating true stock-picking ability from systematic factor tilts.

The Ongoing Debate: Risk or Mispricing?

The paper left open a fundamental question: why do small and cheap stocks earn higher returns? Two competing explanations have been debated ever since.

The risk explanation argues that small and cheap stocks are genuinely riskier. Small companies are more vulnerable to economic downturns, and cheap stocks are often cheap because the company is in financial difficulty. Investors demand higher returns to compensate for this extra risk, so the premiums are fair payment for bearing risk and should persist.

The mispricing explanation argues that investors systematically undervalue small and cheap stocks because of behavioral biases. Investors may overreact to bad news, pushing prices too low, or they may neglect small companies that receive little analyst coverage. Under this view, the premiums exist because of persistent pricing errors, and they may shrink as more investors become aware of them.

Fama and French themselves were careful not to take a definitive position. The model describes the pattern in returns; whether that pattern reflects risk or mispricing remains an active area of research more than three decades later.

How the Researchers Tested This

How the Factors Were Built

Each year, the researchers sorted all stocks on the New York Stock Exchange, American Stock Exchange, and NASDAQ by their market capitalization (company size). Stocks below the median NYSE market cap were classified as "small"; those above were "large." Independently, stocks were sorted by book-to-market ratio into three groups: the top 30% (value), the middle 40%, and the bottom 30% (growth).

The SMB factor was calculated as the average return of the three small portfolios minus the average return of the three large portfolios. The HML factor was calculated as the average return of the two value portfolios minus the average return of the two growth portfolios. This double-sort procedure ensures that each factor captures its intended effect while controlling for the other.

Data and Time Period

The study covered U.S. stocks from July 1963 through December 1991, nearly three decades of monthly return data. The researchers used accounting data from COMPUSTAT and stock return data from CRSP, two of the most comprehensive financial databases available. The long time period and broad coverage (all NYSE, AMEX, and NASDAQ stocks) gave the results strong statistical foundation.

Bond data covered government and corporate bonds over the same period. The term factor used long-term government bond returns minus one-month Treasury bill returns. The default factor used long-term corporate bond returns minus long-term government bond returns.

The Regression Framework

The model is tested using time-series regression. For each portfolio, the researchers regressed monthly excess returns (portfolio return minus the risk-free rate) on the three factors. The regression produces factor loadings (how sensitive each portfolio is to each factor) and an intercept (alpha). If the model fully explains returns, the intercept should be zero. Small, statistically insignificant intercepts across all 25 test portfolios confirmed that the three factors captured the major patterns in returns.

Limitations and Caveats

Related Research

Further Reading

• Fama, E.F. and French, K.R. (1993). "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics, 33(1), 3–56.
• Fama, E.F. and French, K.R. (1992). "The Cross-Section of Expected Stock Returns." The Journal of Finance, 47(2), 427–465.
• Fama, E.F. and French, K.R. (2015). "A Five-Factor Asset Pricing Model." Journal of Financial Economics, 116(1), 1–22.
• Carhart, M.M. (1997). "On Persistence in Mutual Fund Performance." The Journal of Finance, 52(1), 57–82.
• Banz, R.W. (1981). "The Relationship Between Return and Market Value of Common Stocks." Journal of Financial Economics, 9(1), 3–18.
• Sharpe, W.F. (1964). "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk." The Journal of Finance, 19(3), 425–442.