Análisis Fundamental

Número de Graham

Q: ¿Qué pasa si la empresa tiene EPS negativo?

La fórmula no aplica — √(negativo) produces imaginary number. Graham intentionalmente excluyó empresas con earnings negativos del universe defensive investor. Su argument: empresa que no ha sido consistentemente profitable 10 años es demasiado risky para defensive portfolio. En práctica moderna, algunos analistas ajustan usando average earnings 5-10 años si reciente year es negative pero historical positive. Pero Graham purists insist en requiring positive earnings every year during 10 years prior.

Q: ¿Por qué Graham Number no funciona para empresas tech?

Porque subestima intangible value. Tech companies típicamente tienen low BVPS relative to market value (software, brands, IP, customer relationships son intangibles). Ejemplo: Microsoft BVPS ~$13, EPS ~$11 → Graham Number = √(22.5 × 11 × 13) = √3,218 = $57. Microsoft cotiza a $400+. El gap entre Graham Number ($57) y market price ($400) no signifies overvaluation — signifies que Graham Number no captures el value de Microsoft's cloud business, Office franchise, gaming, y AI positioning. Para tech, usar DCF, EV/EBITDA, EV/Sales en lugar de Graham Number. Para banks, consumer staples, industrials with physical assets, Graham Number remains más applicable.

Q: ¿Walter Schloss usaba Graham Number strictly?

Sí, rigurosamente. Walter Schloss (1916-2012), disciple directo de Graham en Graham-Newman Corporation, operó portfolio de 50-100 positions during 50+ years (1955-2002), rigorously screening candidates using Graham frameworks incluyendo Graham Number. Retornos: ~15.3% anualizado vs S&P 500 ~10% — 5 percentage points of alpha anualizado durante half-century. Schloss frequently bought stocks en single-digit P/E y debajo de Book Value, muchos of which eran Graham Number candidates. Su track record es proof empírico que disciplined application de Graham methodology works long-term, even in supuestamente "efficient" US market. Schloss operated from small office en NYC sin research staff — solo él y su son. Pure Graham value investing adapted successfully to modern era.

Q: ¿Qué opciones uso con Graham Number framework?

Value-seeking strategies: (1) Cash-secured puts con strike at Graham Number level — si asignan, entry at defensive value. (2) Long calls o LEAPS sobre stocks temporarily below Graham Number during crises — mean reversion plays. (3) Bull put spreads con short strike at Graham Number — income with defined risk. (4) Covered calls sobre holdings trading well above Graham Number — locks partial gains. Risk management: (5) Protective puts en holdings trading 2×+ Graham Number — limits downside while maintaining upside. (6) Avoid naked short puts en stocks trading >3× Graham Number — no margin of safety means reversion can be severe. Framework: treat Graham Number as fundamental value floor; structure options strategies alrededor de proximity to ese floor.

EN: Graham Number / Graham Formula PT: Número de Graham

La fórmula más famosa de Benjamin Graham para determinar el valor máximo defensivo de una acción — raíz cuadrada de (22.5 × EPS × Book Value per Share). Combina P/E ≤15 y P/B ≤1.5 en un solo número que define el ceiling de precio que un investor conservador debería pagar.

Neutral Fuerza: Media Tasa histórica: Graham Number + quality confirmation produces excellent long-term returns pero filter muy restrictivo en mercados modernos (produces pocos candidates excepto durante crises) Confirmación: Opcional Defensive screening, market crashes, emerging markets, small-caps underfollowed, industrials/financials con tangible assets.

Qué es el Número de Graham

El Número de Graham (Graham Number o Graham Formula, en portugués Número de Graham) es una fórmula elegante desarrollada por Benjamin Graham —el padre del value investing— en su libro clásico "The Intelligent Investor" (1949, revised editions 1959, 1973). La fórmula calcula el valor máximo intrínseco que un investor defensivo debería pagar por una acción. Fórmula: Graham Number = √(22.5 × EPS × Book Value per Share). El coeficiente 22.5 viene de combinar dos constraints defensive: P/E máximo de 15 × P/B máximo de 1.5 = 22.5. Graham argumentaba: (a) un investor defensivo no debería pagar más de 15× earnings (implicando earnings yield ≥6.7%); (b) similarly no debería pagar más de 1.5× book value (margin of safety relative to tangible assets). Estas dos conditions simultáneas produce la fórmula. Ejemplo: empresa con EPS $3 y Book Value per Share $20 → Graham Number = √(22.5 × 3 × 20) = √1,350 = $36.74. Si la acción cotiza a $30, está cotizando debajo de Graham Number — potencialmente undervalued para defensive investor. Si cotiza a $50, está sobre Graham Number — overvalued en framework defensive de Graham. La fórmula representa el "margin of safety" cuantitativamente — comprando debajo de Graham Number, tu thesis tiene amortiguación doble (earnings support + asset support). Warren Buffett repite: "The three most important words in investing are margin of safety." El Graham Number es la implementación matemática más simple de ese concepto.

Matemática Detrás del 22.5

La constante 22.5 no es arbitraria — deriva matemáticamente de los thresholds defensivos que Graham consideraba sensatos. Derivación: si P/E max = 15 y P/B max = 1.5, entonces el producto P/E × P/B = 15 × 1.5 = 22.5. Ahora, (P/E) × (P/B) = (Price/EPS) × (Price/BVPS) = Price² / (EPS × BVPS). Resolviendo para Price: Price² = (P/E × P/B) × EPS × BVPS = 22.5 × EPS × BVPS. Tomando raíz cuadrada: Price_max = √(22.5 × EPS × BVPS) = Graham Number. Esto significa que el Graham Number representa el precio al cual simultaneously P/E = 15 y P/B = 1.5. A precios menores, ambos ratios mejoran (más margen de seguridad); a precios mayores, al menos uno está above threshold. Variantes históricas: Graham publicó variants durante su carrera. (1) Versión original (1949): P/E max 15, P/B max 1.5 → constant 22.5. (2) Versión 1959 (revised): ajustado para considerations inflation. (3) Versión moderna (algunos analistas): usan P/E max 20 y P/B max 2.5 → constant 50, produciendo valoraciones más "generosas" pero menos defensive. Para análisis riguroso, stick with original 22.5. La elegancia del insight es que la combinación de earnings y book value captures both income-producing capacity (EPS) y downside protection (BVPS). Graham: "Los números son las únicas palabras que el mercado entiende sin traducir." El Graham Number reduce valuation a un single number calculable quickly, comparable directly con market price.

Cómo Usar el Graham Number

La aplicación práctica del Graham Number es sistemática. Paso 1: obtener EPS (trailing 12 months o average últimos 3-5 años para smoother). Paso 2: obtener Book Value per Share del balance sheet más reciente. Paso 3: calcular Graham Number = √(22.5 × EPS × BVPS). Paso 4: comparar con market price. Paso 5: si Market Price < Graham Number, potential value. Si >, overvalued for defensive investor. Ejemplo práctico: JPMorgan Chase en Q1 2023: EPS $15, BVPS $95. Graham Number = √(22.5 × 15 × 95) = √32,062 = $179. Si JPM cotiza a $130, claramente debajo de Graham Number = defensive value signal. Si cotiza a $200, overvalued en framework defensive. Thresholds adicionales Graham: para un stock pasar "defensive investor test" completo (no solo Graham Number), también debería: (1) Dividend yield > 2/3 of AAA bond yield; (2) Current Ratio > 2.0; (3) Positive earnings cada año últimos 10 años; (4) Dividend uninterrupted por 20+ años; (5) Earnings growth ≥ 33% over 10 years (using 3-year averages). Graham Number alone es insuficiente — es uno de múltiples filters. Modern Graham-style screens combinan Graham Number con Altman Z-Score, ROE sostenido, y low debt. When Graham Number fails: (a) Tech companies con low BVPS y high EPS —Graham Number suele dar valores nonsensically low para Apple, Microsoft, Google. Obvio: Graham Number no captures intangible value. (b) Early-stage companies con negative EPS —fórmula produces complex (imaginary) numbers. No applicable. (c) Cyclical businesses at peak earnings —normalized earnings are better than trailing. (d) High-quality businesses que merecen premium (Buffett: "It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price"). Graham Number tiende a filter out todas las wonderful businesses — las finds solo durante crises.

Evolución del Value Investing: Graham a Buffett

El Número de Graham representa el early value investing de los 1930s-1950s, antes de que Warren Buffett (estudiante de Graham en Columbia) evolucionara el approach hacia "quality at reasonable price." Graham approach (deep value): buy below tangible liquidation value (Net-Nets), buy debajo de Graham Number, diversify extensively (100+ positions) porque individual companies pueden ser low-quality. Focus en statistical bargains. Funciona excepcionalmente durante market crashes y bear markets. Durante los 1930s-1960s produjo retornos del 20%+ anualizado. Buffett evolution (quality): influenced por Charlie Munger, Buffett pivoted de Graham Net-Nets a buying wonderful businesses at fair prices. "It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price." Focus en moats, pricing power, sustainable ROE. Pay premium over book value para access quality. Coca-Cola en 1988 era at ~$10 con BVPS ~$3 (P/B 3.3×) — Graham Number <$10 no applicable. Pero Buffett paid $1B anyway porque quality of franchise. Position valio $25B+ eventually. Modern reality: pocos analistas aplican Graham Number strictly. Razones: (a) US markets más efficient hoy —Graham Number candidates son raros excepto en crises. (b) Intangible-heavy economy —book value menos relevant para muchos quality businesses modern. (c) Growth investing dominates — willingness to pay higher multiples for growth. Pero el concepto de margin of safety sigue siendo foundational. Terry Smith (Fundsmith) applies modified Graham thinking: "Do not overpay" es principio core. Walter Schloss (Graham disciple) seguía aplicando Graham Number strictly through 2010s con retornos excellent. Seth Klarman, Bruce Berkowitz, y otros value investors continuan usando Graham frameworks adapted to modern reality. When Graham Number is most useful today: (a) durante market crashes (2008, 2020, 2022) cuando multiples compress hacia Graham levels; (b) en emerging markets menos efficient; (c) en small/microcaps underfollowed by institutional analysts; (d) como sanity check for traditional value metrics rather than primary filter.

Operativa y Aplicación en Opciones

El uso operativo del Graham Number. Defensive screening: filtrar universe a stocks trading below Graham Number + Altman Z-Score >2.5 + positive earnings multi-year. Esta combinación identifica statistically-cheap-and-safe candidates. Market crash opportunity identification: durante major corrections (2008, 2020), muchos quality stocks cross below Graham Number temporarily. Buying durante estos moments históricamente produce excellent forward returns. Conservative portfolio construction: para retirement accounts o capital preservation, restrict purchases a stocks below Graham Number + quality confirmation. Aunque los returns pueden be below market during bull markets, drawdowns son significantly smaller during bear markets. Peer comparison: within industry, stocks trading closest to Graham Number with comparable business quality = best relative value. Defensive investor test: combinar Graham Number con other Graham criteria (Current Ratio >2, positive earnings 10 years, dividend 20 years, earnings growth 33% over 10 years) produces rigorous defensive screen. Empresas passing all tests son extremely rare pero historically outperformed. Opciones: (a) Cash-secured puts con strike at Graham Number level — si asignan, entras at defensive-value price. Meanwhile collect premium. Ejemplo: stock at $50, Graham Number $40, sell puts strike $40 collecting $2 premium → effective entry $38 if assigned, or free $2 if not. (b) Long calls sobre stocks briefly below Graham Number during market stress — leveraged exposure to mean reversion. Ejemplo histórico: March 2020, many quality stocks briefly below Graham Number, LEAPS calls produced 5-10× returns over 2 years. (c) Bull put spreads con short strike at Graham Number — risk-defined income strategy con meaningful value floor. (d) Covered calls sobre holdings trading well above Graham Number — locks in gains partial sin sacrificing all upside. (e) Avoid naked calls o high-premium strategies en stocks trading significantly above Graham Number — no margin of safety means any reversion is severe. (f) Contrarian plays: when entire market sector (banks, energy, etc.) trades below Graham Number simultáneamente, ETF options (XLF, XLE) provide diversified exposure con reduced single-stock risk. Caso histórico: March 2020 COVID crash — JPMorgan Chase briefly traded at $75 cuando Graham Number era ~$130. Cash-secured puts at $75 strike collecting 10% premium produced: if assigned, entry at $67 (putting holder at extreme defensive value); if not assigned, 40%+ annualized return en collateral. Equivalent opportunities arise every 5-10 years during major crises. Graham Number es tool para identificar estos moments cuantitativamente en lugar de depend on gut feeling.

Graham Number vs. Otros Modelos de Valor Intrínseco

Graham Number es la forma más simple; otros modelos son más comprehensive pero require más assumptions.

Modelo	Simplicidad	Inputs	Mejor Uso
Graham Number	Máxima (3 inputs)	EPS, BVPS, constant	Quick value screening
DDM (Gordon)	Alta	D, r, g	Dividend payers
DCF	Baja (detailed)	Full forecasts + WACC	Comprehensive valuation
P/E × Book	Muy alta	P/E, BVPS	Quick ceiling estimate
Residual Income	Media	Book value, ROE, r	Intermediate analysis

Preguntas Frecuentes

¿Por qué 22.5 y no otro número?

Deriva matemáticamente de las dos conditions defensive de Graham: P/E máx 15 × P/B máx 1.5 = 22.5. Graham argued que 15× earnings es el máximo razonable para defensive investor (implying earnings yield ≥6.7%, better than bonds), y 1.5× book value es el máximo razonable para mantener margin of safety relative to tangible assets. La combinación produce 22.5. Graham considered estos thresholds the floor of "conservative" pricing — comprar por arriba violates defensive principles.

¿Qué pasa si la empresa tiene EPS negativo?

La fórmula no aplica — √(negativo) produces imaginary number. Graham intentionalmente excluyó empresas con earnings negativos del universe defensive investor. Su argument: empresa que no ha sido consistentemente profitable 10 años es demasiado risky para defensive portfolio. En práctica moderna, algunos analistas ajustan usando average earnings 5-10 años si reciente year es negative pero historical positive. Pero Graham purists insist en requiring positive earnings every year during 10 years prior.

¿Por qué Graham Number no funciona para empresas tech?

Porque subestima intangible value. Tech companies típicamente tienen low BVPS relative to market value (software, brands, IP, customer relationships son intangibles). Ejemplo: Microsoft BVPS ~$13, EPS ~$11 → Graham Number = √(22.5 × 11 × 13) = √3,218 = $57. Microsoft cotiza a $400+. El gap entre Graham Number ($57) y market price ($400) no signifies overvaluation — signifies que Graham Number no captures el value de Microsoft's cloud business, Office franchise, gaming, y AI positioning. Para tech, usar DCF, EV/EBITDA, EV/Sales en lugar de Graham Number. Para banks, consumer staples, industrials with physical assets, Graham Number remains más applicable.

¿Walter Schloss usaba Graham Number strictly?

Sí, rigurosamente. Walter Schloss (1916-2012), disciple directo de Graham en Graham-Newman Corporation, operó portfolio de 50-100 positions during 50+ years (1955-2002), rigorously screening candidates using Graham frameworks incluyendo Graham Number. Retornos: ~15.3% anualizado vs S&P 500 ~10% — 5 percentage points of alpha anualizado durante half-century. Schloss frequently bought stocks en single-digit P/E y debajo de Book Value, muchos of which eran Graham Number candidates. Su track record es proof empírico que disciplined application de Graham methodology works long-term, even in supuestamente "efficient" US market. Schloss operated from small office en NYC sin research staff — solo él y su son. Pure Graham value investing adapted successfully to modern era.

¿Qué opciones uso con Graham Number framework?

Value-seeking strategies: (1) Cash-secured puts con strike at Graham Number level — si asignan, entry at defensive value. (2) Long calls o LEAPS sobre stocks temporarily below Graham Number during crises — mean reversion plays. (3) Bull put spreads con short strike at Graham Number — income with defined risk. (4) Covered calls sobre holdings trading well above Graham Number — locks partial gains. Risk management: (5) Protective puts en holdings trading 2×+ Graham Number — limits downside while maintaining upside. (6) Avoid naked short puts en stocks trading >3× Graham Number — no margin of safety means reversion can be severe. Framework: treat Graham Number as fundamental value floor; structure options strategies alrededor de proximity to ese floor.