Source: Fama & MacBeth (1973) · Journal of Political Economy · DOI: 10.1086/260061
TL;DR
This paper does two enduring things: (1) it introduces the Fama-MacBeth two-pass cross-sectional regression, now the workhorse method for testing whether a characteristic is priced; and (2) it provides the canonical early test of the CAPM, finding a positive, roughly linear relation between market beta and average return over 1926–1968, with no extra role for non-beta risk. The methodology outlived the result — Fama & French (1992) later showed the beta-return relation is essentially flat.
What it documents
Methodological contribution (the lasting one): estimate betas in a first pass, then in each time period run a cross-sectional regression of returns on betas; the time series of the period-by-period slope estimates gives both the average risk premium and a valid t-statistic that accounts for cross-sectional correlation. This "FM regression" is how virtually every cross-sectional asset-pricing claim is now tested.
Empirical finding (since overturned): over the full 1926–1968 sample, average returns rise with beta, the relation is approximately linear, and squared beta and idiosyncratic volatility add no explanatory power — consistent with the Sharpe-Lintner-Black CAPM at the time.
OSAP predictor: Beta (sorting stocks on market beta).
How to construct it
The FM test (not a tradeable factor per se):
First pass: estimate each stock's (or portfolio's) market beta from a time-series regression of excess returns on the market excess return over an estimation window.
Second pass: for each month t, run a cross-sectional regression: R_{i,t} = γ_{0,t} + γ_{1,t}·β_i + (other characteristics) + e_{i,t}.
Inference: average the monthly γ estimates; the t-stat is the mean slope divided by the standard error of the time series of slopes. A nonzero average γ_1 means beta is priced.
Portfolio grouping: the paper sorts stocks into beta-ranked portfolios to mitigate the errors-in-variables problem from estimating individual betas.
For the "Beta" anomaly itself: sort stocks on estimated beta and form high-minus-low-beta portfolios — though see the BAB literature, which shows the low-beta end is the one with positive alpha.
Evidence and replication
Period
Finding
Source
IS (1926–1968)
positive, ~linear beta-return relation; no residual-risk effect
this paper
Post-1963 re-examination
beta-return relation flat once size/value controlled
Fama & French 1992
Modern (leverage constraints)
low-beta has positive alpha — the SML is too flat
Frazzini-Pedersen 2014
OSAP (Beta)
weak / not significant standalone premium
Chen & Zimmermann 2022
The 1973 result was the high-water mark of CAPM empirical support. The same FM methodology was later turned against the CAPM: Fama & French (1992) used cross-sectional regressions to show beta has no marginal explanatory power once size and book-to-market are included.
Modern work (Betting Against Beta) goes further — the security market line is flatter than the CAPM predicts, so high beta is actually associated with lower risk-adjusted returns, the opposite of a positive beta premium.
Why it matters
As methodology: the FM regression is foundational infrastructure — almost every "is factor X priced?" question in this library is answered with some variant of it. Understanding its two-pass structure and the errors-in-variables and portfolio-grouping issues is core to reading empirical asset pricing.
As intellectual history: it documents the CAPM's empirical peak, making the subsequent flat-beta and betting-against-beta findings the central cautionary tale about how a "confirmed" relation can reverse out of sample.
Limitations and risks
Errors-in-variables: individual betas are estimated with noise, biasing second-pass slopes toward zero; portfolio grouping helps but introduces its own choices.
Beta instability: betas vary over time, so first-pass estimates are stale.
The result didn't hold: the positive beta-return relation is the textbook example of an in-sample finding that failed out of sample — treat the empirical conclusion as historical, not actionable.
No free full text: paywalled; see DOI.
Key references
Fama, E. & MacBeth, J. (1973) — Risk, Return, and Equilibrium: Empirical Tests — Journal of Political Economy — DOI: 10.1086/260061
Fama, E. & French, K. (1992) — The Cross-Section of Expected Stock Returns — Journal of Finance
Frazzini, A. & Pedersen, L. (2014) — Betting Against Beta — Journal of Financial Economics
Black, F., Jensen, M. & Scholes, M. (1972) — The Capital Asset Pricing Model: Some Empirical Tests
Chen, A. & Zimmermann, T. (2022) — Open Source Cross-Sectional Asset Pricing — Critical Finance Review
