What is F_SCORE and how is it constructed?

F_SCORE = sum of 9 binary signals from a company's most recent annual financial statements. Each signal equals 1 if the underlying realisation is 'good', 0 if 'bad'. Range: 0 to 9. The 9 signals in three categories: (a) Profitability — F_ROA = 1 if current-year ROA > 0; F_ΔROA = 1 if current-year ROA > prior-year ROA; F_CFO = 1 if current-year cash flow from operations > 0; F_ACCRUAL = 1 if CFO > ROA (accruals negative). (b) Leverage/liquidity/source of funds — F_ΔLEVER = 1 if long-term-debt/assets DECREASED YoY; F_ΔLIQUID = 1 if current ratio INCREASED YoY; EQ_OFFER = 1 if the firm did NOT issue equity this year. (c) Operating efficiency — F_ΔMARGIN = 1 if gross margin INCREASED YoY; F_ΔTURN = 1 if asset turnover (sales/assets) INCREASED YoY. All signals compute directly from Compustat with no estimation, no lookahead, and no free parameters.

What are the key hedge portfolio return findings?

Three headline numbers from the paper, all verbatim from the primary source: (1) Screening high-BM firms for F_SCORE ≥ 5 vs holding the entire high-BM portfolio: mean one-year market-adjusted return lifts from 5.9% to 13.4% (a 7.5 pp gain — verbatim '7½% annually'). Proportion of firms with positive market-adjusted returns lifts from 31.8% to 43.7% (binomial test significant). (2) Long-short hedge portfolio (long high F_SCORE ≥ 5, short low F_SCORE < 5): 23% annual return between 1976 and 1996 (verbatim abstract sentence 2). (3) Highest vs lowest F_SCORE quintile: mean return difference 9.2 pp (median 11.3 pp), both significant at the 1% level. Effect concentrated in small and medium-sized firms, companies with low share turnover, and firms with no analyst following.

How does Piotroski 2000 connect to yesterday's PT #27 (Sloan 1996)?

Direct-lineage. F_ACCRUAL — the fourth signal in Piotroski's profitability block — is a BINARY version of Sloan 1996's accruals variable. Sloan defined accruals = (ΔCA - ΔCash) - (ΔCL - ΔSTD - ΔTP) - Dep and showed the accruals-slope in Fama-MacBeth returns regressions was significantly negative (FF06 later reported t=-6.82). Piotroski simplifies: F_ACCRUAL = 1 if CFO > ROA (equivalent to negative accruals, since accruals = ROA - CFO in the working-capital sense). It's the same underlying signal reduced to a 0/1 indicator, so it fits the F_SCORE 9-binary framework without adding a continuous covariate. Piotroski explicitly cites Sloan 1996 in the paper's F_ACCRUAL motivation. Same pattern for F_ROA (Sloan's profitability persistence a_1 = 0.841 becomes 'ROA > 0'). The F_SCORE framework is a way to compose Sloan's accruals + Ou-Penman fundamentals + Lev-Thiagarajan signal-based analysis into ONE composite score you can screen on.

How does F_SCORE relate to Novy-Marx 2013 gross profitability (PT #24)?

F_ΔMARGIN — Piotroski's operating-efficiency signal for whether gross margin (gross profit / sales) increased YoY — is a binary version of Novy-Marx 2013's gross profitability change. Novy-Marx uses GP/Assets as a continuous predictor and shows it hedges value with correlation -0.57. Piotroski's F_ΔMARGIN is only about the CHANGE in margin, and only in {0, 1} — no per-firm variation beyond the direction. But the underlying signal is the same: operational improvement is a positive-return indicator inside the value portfolio. Novy-Marx's contribution 13 years later is (a) using level not change; (b) using gross profit not net (avoids the earnings-management concerns Sloan flagged); (c) treating it as a continuous predictor rather than a binary. Piotroski 2000 is the earliest paper to document a positive alpha from a profitability-tilted screen WITHIN value portfolios.

Does F_SCORE still work out-of-sample?

Piotroski's own paper only covers 1976-1996. There are extensive out-of-sample replication studies since then. Green-Hand-Zhang 2017 (NBER WP 22894) — extending to 1976-2015 — reports the F_SCORE effect survives but is roughly halved in magnitude (a ~11% high-vs-low F_SCORE spread instead of Piotroski's original 23%). Piotroski & So 2012 (JFE) extends F_SCORE with analyst forecast dispersion. Within-sample robustness in the original paper: 20 of 21 sample years the strong minus weak return spread is positive; strategy 'appears to be robust across time and to controls for alternative investment strategies' (verbatim). The 7.5 pp mean-return improvement holds across all firm sizes but is concentrated in smaller firms with less analyst coverage. Today's post reports Piotroski's own primary numbers and lineage; the out-of-sample degradation is documented in the follow-up literature Green-Hand-Zhang cite.

Why is the 'no equity issuance' signal (EQ_OFFER) in the leverage block?

F_SCORE's leverage / liquidity / source-of-funds block asks: 'has this firm's balance sheet strengthened over the past year?' Three sub-signals: F_ΔLEVER = long-term debt shrinks (less financial risk); F_ΔLIQUID = current ratio grows (better short-term liquidity); EQ_OFFER = no equity issuance (firm didn't need to dilute to fund operations). Piotroski's framing: high-BM firms are already distressed by definition, so signal 8 (no equity issuance) captures 'firm didn't need external capital this year' as a proxy for cash-flow sufficiency. The 3-signal leverage/liquidity/source-of-funds bundle picks up firms that were financially distressed at portfolio formation but haven't required raising outside capital in the year since — a strong survival indicator inside the value cohort. Empirical hit rate: EQ_OFFER = 1 for the vast majority of high-BM firms (approx 71% per Piotroski Table 1 Panel A 'Proportion with Positive Signal'), so it acts more as an exclusion filter than a discriminator.

What's the 'quarterly earnings announcements' cross-link to PEAD?

Piotroski reports in his abstract that 'roughly ⅙ of the annual return difference between ex ante strong and weak firms is earned over the four three-day periods surrounding these quarterly earnings announcements' (verbatim). Roughly translated: the F_SCORE screen predicts future earnings SURPRISES — high F_SCORE firms subsequently release earnings that beat expectations more often than low F_SCORE firms, and the price reaction on those quarterly-announcement days explains ~17% of the full annual return spread. Direct link to PT #6 Bernard-Thomas 1989 post-earnings announcement drift (PEAD). Piotroski's contribution: the F_SCORE screen at portfolio formation identifies future PEAD winners AHEAD of time, at zero cost, using only public accounting data. Practical implication: the market underreacted to information already in the balance sheet, and the earnings-announcement window is where that underreaction gets partially corrected.

Where's the full paper?

Journal of Accounting Research 38, Supplement (2000): pages 1-41. JSTOR stable URL https://www.jstor.org/stable/2672906 (paywalled). DOI 10.2307/2672906. Piotroski's own University of Chicago Graduate School of Business reprint (Selected Paper No. 84, © 2002) hosted at chicagobooth.edu — that's the version verified end-to-end today via WebFetch + pymupdf (42 pages, 106,153 chars text-native). Piotroski was on the University of Chicago Booth faculty from 1999-2007; he's currently at Stanford GSB. His subsequent papers extending F_SCORE include Piotroski & So 2012 JFE 'Identifying expectation errors in value/glamour strategies' and Piotroski & Roulstone 2004 'The influence of analysts, institutional investors and insiders on the incorporation of market, industry and firm-specific information into stock prices'.

← All insights

Research28 August 2026· 5 min read

Paper Trail #28: Value Investing (Piotroski, 2000) — the paper that turned 9 binary accounting signals into a 7.5% annual return improvement inside the high book-to-market portfolio, and gave the value strategy a fundamental-analysis filter that survives 25+ years of out-of-sample tests

Q: How does Piotroski 2000 connect to yesterday's PT #27 (Sloan 1996)?

Direct-lineage. F_ACCRUAL — the fourth signal in Piotroski's profitability block — is a BINARY version of Sloan 1996's accruals variable. Sloan defined accruals = (ΔCA - ΔCash) - (ΔCL - ΔSTD - ΔTP) - Dep and showed the accruals-slope in Fama-MacBeth returns regressions was significantly negative (FF06 later reported t=-6.82). Piotroski simplifies: F_ACCRUAL = 1 if CFO > ROA (equivalent to negative accruals, since accruals = ROA - CFO in the working-capital sense). It's the same underlying signal reduced to a 0/1 indicator, so it fits the F_SCORE 9-binary framework without adding a continuous covariate. Piotroski explicitly cites Sloan 1996 in the paper's F_ACCRUAL motivation. Same pattern for F_ROA (Sloan's profitability persistence a_1 = 0.841 becomes 'ROA > 0'). The F_SCORE framework is a way to compose Sloan's accruals + Ou-Penman fundamentals + Lev-Thiagarajan signal-based analysis into ONE composite score you can screen on.

Joseph D. Piotroski (University of Chicago, 2000): 9 binary accounting signals summing to F_SCORE ∈ [0, 9]. Screening the high book-to-market portfolio for F_SCORE ≥ 5 lifts mean one-year market-adjusted return from 5.9% to 13.4% — a 7.5 pp improvement. A long-short hedge portfolio (long high F_SCORE, short low) earns 23% annual return between 1976 and 1996. Twentieth Paper Trail with full primary-source access.

Verified today via WebFetch + pymupdf on Piotroski’s own University of Chicago GSB Selected Paper 84 reprint of the JAR 2000 paper — 42 pages, 106,153 characters text-native no OCR. Piotroski’s own institutional reprint, so it counts as full primary-source access.

A three-section schematic diagram. Top: title card 'Piotroski 2000 — Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers' with JAR 38 Supplement citation. Middle: three color-coded blocks showing the 9 F_SCORE signals — Profitability block (4 signals: F_ROA, F_ΔROA, F_CFO, F_ACCRUAL) in green; Leverage/Liquidity/Source-of-Funds block (3 signals: F_ΔLEVER, F_ΔLIQUID, EQ_OFFER) in coral; Operating Efficiency block (2 signals: F_ΔMARGIN, F_ΔTURN) in blue. Each signal has a one-line binary definition. Below the blocks: the composite formula F_SCORE = sum of 9 signals, range [0, 9]. Bottom: three key-finding tiles — high F_SCORE (≥5) mean market-adjusted return 13.4% vs full high-BM portfolio 5.9% (7.5 pp gain); highest vs lowest F_SCORE quintile spread 9.2 pp mean 11.3 pp median; long-short hedge 23% annual return 1976-1996. Sample size: 14,043 high book-to-market firm-year observations 1976-1996. — F_SCORE composition and headline findings. Three signal-category blocks summing to a 0-9 composite; three headline return numbers from the primary source (verbatim).

The 9 signals

Block	Signal	= 1 if ...
Profitability	F_ROA	current-year ROA > 0
Profitability	F_ΔROA	current-year ROA > prior-year ROA
Profitability	F_CFO	current-year cash flow from operations > 0
Profitability	F_ACCRUAL	CFO > ROA (accruals negative)
Leverage/Liq	F_ΔLEVER	long-term-debt/assets decreased YoY
Leverage/Liq	F_ΔLIQUID	current ratio increased YoY
Leverage/Liq	EQ_OFFER	no equity issuance during current fiscal year
Op Efficiency	F_ΔMARGIN	gross margin (GP/sales) increased YoY
Op Efficiency	F_ΔTURN	asset turnover (sales/assets) increased YoY

Composite: F_SCORE = sum of the 9 signals, range [0, 9]. All signals compute directly from Compustat with no estimation, no lookahead, and no free parameters. High F_SCORE = firm with mostly-good signals; low F_SCORE = mostly-bad.

The three headline return numbers

Portfolio	Mean 1-yr Mkt-Adj Return	Notes
All high-BM (baseline)	5.9%	n=14,043; 31.8% positive returns
High F_SCORE (≥5) subset	13.4%	+7.5 pp gain vs baseline; 43.7% positive
Long-short hedge (high − low)	23% annually	1976-1996; buy F≥5, short F<5
Highest − lowest F_SCORE quintile	+9.2 pp mean / +11.3 pp median	both significant at 1% level

Direct-lineage chain: Sloan 1996 → Piotroski 2000

F_ACCRUAL — the fourth signal in Piotroski’s profitability block — is a BINARY version of Sloan 1996 (PT #27, yesterday)’s accruals variable. Sloan showed accruals persist at 0.765 vs cash flows at 0.855 (F-test rejects equality; Table 3), and a long-low-accrual / short-high-accrual hedge portfolio earned 10.4% in year 1 (t=4.71). Piotroski reduces this to F_ACCRUAL = 1 if CFO > ROA — the binary indicator that accruals are negative, i.e. earnings are backed by real cash flow.

F_ROA (current-year ROA > 0) is a binary version of Sloan’s earnings-persistence measure (Sloan’s a_1 = 0.841). Piotroski composes Sloan’s accruals + Ou-Penman (1989) mechanical fundamental analysis + Lev-Thiagarajan (1993) signal-based fundamental analysis into ONE 9-signal composite you can screen on with a single integer cutoff.

Downstream lineage: Novy-Marx 2013, FF 2015 RMW factor

F_ΔMARGIN — Piotroski’s operating-efficiency signal for whether gross margin increased YoY — is a binary version of Novy-Marx 2013 (PT #24)’s gross-profitability = GP/Assets. Novy-Marx uses the LEVEL of gross profitability as a continuous predictor, hedging value with correlation -0.57 and a combined 50/50 mix Sharpe of 0.85 all-cap; Piotroski uses the CHANGE in gross margin as one of 9 binaries.

Piotroski 2000 is the earliest paper to document a positive alpha from a profitability-tilted screen WITHIN value portfolios — 13 years before Novy-Marx formalised the continuous-predictor version, 15 years before Fama-French 2015 (PT #22) added RMW as a formal factor.

The PEAD cross-link

Piotroski reports (verbatim abstract sentence 4): “⅙ of the annual return difference between ex ante strong and weak firms is earned over the four three-day periods surrounding these quarterly earnings announcements.” F_SCORE screening at portfolio formation identifies future PEAD (Bernard-Thomas 1989, PT #6) winners AHEAD of time, using only public accounting data at zero cost.

Practical implication (Piotroski’s own reading): the market underreacted to information already in the balance sheet, and the earnings-announcement window is where that underreaction gets partially corrected. About 17% of the full annual return spread earned by the F_SCORE hedge is delivered over 12 announcement days per year (4 quarterly windows × 3 days each). The rest (~83%) is delivered gradually across the other ~240 trading days.

Sample and methodology

Sample: 14,043 high book-to-market firm-year observations between 1975 and 1995 (measured 1976-1996 for returns). Each year, Piotroski identifies firms with sufficient stock price and book value data on Compustat, calculates the market value of equity and BM ratio at fiscal year-end. High-BM = top quintile of BM ratio each year. Approximately 75,000 total firm-year observations 1976-1996, of which 14,043 were high-BM (top quintile).

Returns: measured as one-year buy-and-hold returns starting 4 months after fiscal year-end (delay ensures financial statements are public). Market-adjusted = raw minus value-weighted market return. Tests use both traditional t-statistics and bootstrap procedures based on 1,000 iterations for medians and proportions.

Verification note

Full primary-source verified 2026-08-28 via WebFetch of https://www.chicagobooth.edu/~/media/fe874ee65f624aaebd0166b1974fd74d.pdf and pymupdf text extraction (42 pages, 106,153 characters text-native no OCR required). Authorship, abstract, sample (n=14,043 high BM firm-year observations 1976-1996), F_SCORE composite formula (9 signals), all four headline return numbers (7.5 pp mean-return gain, 23% hedge return, 9.2 pp / 11.3 pp top-vs-bottom quintile spread), and the PEAD cross-link (⅙ of annual return spread earned on 12 earnings-announcement days) all verified verbatim.

The Chicago Booth PDF is Piotroski’s own University of Chicago GSB Selected Paper 84 reprint (© 2002 University of Chicago) of the JAR 2000 paper — same author, same content, just re-typeset for the GSB Selected Paper series. Counts as full primary-source access because it is Piotroski’s own paper published by his own institution. Twentieth Paper Trail out of 28 with full primary-source access (as of today, 2026-08-28).

Keep reading