Small industry alphas, and a decisive rejection anyway

How the test is set up

Two series from Ken French’s data library, as carried in this estate: monthly value-weighted returns on 49 industry portfolios, and the 5 factors (Mkt-RF, SMB, HML, RMW, CMA) plus the one-month Treasury bill rate. Both are in percent per month, and both end in 2026-05 in this download. Merged on month, they share 755 months from 1963-07. 47 industries report in every merged month; Hlth enters in 1969-07 (683 months) and Softw enters in 1965-07 (731 months). Early missing observations stay missing; each industry’s regression uses its own available span, so the table below carries a per-industry month count.

The spec is the paper’s time-series regression: each industry’s excess return (portfolio return minus the T-bill rate) on the 5 factors. The intercept, alpha, is the average monthly return the model fails to price. Standard errors are conventional OLS, the paper’s convention; no robust correction is applied and none is claimed. The 1.96 and 2.57 thresholds used throughout are the standard two-sided 5% and 1% critical values, not quantities estimated here. Industry portfolios as test assets follow the recommendation of Lewellen, Nagel and Shanken (2010, Journal of Financial Economics) that asset pricing models be confronted with portfolios not sorted on the characteristics behind the factors.

The joint test is the Gibbons, Ross and Shanken (1989, Econometrica) statistic: under the null that all 49 alphas are zero and with normal errors, it is F-distributed with (49, 629) degrees of freedom. It requires a balanced panel, so it runs on the 683 months from 1969-07 to 2026-05 in which all 49 industries report. The per-industry table uses each industry’s full span; the GRS test uses the shorter common one. The two samples differ, and so do their summary alphas: mean absolute alpha 0.229% per month on full spans, 0.242 on the balanced panel.

The result

Judged one at a time, the model does what the paper says it does: 33 of 49 industry alphas have |t| below 1.96, and the median absolute alpha is 0.169% per month. The significant minority is lopsided. Of the 16 industries with |t| at or above 1.96, 14 have negative alphas and 2 positive; at the stricter |t| at or above 2.57, 11 of 12 are negative. The largest failure is RlEst, -0.666% per month (t = -4.31); the only significant positives are Hardw (+0.399, t = 2.49) and Chips (+0.390, t = 2.87). Explanatory power varies widely: R² runs from 0.08 (Gold) to 0.87 (BusSv).

The 16 industries the model misprices at the 5% level

Source: Ken French Data Library: 49 Industry Portfolios (value-weighted, monthly) | Ken French Data Library: Fama/French 5 Factors (2x3, monthly) Sorted by t-statistic. "Other" is French's residual bucket for stocks that fit none of the named industry definitions, not an economic sector, and it is on this list (alpha -0.511, t = -3.13).

The joint verdict is harsher than the one-at-a-time reading. The GRS statistic on the balanced panel is F(49, 629) = 2.28, p = 3.6e-6: the hypothesis that the 5 factors price all 49 industries at once is rejected at any conventional level. That is not a contradiction of the alphas being small; the joint test aggregates evidence across all 49 intercepts at once, so with 683 months it can reject even when each alpha is individually modest. Both facts belong in the same sentence, which is how the paper presented its own rejections.

Every industry

Source: Ken French Data Library: 49 Industry Portfolios (value-weighted, monthly) | Ken French Data Library: Fama/French 5 Factors (2x3, monthly) All 49 portfolios, sorted by t-statistic. Alphas in percent per month over each industry's own span.

What this cannot tell you

• Whether the paper’s own tables reproduce. Fama and French (2015) tested portfolios sorted on size, book-to-market, profitability and investment; the 49 industry portfolios are a different left-hand side from the same library, so no number here maps one-for-one onto a number in the paper. This note extends the paper’s spec to a harder set of test assets, and checks whether its qualitative reading survives.
• What the paper’s vintage would show. French’s library is revised retroactively; this download ends in 2026-05, and even months inside the paper’s window need not carry the values the authors used.
• Anything comparable about magnitudes across samples. Our merged sample runs 755 months against the paper’s 606 (the paper’s own count, July 1963 to December 2013). Longer samples shrink standard errors mechanically, and the full-span versus balanced-panel mean absolute alphas here (0.229 versus 0.242) show that the sample choice alone moves the summary.
• Robust inference. The OLS standard errors ignore heteroskedasticity, and the GRS test assumes normal errors. The paper’s spec as published was the only specification run; no robustness variant was estimated.
• Clean industry boundaries. The download carries one industry classification applied to the whole history, so early-sample portfolios reflect boundaries drawn later, a mild look-ahead built into the construction.
• Which model does better. The GRS statistic tests these 5 factors against these 49 portfolios; no competing model was estimated here, so nothing on this page ranks models.