Method and sources
Every rule that sets a number or a verdict in a report, in plain words, with the research behind it. Each report marks its numbers with small note numbers 1 and lists the sources it used at the end.
25 rules, 44 published sources (23 checked in the full text, 16 from a summary, 5 not verified yet) and 6 of our own tests. How we mark each source:
- Checked we read the passage in the full source.
- Summary taken from the abstract or a published summary.
- Not verified yet named in our reviews but not checked; never the only support for a rule and never stated as fact.
- Our test a test we ran ourselves. Where it decides anything, the test was written down before we saw its result.
The rules
Grouped by topic. Each rule says what it does, which sources back it and where it lives in our code.
Discount rate and risk
Market risk premium
The discount rate uses the market risk premium implied by S&P 500 prices (Damodaran's monthly figure, restated on the report's Treasury rate), never one solved from our own model.
Beta pulled toward 1
A company's beta is pulled toward 1 (two-thirds its own, one-third the market's) within 0.8-1.6, and is 1 for the years after the forecast.
Growth and base rates
Growth held to base rates
Years 1-2 use the analysts' revenue forecasts; years 3-5 are held to what companies of the same size achieved after a fast year (75th percentile in the base case, 90th only in the bull case).
Growth fades by year 10
Growth fades to the long-run rate by year 10 for every company: a moat lengthens high returns, not high growth.
Bull and bear from what companies really did
The bull and bear cases grow sales at the 90th and 10th percentile of five-year growth of companies of the same type and size (the size class when the type has too few), because real growth is about twice as spread out as forecasts and skewed upward.
Competitive advantage and returns on capital
Moat from the company's own record
The moat rating comes from reported numbers: how often and by how much return on capital beat the cost of capital over up to 10 years, and how stable margins were. It sets how long excess returns last.
Returns on new investment fade
Returns on new investment start at no more than 35% and fade toward the cost of capital from year 1, slower for wide moats and steady sectors, faster for energy and materials; growth adds value only while they exceed the cost of capital.
Small permanent excess return for moats
After the forecast, new investment by a wide-moat company keeps at most 4 points above the cost of capital (narrow 1.5, none 0) instead of exactly the cost of capital.
Valuation methods and the blend
Several valuation methods, blended
The fair value blends several methods because cash-flow and comparable-company values together explain prices better than either alone; no single method gets more than 35% of the weight.
Cyclicals valued on mid-cycle margins
For cyclical companies, cash flow and the own-history value use the median margin of up to 10 years times today's revenue, not this year's margin.
Peer multiples: harmonic mean, forward P/E first
Peer multiples use the harmonic mean of comparable companies, with forward P/E weighted most and price/sales least.
Drug pipelines valued by phase success rates
Each drug is valued by its chance of approval for its phase and disease area and by the years still to launch (9, 6, 3 and 1 from phases I, II, III and filing).
Buy and sell lines, uncertainty
Buy and sell lines grow with uncertainty
The upside needed for a Buy (and the downside for a Sell) grows with how uncertain the value is; the strong-buy and strong-sell lines are Morningstar's 5-star and 1-star levels, and at extreme uncertainty the buy and sell lines are its 4-star and 2-star levels; higher-quality companies may be held longer.
What sets the uncertainty level
Uncertainty rises with 12-month price swings (100% or more a year is extreme), with how far apart the analysts' earnings forecasts are (top fifth or tenth of companies), and with a distress score in the riskiest 5% of companies.
Not reliably valued
When our methods disagree too much and fewer than two fundamental methods give a value, we publish the range they support and no single fair value, and the call stays at Hold.
What the price expects, analysts
Analyst targets: small weight
The analysts' average price target, in today's money, gets at most 15% of the blend because targets are optimistic and often missed.
What you need to believe
We state the sales growth today's price needs on the same model as ours, next to how often companies of this size grew that fast.
What the price expects
We turn the price back into the growth it implies and compare it with the company's trend; the most optimistic expectations were followed by low returns, so 'priced for perfection' can hold a Buy back.
Accounting quality and red flags
Accounting red flags: scores, not AI labels
Only scores the code computes can disqualify a stock for its accounts (an earnings-manipulation score, accruals and a misstatement score), and only when at least two agree; an AI red flag can at most lower conviction one level.
Debt distress
A company in its industry's highly leveraged band whose market distance to default is 1 or less is disqualified; in our 2012-2022 test such companies became distressed far more often than the rest.
Distress score: shown, never a disqualification
We show a published 12-month failure probability built from profits, debt, cash, returns, volatility and size; in our 2012-2019 test it was less precise than the distance to default, so it only raises the uncertainty and never disqualifies.
Value-trap check
A cheap stock whose F-score is 3 or less cannot get a Buy: the F-score separates winners from losers among cheap stocks.
Return signals: share issuance and profitability
Share issuance + cash profitability screen
Companies that issue few new shares and earn high cash operating profits did better than their industry peers; the screen passed a pre-registered test on years it had not seen, so it may move conviction one level, never the action.
Signal composite: information only
The wider seven-theme signal composite failed its pre-registered test on 2012-2022, so it is shown for information only and never moves the verdict.
AI forecasts and probabilities
Scenario chances from base rates
Scenario chances are fixed (30% bear, 40% base, 30% bull, the weights that keep the spread of outcomes with bull and bear at the 90th and 10th percentile), not an AI's guess: AI-stated probabilities tend to be optimistic and overconfident.
Bibliography
Every source the rules cite, grouped by topic.
Discount rate and risk
Blume (1975). Betas and their regression tendencies. Journal of Finance. Not verified yet
Named in our reviews; we have not checked it yet, so we do not rely on it alone.
Damodaran (2026). Implied equity risk premium, monthly update of 1 September 2026. NYU Stern, author home page. Checked
The implied equity risk premium of the S&P 500 was 4.14% on 1 September 2026 with a 4.75% Treasury rate, backed out from index prices and expected cash flows.
Damodaran (2026). The Price of Risk. Musings on Markets (blog), March 2026. Checked
Use the current implied premium to stay market-neutral; a fixed premium in a crisis makes most companies look undervalued.
Growth and base rates
Chan, Karceski & Lakonishok (2003). The Level and Persistence of Growth Rates. Journal of Finance 58(2). Checked
Analysts' long-term growth forecasts were far above realized growth (median 14.5% forecast vs about 9% realized over five years), and only about 10% of firms grew above 18% a year over 10 years.
Keefer & Bodily (1983). Three-point approximations for continuous random variables. Management Science 29(5). Not verified yet
Named in our reviews; we have not checked it yet, so we do not rely on it alone.
Koller, Goedhart & Wessels (McKinsey) (2010). Valuation, 5th edition. Wiley. Checked
Companies growing faster than 20% a year after inflation typically grow about 8% within five years and fall below 5% within 10; returns on capital fade much more slowly than growth, and assuming new investment earns only the cost of capital understates firms with lasting brands or patents.
Mauboussin, Callahan & Majd (2016). The Base Rate Book. Credit Suisse, 26 September 2016. Checked
Of companies with sales above $50 billion, about 3 in 100 grew more than 20% a year after inflation over three years; returns on capital fade at sector-specific speeds (four-year persistence 0.35 for energy to 0.78 for consumer staples).
Competitive advantage and returns on capital
Damodaran (n.d.). The Little Book of Valuation: terminal value. NYU Stern, author web page. Checked
Firms with strong, lasting advantages may keep modest excess returns forever (under 4-5%); betas move toward one in stable growth; stable growth should not exceed the riskless rate.
Fama & French (2000). Forecasting Profitability and Earnings. Journal of Business 73(2). Summary
Profitability reverts toward its expected level by about 38% a year, faster when it is below the mean.
Mauboussin & Callahan (2014). What Does a Price-Earnings Multiple Mean?. Credit Suisse, 29 January 2014. Checked
Steady-state value is normalized after-tax operating profit divided by the cost of capital; growth adds value only when new investment earns more than the cost of capital.
Mauboussin & Callahan (2016). Measuring the Moat. Credit Suisse, 1 November 2016. Checked
Value creation has two dimensions: how far returns exceed the cost of capital and how long that lasts; high returns with heavy investment fade fastest.
Nissim & Penman (2001). Ratio Analysis and Equity Valuation. Review of Accounting Studies 6. Checked
Residual operating income persists at a non-zero level for many portfolios, so a typical terminal value keeps a constant positive residual income rather than none.
Valuation methods and the blend
BIO, Informa Pharma Intelligence & QLS Advisors (2021). Clinical Development Success Rates and Contributing Factors 2011-2020. Biotechnology Innovation Organization, February 2021. Checked
Likelihood of approval from phase I is 7.9% (phase II 15.1%, phase III 52.4%, filed 90.6%), from 5.3% in oncology to 23.9% in hematology; phase I to approval takes 10.5 years on average (2.3 + 3.6 + 3.3 + 1.3).
Clemen (1989). Combining forecasts: a review. International Journal of Forecasting. Not verified yet
Named in our reviews; we have not checked it yet, so we do not rely on it alone.
Damodaran (n.d.). Normalized earnings (valuation questions). NYU Stern, author web page. Summary
For cyclical firms, normalized operating income is revenue times the average margin over a whole cycle (5-10 years) rather than a forecast of the next cycle.
Graham & Dodd (1934). Security Analysis. Not verified yet
Named in our reviews; we have not checked it yet, so we do not rely on it alone.
Kaplan & Ruback (1995). The Valuation of Cash Flow Forecasts: An Empirical Analysis. Journal of Finance 50(4). Checked
Using discounted cash flow and comparable-company methods together explains significantly more of transaction values than either method alone.
Liu, Nissim & Thomas (2002). Equity Valuation Using Multiples. Journal of Accounting Research 40(1). Checked
Forward earnings multiples explain prices best and sales multiples worst; accuracy improves with the harmonic mean and with same-industry peers.
Wong, Siah & Lo (2019). Estimation of clinical trial success rates and related parameters. Biostatistics 20(2). Checked
Over 2000-2015, 13.8% of drug development programs went from phase I to approval (3.4% in oncology), higher than counts by phase transition.
Buy and sell lines, uncertainty
Asness, Frazzini & Pedersen (2013). Quality Minus Junk. AQR working paper, 9 October 2013 (Review of Accounting Studies 24(1), 2019). Checked
High-quality stocks (profitable, growing, safe) have higher prices on average, but not by a very large margin, and earn positive risk-adjusted returns.
Diether, Malloy & Scherbina (2002). Differences of Opinion and the Cross Section of Stock Returns. Journal of Finance 57(5). Summary
Stocks with a higher dispersion of analysts' earnings forecasts earn lower future returns, most in small stocks and past losers.
Morningstar (2022). Equity Research Methodology. Morningstar, 29 September 2022. Checked
A moat is the duration of excess returns (narrow at least 10 years, wide likely 20); the star ratings need a larger discount to fair value as uncertainty rises: 5 stars at a price / fair value of 0.80 (low), 0.70 (medium), 0.60 (high), 0.50 (very high) and 0.25 (extreme), 1 star at 1.25 / 1.35 / 1.55 / 1.75 / 4.00; at extreme uncertainty 4 stars at 0.50 and 2 stars at 2.00.
van der Bles, van der Linden, Freeman & Spiegelhalter (2020). The effects of communicating uncertainty on public trust in facts and numbers. PNAS 117(14). Summary
Showing a numeric range lowers confidence in the number but not trust in the source.
What the price expects, analysts
Bordalo, Gennaioli, La Porta & Shleifer (2019). Diagnostic Expectations and Stock Returns. Journal of Finance 74(6). Checked
Stocks with the most optimistic analyst long-term growth earned about 3% in the next year, against 15% for the least optimistic.
Bordalo, Gennaioli, La Porta & Shleifer (2024). Belief Overreaction and Stock Market Puzzles. Journal of Political Economy 132(5). Checked
Long-term growth expectations predict both the errors in those expectations and stock returns: good news leads to over-optimism, then disappointment and low returns.
Bradshaw, Brown & Huang (2013). Do sell-side analysts exhibit differential target price forecasting ability?. Review of Accounting Studies 18(4). Summary
Only 38% of 12-month price targets were met at the 12-month horizon, and target-implied returns were about 15% above realized returns on average.
Rappaport & Mauboussin (2001). Expectations Investing. Harvard Business School Press (revised edition Columbia Business School Publishing, 2021). Summary
Start from what the price implies (a reverse DCF) and ask how likely the needed revisions are.
Accounting quality and red flags
Beneish (1999). The Detection of Earnings Manipulation. Financial Analysts Journal 55(5). Checked
At the cut-off M > -1.78 (error costs 20:1 to 30:1) the model flagged 13.8% of non-manipulators and missed 26% of manipulators in the estimation sample, 7.2% and 50% in the holdout.
Bharath & Shumway (2008). Forecasting Default with the Merton Distance to Default Model. Review of Financial Studies 21(3). Summary
A naive distance to default performs slightly better in hazard models and out of sample than the solved Merton model.
Campbell, Hilscher & Szilagyi (2008). In Search of Distress Risk. Journal of Finance 63(6). Checked
A logit on profitability, leverage, past excess returns, volatility, size, cash, market-to-book and price predicts failure 12 months ahead (pseudo-R2 0.114); distance to default adds little once it is in (NBER working paper 12362, Tables 4-5).
Dechow et al. (n.d.). Misstatement F-score. Not verified yet
Named in our reviews; we have not checked it yet, so we do not rely on it alone.
Green, Hand & Soliman (2011). Going, going, gone? The apparent demise of the accruals anomaly. Management Science 57(5). Summary
Accrual hedge returns decayed until they were no longer reliably positive, so accruals are a quality check, not a return signal.
Piotroski (2000). Value investing: the use of historical financial statement information to separate winners from losers. Journal of Accounting Research 38 (Supplement). Checked
Among cheap (high book-to-market) stocks, picking financially strong firms added at least 7.5% a year; it is a screen within value stocks, not a general quality score.
Sloan (1996). Do stock prices fully reflect information in accruals and cash flows about future earnings?. The Accounting Review 71(3). Summary
The founding result on accruals: earnings driven by accruals rather than cash are less persistent.
Return signals: share issuance and profitability
Ball, Gerakos, Linnainmaa & Nikolaev (2016). Accruals, cash flows, and operating profitability in the cross section of stock returns. Journal of Financial Economics 121(1). Summary
Cash-based operating profitability outperforms profitability measures that include accruals and subsumes accruals in predicting returns.
Daniel & Titman (2006). Market reactions to tangible and intangible information. Journal of Finance 61(4). Summary
A composite equity issuance measure independently forecasts returns.
Jensen, Kelly & Pedersen (2023). Is there a replication crisis in finance?. Journal of Finance 78(5). Checked
Most return factors replicate; 153 factors form 13 themes, among them leverage, debt issuance and quality; a positive but smaller return after publication is the expected outcome.
Kozak, Nagel & Santosh (2020). Shrinking the cross-section. Journal of Financial Economics 135(2). Summary
A few principal components with an economic shrinkage prior hold up out of sample; models built on a handful of characteristics cannot summarize the cross-section.
McLean & Pontiff (2016). Does academic research destroy stock return predictability?. Journal of Finance 71(1). Summary
Across 97 predictors, returns were 26% lower out of sample and 58% lower after publication.
Pontiff & Woodgate (2008). Share issuance and cross-sectional returns. Journal of Finance 63(2). Summary
After 1970, share issuance predicts returns more significantly than size, book-to-market or momentum on their own.
AI forecasts and probabilities
Chen, Green, Gulen & Zhou (2024). What Does ChatGPT Make of Historical Stock Returns? Extrapolation and Miscalibration in LLM Stock Return Forecasts. arXiv 2409.11540. Checked
A large language model extrapolated past returns, was more optimistic than history, and its forecast intervals covered fewer outcomes than a plain historical range.
Halawi et al. (2024). Approaching Human-Level Forecasting with Language Models. Checked
On questions after the model's training cut-off, an LLM forecasting system came close to, but stayed behind, the human crowd.
Schoenegger et al. (2024). Wisdom of the Silicon Crowd. Summary
An ensemble of 12 language models matched a human crowd on 31 questions, but its forecasts leaned toward yes (mean above 50%).
Xiong et al. (2023). Can LLMs Express Their Uncertainty?. ICLR 2024. Summary
Confidence stated in words by language models is overconfident; agreement across samples helps.
Our own tests and reviews
StockXray research (2026). Growth after a fast year: conditional base rates of 3-5 year revenue growth. internal study. Our test
Companies with revenue of $50 billion or more that grew at least 25% in a year grew a median 6.7% a year in years 3-5 afterwards (75th percentile 14.5%, 90th 24.9%). Internal write-up, not yet published.
StockXray research (2026). Survivorship-free S&P 500 + 400 point-in-time panel (FW-86). internal backtest. Our test
1,466 companies on 43 dates from 2012 to 2022, using only data known at each date; highly leveraged companies with a market distance to default of 1 or less became distressed within 24 months in 59-66% of cases in 2012-19 and 43% in 2020-22. Internal write-up, not yet published.
StockXray research (2026). Signal composite: pre-registration and result. internal. Our test
An equal-weight composite of seven return-signal themes failed its pre-registered bar on 2012-2022 (12-month rank IC +0.016), so it is shown for information only and never moves a verdict. Internal write-up, not yet published.
StockXray research (2026). Issuance + cash profitability screen: pre-registration. internal. Our test
The screen's exact formula, pass bar and one-time use of the sealed 2023-2025 period were written down and committed before any of that period's data was computed. Internal write-up, not yet published.
StockXray research (2026). Issuance + cash profitability screen: sealed 2023-2025 test. internal. Our test
On years it had not seen (2023-2025, 11 dates), the screen ranked 12-month sector-neutral returns with a rank IC of +0.074 (t 2.8), top minus bottom decile +6.9%; it passed the pre-registered bar, with 3 of 14 industry families negative (energy, semis, tech). Internal write-up, not yet published.
StockXray research (2026). Campbell-Hilscher-Szilagyi distress score on the 2012-2019 point-in-time panel (SC-08). internal backtest. Our test
On 23,329 company-dates in 2012-2019, the top 5% by the score were distressed within 24 months in 46% of cases (base rate 13%), but among highly leveraged companies the score alone (distance to default above 1) caught distress in 49% of cases against 62% for a distance to default of 1 or less, so it raises uncertainty and never disqualifies. Internal write-up, not yet published.