Size and Book-to-Market Factors in Earnings and Returns
Source: Fama, E. F. & French, K. R. (1995) · Journal of Finance 50(1), 131–155 · DOI: 10.1111/j.1540-6261.1995.tb05169.x
TL;DR
This is the economic companion to the 1993 three-factor model: it asks why size and book-to-market (BE/ME) predict returns by checking whether they track firm fundamentals. Over 1963–1992 the authors confirm that high-BE/ME ("distressed") and small firms are persistently less profitable, and that there are market, size, and BE/ME factors in earnings that look like the corresponding factors in returns. The rational-pricing story works for the market and size factors — they show up in both earnings and returns — but the key prediction fails for BE/ME: there is no evidence that the book-to-market factor in earnings drives the book-to-market factor in returns. So HML's risk story is left incomplete (attributed by the authors to measurement noise).
The question
Fama–French (1992, 1993) show that size and BE/ME proxy for sensitivity to common risk factors in returns, and that a three-factor model (market, SMB, HML) captures the cross-section of average U.S. returns. But "return tests cannot tell a complete economic story" — size and BE/ME remain arbitrary indicator variables. If pricing is rational, the size/BE/ME risk factors in returns must be driven by common factors in shocks to expected earnings that line up with size and BE/ME. This paper tests that fundamentals-based rationale directly.
The model
Not a formal equilibrium model but a rational-pricing test framework built on the discounted-earnings identity (rational prices = discounted expected future net cash flows):
Portfolios: six size-BE/ME portfolios from an independent 2×3 sort (NYSE breakpoints), formed yearly, 1963–1992; covers NYSE/AMEX/NASDAQ firms with COMPUSTAT and CRSP data.
Profitability measure: return on book equity, EI(t)/BE(t−1), tracked for the 11 years (i = −5…+5) around each formation date and averaged across formation years.
Factors in earnings: time-series regressions (Table II–IV) project portfolio earnings/yield changes (ΔEI/BE, growth in earnings-before-interest EBI, and sales growth) on market, size, and BE/ME factors built from earnings, mirroring the SMB/HML construction in returns.
Link test: regress annual portfolio returns on one-year-ahead changes in fundamentals and on the market/size/BE/ME factors in fundamentals (Tables V–VI), with NYSE dividend yield as a rough control for expected-return variation.
Key predictions
If size/BE/ME risk in returns is rational, then:
BE/ME tracks persistent profitability — high BE/ME signals sustained low return on book equity; low BE/ME signals strong, growth-firm profitability.
Size tracks profitability — small firms are less profitable than big firms.
Prices forecast earnings reversion — the market anticipates that the large pre-formation earnings-growth gap between low- and high-BE/ME firms converges afterward (unbiased forecasts, contra the LSV mispricing/extrapolation story).
Common factors in earnings drive the factors in returns — market, size, and BE/ME factors in earnings should explain the corresponding factors in returns.
Empirical status
(1) Confirmed. High-BE/ME stocks are less profitable than low-BE/ME stocks for ~4 years before and at least 5 years after ranking; high BE/ME ⇒ relative distress, low BE/ME ⇒ high return on capital (growth).
(2) Confirmed, but era-dependent. Controlling for BE/ME, small stocks are less profitable — though the size effect in earnings is largely driven by a post-1980 earnings depression for small firms; before 1981 profitability had little relation to size.
(3) Confirmed. Earnings/price and return behavior imply the market makes roughly unbiased forecasts of the post-formation earnings convergence; the LSV irrational-extrapolation story is not supported.
(4) Partly confirmed — the crux. There are market, size, and BE/ME factors in earnings paralleling those in returns. The three-factor return regressions are strong (SMB slopes for small-stock portfolios have t > 35; HML slopes all > 6 standard errors from zero; high R²). And the market and size factors in fundamentals do show up in returns. But the BE/ME factor in earnings does NOT drive the BE/ME factor in returns: regressing the HML return factor on the BE/ME fundamentals factor gives a near-zero slope (t ≈ 0.04) and negative adjusted R² (≈ −0.08). The authors attribute this weak link to noise in their proxy for shocks to expected earnings.
Limitations
The headline rational-pricing chain is broken at HML — the very factor most associated with the "value premium" — so the paper does not fully close the economic case for the three-factor model.
Earnings-yield/fundamentals factors are noisy; the split-sample regressions show R² dropping and slopes attenuating relative to the return regressions, consistent with measurement error.
The size-profitability link is partly a post-1980 artifact, raising questions about its stability across regimes.
Negative EI/BE for some portfolios forces reliance on EBI and sales growth as alternative (positive-valued) shock measures.
Key references
Fama, E. F. & French, K. R. (1992) — The Cross-Section of Expected Stock Returns — Journal of Finance (size and BE/ME as return predictors)
Fama, E. F. & French, K. R. (1993) — Common Risk Factors in the Returns on Stocks and Bonds — Journal of Financial Economics (the SMB/HML three-factor model whose factors are mimicked here in earnings)
Lakonishok, Shleifer & Vishny (1994) — Contrarian Investment, Extrapolation, and Risk — Journal of Finance (the mispricing/extrapolation alternative this paper tests against)
Penman, S. H. (1991) — An Evaluation of Accounting Rate-of-Return — (profitability persistence after BE/ME sorts)
Fama, E. F. & French, K. R. (2015) — A Five-Factor Asset Pricing Model — Journal of Financial Economics (later formalizes profitability as a pricing factor)
Provenance: verified/generated from the paper's full text.
