What's the one-line summary?

Fama & French start from the dividend discount model, do a bit of algebra to divide through by book equity, and get a valuation identity that makes three testable predictions: (i) higher Bt/Mt → higher expected return, (ii) higher expected profitability → higher expected return, (iii) higher expected investment (asset growth) → LOWER expected return. They then run Fama-MacBeth cross-section regressions over 1963-2003 on NYSE/AMEX/Nasdaq stocks (excluding financials, SIC 6000-6999) and confirm all three: Bt/Mt slope near 3 standard errors above zero, lagged profitability slope t = 2.55, lagged asset growth slope t = -3.87, and Sloan's positive-accruals slope t = -6.82 as a bonus confirmation of the accruals anomaly. The catch: their 'profitability' variable is earnings before extraordinary items divided by book equity (Compustat item IB / B), which is what Novy-Marx 2013 (PT #24 yesterday) later replaced with gross profits (item GP / A) to produce a much stronger, cleaner signal.

Why does this paper matter as its own reading, given Novy-Marx already 'won'?

Three reasons. First, the theoretical setup is more careful than any of the successor papers. FF06 doesn't just say 'profitability is a factor' — they derive it from dividend discount + clean surplus accounting, so the paper's three predictions have an actual valuation-theory motivation, not just an empirical fit. Second, it's the first paper to formally introduce the INVESTMENT effect (higher asset growth → lower expected returns) that later became the CMA factor in Fama-French 2015 (PT #22). CMA didn't come from nowhere; it came from FF06's asset-growth slope of t = -3.87. Third, reading it teaches you exactly WHY earnings-based profitability signals are noisy — the paper writes it in Section III explicitly: 'higher accruals predict lower stock returns' because accruals cause transitory variation in earnings, so earnings-based profitability signals mix real profitability with accrual noise. That's exactly the noise Novy-Marx sidesteps by measuring profitability higher up the income statement (before any accruals accrue).

How is the paper structured?

Section I: derives valuation equation (3) from the dividend discount model with clean surplus accounting. Section II: reduced-form Fama-MacBeth regressions to construct proxies for expected profitability (Y_{t+τ}/B_t) and expected asset growth (dA_{t+τ}/A_t). Section III: cross-section return regressions using either lagged accounting variables directly (Baseline Tests A) or the Section II fitted values as more elaborate expected-profitability / expected-investment proxies. Section IV: portfolio tests to check the profitability and investment effects hold within size × B/M portfolios. Section V: conclusions. The paper also runs I/B/E/S analyst-forecast tests as a robustness check (sample restricted to post-1976 for those). Sample restriction: exclude financials (SIC 6000-6999), require B/M and market cap available, exclude negative book equity firms. Independent variables winsorized at 0.5 / 99.5 percentiles to control outlier leverage in the Fama-MacBeth slopes.

The three key t-statistics from Table 3?

Baseline model (size + Bt/Mt only): Bt/Mt slope has t-statistic near +3 (verbatim from Section III.A: 'The t-statistic for the average Bt/Mt slope is near three standard errors from zero'). Size slope t = -1.20 in baseline. Adding lagged profitability and lagged asset growth: profitability slope t = +2.55; asset growth slope t = -3.87; size slope amplifies to t = -1.83 (i.e., adding the two new controls doesn't wash out the size effect, and slightly strengthens it). Adding positive accruals separately: +ACt/Bt slope t = -6.82 (verbatim: 'an impressive 6.82 standard errors below zero'). The signs all confirm the paper's three valuation-equation predictions plus the Sloan (1996) accruals result as a bonus. The profitability slope's t = 2.55 is 'reliable' by the paper's own language but visibly weaker than Novy-Marx 2013 would later achieve with gross profits (Novy-Marx doesn't quote a single-slope t-statistic for GP/A because his portfolio spreads are much larger, but the annualized Sharpe of 0.85 for the all-cap 50/50 mix implies a t-statistic near 6 over the same sample length).

How does this fit with the other FF papers in the ledger?

Paper Trail #8 (Fama-French 1993 three-factor, 2026-08-08) is the parent. Paper Trail #22 (Fama-French 2015 five-factor, 2026-08-22) is the eventual child. Today's Paper Trail #25 (FF 2006) is the middle child that first identified BOTH the profitability effect AND the investment effect as separate risk factors — but with an earnings-based profitability measure that Novy-Marx 2013 (Paper Trail #24, yesterday) later replaced with gross profits. Then Fama-French adopted Novy-Marx's definition in FF15 and formally packaged both as the RMW (profitability) and CMA (investment) factors. So the paper trail is: FF93 (3 factors) → FF06 (identifies profitability and investment effects but with weaker profitability numerator) → Novy-Marx 2013 (fixes the profitability numerator to GP/A) → FF15 (packages RMW using Novy-Marx's definition + CMA using FF06's investment finding). Paper Trail #25 sits between the empirical discovery (FF06) and the corrective refinement (Novy-Marx 2013) — reading them in that order makes the arc visible.

Where can I read the paper?

Ken French's own Tuck School of Business faculty page hosts the June 2005 preprint at mba.tuck.dartmouth.edu/pages/faculty/ken.french/acrobat/Profitability%20Growth%20and%20Average%20Returns_2005_06.pdf. This is the version verified for this post — 41 pages, text-native (no OCR needed), no paywall. The published JFE version (Vol 82, Issue 3, December 2006, pages 491-518, DOI 10.1016/j.jfineco.2006.03.004) is behind a paywall via ScienceDirect. There's also a working paper version at CRSP (University of Chicago) from 2001, but the 2005 Tuck version is the closest match to the published paper. SSRN abstract 570343 corresponds to an earlier preprint titled 'Profitability, Growth, and Average Returns' (Fama & French's own title revision reflects the paper's evolution from 2001 through 2006).

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Research25 August 2026· 6 min read

Paper Trail #25: Profitability, Investment and Average Returns (Fama & French, 2006) — the 'before' picture that Novy-Marx 2013 (yesterday's PT #24) later corrected by replacing earnings with gross profits

Q: So the paper says everything you'd expect — is it just an also-ran?

The paper's own conclusions section is unusually candid about a puzzle. Direct quote: 'A puzzle arises when the fitted values from the cross-section regressions to forecast profitability and asset growth are used as proxies for expected profitability and investment in the cross-section return regressions. Many variables contribute to the regression forecasts of profitability and asset growth. Thus, there seems to be much information about expected profitability and asset growth beyond that in lagged profitability and asset growth. Better proxies for expected profitability and investment should do a better job identifying the profitability and investment effects in average returns predicted by (3). But this is not what we observe.' In other words: they can build sophisticated fitted-value proxies for expected profitability using many predictors, but those sophisticated proxies don't outperform simple lagged profitability in explaining returns. The paper flags this as a puzzle and suggests either measurement error or collinearity with book-to-market is to blame. Novy-Marx 2013 provided the direct answer seven years later: the wrong profitability numerator (earnings instead of gross profits) is the actual reason, not measurement error in a well-chosen numerator.

Fama & French’s 2006 Journal of Financial Economics paper derives three testable predictions about the cross-section of expected stock returns from the dividend-discount identity: higher book-to-market → higher return; higher expected profitability → higher return; higher expected investment (asset growth) → LOWER return. On 1963-2003 Fama-MacBeth cross-section regressions of NYSE/AMEX/ Nasdaq firms (excluding financials), all three predictions come out with the sign the theory requires and the profitability slope clocks in at t = +2.55, asset-growth slope t = -3.87, positive-accruals slope t = -6.82.

This is Paper Trail #25 — and it’s the direct predecessor to yesterday’s Paper Trail #24 (Novy-Marx 2013). FF06 measures profitability as earnings before extraordinary items (Compustat item IB), the noisy accounting figure Novy-Marx replaced with gross profits (item GP) seven years later. Reading FF06 immediately after PT #24 gives the “before” picture that Novy-Marx’s cleaner numerator improved on.

Schematic diagram of Fama & French 2006. Top: the valuation equation Mt / Bt = sum over tau of E(Y_{t+tau} - dB_{t+tau}) / B_t / (1+r)^tau, with clean-surplus dividend = earnings minus change in book equity written above it. Middle: three prediction tiles side by side. Left tile in green shows PREDICTION (i): higher book-to-market → higher return, confirmed by t ≈ 3 in Table 3 baseline. Center tile in green shows PREDICTION (ii): higher profitability → higher return, confirmed by t = +2.55 (Compustat item IB / B). Right tile in coral shows PREDICTION (iii): higher asset growth → LOWER return, confirmed by t = -3.87. Bottom coral tile: bonus confirmation of Sloan 1996 accruals anomaly, positive accruals slope t = -6.82. Underneath: 'Direct predecessor to Novy-Marx 2013 (Paper Trail #24). FF06's IB/B was replaced by Novy-Marx's GP/A.' — Fama & French 2006’s three valuation-equation predictions, with the Table 3 t-statistics that confirm each. The middle tile — profitability — was the one Novy-Marx 2013 later strengthened by changing the numerator from IB to GP.

The valuation equation and its three predictions

The paper starts from the dividend discount model Mt = Σ E(Dt+τ) / (1+r)^τ and uses clean-surplus accounting (dividend = earnings − change in book equity, so Dt = Yt − dBt) to rewrite it as:

Mt / Bt = Σ_{τ=1..∞} E(Y_{t+τ} − dB_{t+τ}) / Bt / (1+r)^τ

This is the paper’s equation (3). Read three ways, holding the other two variables fixed, it predicts:

#	Prediction	Direction	Confirmed by
(i)	Bt/Mt → r	positive	Table 3 Bt/Mt slope t ≈ +3
(ii)	E(Y_{t+τ}) / Bt → r	positive	Table 3 profitability slope t = +2.55
(iii)	E(dB_{t+τ}) / Bt → r	NEGATIVE	Table 3 asset-growth slope t = −3.87

Predictions (i) and (ii) are intuitive: cheap stocks or profitable stocks should have higher expected returns. Prediction (iii) is the counter-intuitive one that FF06 puts on the map: firms expected to reinvest heavily (grow book equity fast) should have LOWER expected returns, given the same current Bt/Mt and expected profitability. This is what later became the CMA (Conservative minus Aggressive investment) factor in Fama-French 2015 (PT #22).

Method: Fama-MacBeth cross-section regressions

The paper uses Fama-MacBeth (1973) year-by-year cross-section regressions estimated monthly, starting July 1963. Independent variables update each July using fiscal-year data ending in the prior calendar year, matched to market equity as of the end of June (following the Fama-French 1992 convention). To control outlier leverage on the slopes, independent variables are winsorized at 0.5 / 99.5 percentiles.

Sample restrictions verbatim from Section III: “We drop firms from the tests for several reasons. First, we exclude financial firms (SIC codes between 6000 and 6999). In addition, to be included in the sample for year t, a firm must have book equity, revenues, cost of goods sold, and total assets for t and t-1. A firm must also have market cap (price times shares outstanding) available on CRSP for its (last) fiscal yearend in t, December of t, and June of t+1. We exclude firms with negative book equity in year t.”

The four verified Table 3 t-statistics

Variable	t (baseline)	t (with prof + growth)	Notes
Bt/Mt (book-to-market)	≈ +3	≈ +3 (essentially unchanged)	confirms Fama-French 1992 baseline; strong throughout
Size (log market cap)	-1.20	-1.83 (strengthens)	weak baseline; adding prof + growth doesn’t wash it out
Lagged profitability (IB/B)	—	+2.55	confirms prediction (ii); the noisy leg Novy-Marx later fixes
Lagged asset growth (dA/A)	—	-3.87	confirms prediction (iii); the future CMA leg
Positive accruals (+ACt/Bt)	—	-6.82	bonus confirmation of Sloan (1996) accruals anomaly

All four coefficients have the sign the valuation equation demands and are reliably different from zero (except the size slope in baseline, which the paper calls out as weak). The profitability slope’s t = +2.55 is the paper’s own answer to “is there an expected-profitability effect in average returns beyond size and B/M?” — yes, but modest.

The candid puzzle FF06 flags

Section V of the paper is unusually candid about a puzzle. Direct quote:

“A puzzle arises when the fitted values from the cross-section regressions to forecast profitability and asset growth are used as proxies for expected profitability and investment in the cross-section return regressions. Many variables contribute to the regression forecasts of profitability and asset growth. Thus, there seems to be much information about expected profitability and asset growth beyond that in lagged profitability and asset growth. Better proxies for expected profitability and investment should do a better job identifying the profitability and investment effects in average returns predicted by (3). But this is not what we observe.”

Translation: FF06 built sophisticated fitted-value proxies for expected profitability using many predictors — accruals, prior profitability, prior returns, Piotroski’s PTt firm-strength score, Ohlson’s OHt default-probability logit fitted value. None of those elaborate proxies outperform simple lagged IB/B in explaining returns. The paper suggests either measurement error or collinearity with book-to-market is to blame. Novy-Marx 2013 provided the direct answer seven years later: the wrong profitability numerator (earnings instead of gross profits) is the actual issue. Once you go higher up the income statement to GP/A (before the accrual-noise line), the effect strengthens dramatically — as PT #24 showed with Sharpe 0.85 on the all-cap 50/50 mix.

The paper trail so far

PT #	Paper	Role in the arc
#8	Fama-French 1993 (3-factor)	the parent 3-factor model everything after builds on
#25 (this post)	Fama-French 2006 (prof + inv)	first identifies BOTH profitability and investment effects; noisy prof measure
#24	Novy-Marx 2013 (GP/A)	fixes FF06’s profitability numerator: gross profits instead of earnings
#22	Fama-French 2015 (5-factor)	packages RMW (Novy-Marx’s GP/A) + CMA (FF06’s dA/A) as tradable factors

Reading order: PT #8 → PT #25 (today) → PT #24 → PT #22 is the clean forward-chronological arc from three-factor to five-factor via the profitability-and-investment story. Today’s post is the middle-child empirical discovery that got refined by the two later papers.

Practical take for the retail trader

This is a paper about firm-level accounting fundamentals; the specifics don’t transfer to FX or single-macro-event trading. But the reading is worth the time for two ideas: (1) the valuation-equation framing shows that value, profitability, and investment aren’t three independent factors picked from a hat — they’re algebraically linked pieces of the same dividend-discount identity, so the model that includes all three has real theoretical constraint that the ad-hoc factor zoo doesn’t; (2) the paper’s own admission that “better proxies for expected profitability should do a better job... but this is not what we observe”is a canonical example of the researcher being honest about a methodological puzzle instead of paperclip-fitting a proxy that works. Novy-Marx 2013 (yesterday’s PT #24) came along seven years later and solved it, so the arc has a happy ending — but FF06’s candor is part of what made the eventual fix possible.

Verification note

Primary-source verification: PDF at mba.tuck.dartmouth.edu/pages/faculty/ken.french/acrobat/Profitability%20Growth%20and%20Average%20Returns_2005_06.pdf (Ken French’s Tuck faculty page, June 2005 preprint of the eventual 2006 JFE paper, no paywall). Extracted with pymupdf on 2026-08-25 into 104,531 characters of text-native content across 41 pages (no OCR required). Every claim above cross-checked against the extracted text: abstract verbatim, sample period (1963-2003) verbatim, valuation equation (3) reproduced verbatim, the three predictions from equation (3) reproduced verbatim from the introduction, sample restrictions (financials-excluded SIC 6000-6999) verbatim, Fama-MacBeth methodology verbatim, winsorization at 0.5% verbatim, and all four t-statistics (Bt/Mt ≈ +3, size -1.20 baseline / -1.83 with controls, profitability +2.55, asset growth -3.87, positive accruals -6.82) verified verbatim from Section III.A. The Section V puzzle-flagging passage is reproduced verbatim. Chart via one-off script using scripts/insights-charts/svg.ts + theme.ts primitives + sharprasterization; not committed under scripts/insights-charts/ since the schematic is single-use.

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