Fama-French Factor Regression Analysis

What this research found

Two pillars of empirical asset pricing were re-estimated on the full modern sample of 726 monthly observations from July 1963 through December 2023: the size of the value and size premia, and whether the Fama–French three-factor model explains away the apparent outperformance of small-value stocks. The value factor earned 3.55% a year and remains statistically significant; the size factor's 2.07% does not. The small-value corner portfolio's large single-factor alpha of 5.84% a year shrinks to 1.92% once size and value exposures are included, because the portfolio loads heavily on both.

• The value premium survives three extra decades of data, including value investing's weak 2010s: 0.296% per month, or 3.55% a year, with a Newey–West t-statistic of 2.22 (p = 0.026).
• The size premium is positive but not distinguishable from zero at conventional levels — 0.173% per month, or 2.07% a year, with a t-statistic of 1.47 (p = 0.141) — mirroring the modern view that the size effect is the more fragile of the two.
• Under the single-factor model the small-value portfolio appears to deliver 5.84% a year of abnormal return (t = 2.75) with a market beta near one at 1.068. Adding size and value cuts that alpha by roughly two-thirds to 1.92% and lifts adjusted R² from 0.579 to 0.907.
• The shrinkage is mechanical rather than mysterious. The small-value portfolio loads 1.108 on size and 0.697 on value, both estimated with t-statistics above 22; at the sample premia those loadings account for about 4.8% a year of expected return above the market.
• The big-growth corner is the mirror image and a useful control. Its single-factor alpha is a trivial 0.26% a year (t = 0.31) with adjusted R² already at 0.884, since large-cap growth names dominate the value-weighted market. It loads negatively on both size (−0.237) and value (−0.356), exactly the profile its label implies.
• Neither corner is priced perfectly by the three-factor model. Small-value retains a small but significant 1.92% alpha, and big-growth's three-factor alpha is positive and significant at 2.03% (t = 3.80) because negative factor loadings make the model forecast a below-market return that the portfolio's market-like realised return then exceeds.

How it was done

Two monthly series from the Kenneth French Data Library — the three research factors and the 25 value-weighted portfolios formed on size and book-to-market — were parsed from the 202605 data vintage, cleaned of the library's missing-data codes, and inner-joined on calendar month, then restricted to July 1963 onward because reliable book-equity data begin in the early 1960s. The result is exactly 726 contiguous months with no gaps and no missing values. The two diagonal corners of the 5×5 grid were extracted, with explicit care over the labelling that makes small-value the highest book-to-market small-cap bucket rather than the lowest. Factor premia were estimated as intercept-only regressions and each corner portfolio's excess return was regressed first on the market factor alone and then on market, size and value together. All standard errors use a Newey–West heteroskedasticity- and autocorrelation-consistent estimator with a six-lag Bartlett kernel, a bandwidth chosen to exceed the usual data-driven rule for a sample this long.

Data sources

• Kenneth French Data Library — Fama–French three factors, monthly (market excess return, size, value, one-month Treasury bill rate), 202605 CRSP vintage
• Kenneth French Data Library — 25 portfolios formed on size and book-to-market, average value-weighted monthly returns
• Aligned sample: 726 monthly observations, July 1963 to December 2023
• Fama & French (1993, 1996) for the three-factor model; Newey & West (1987) for HAC inference