Graham Number How to Measure Stock Value Easily

Core Description

• The Graham Number is a classic value investing metric that provides a conservative upper-bound stock price by blending earnings and book value.
• Modern investors utilize it as a first-pass screening tool, recognizing its strengths and limitations amid evolving accounting norms and business models.
• Used correctly, it encourages disciplined entry prices, but should always be supplemented with deeper fundamental and qualitative analysis.

Definition and Background

The Graham Number originated from Benjamin Graham’s foundational work on value investing, most notably in Security Analysis and The Intelligent Investor. Graham proposed that investments should be anchored to tangible assets and historically demonstrated earning power, especially for conservative or “defensive” investors who are cautious about speculation. Over the years, practitioners formalized the Graham Number formula, which encapsulates Graham’s philosophy by setting a ceiling for a stock’s fair price based on its profitability and asset protection.

Historical Roots and Evolution
During the mid-20th century, U.S. asset managers and insurance companies informally used Graham-like screens by applying combined price-to-earnings (P/E) and price-to-book (P/B) constraints to avoid overpaying for companies—especially cyclicals and industrials. This practice led to the widely cited formula:
Graham Number = sqrt(22.5 × EPS × BVPS)

The constant 22.5 was derived from the maximum multipliers Graham considered reasonable (P/E of 15 and P/B of 1.5), providing a “defensible” upper price limit for prudent investors.

Academic and Practitioner Influence
Academic research since the 1980s examined the effectiveness of screens based on the Graham Number, indicating excess returns in certain markets, while recommending caution due to industry effects and accounting differences. Distinguished investors such as Warren Buffett, who studied under Graham, emphasized the need for a “margin of safety,” reinforcing the relevance of conservative metrics for both professional and individual investors.

Today, the Graham Number is present in educational materials, stock screening software, and brokerage platforms, serving as a starting point for those learning valuation discipline or seeking rapid filters for large stock lists.

Calculation Methods and Applications

Formula and Inputs
The Graham Number formula is straightforward:

Graham Number = sqrt(22.5 × EPS × BVPS)

Where:

• EPS: Earnings Per Share (preferably trailing twelve-month, diluted, from continuing operations)
• BVPS: Book Value Per Share (common equity per share, often adjusted for intangibles and goodwill)

Step-by-Step Calculation

1. Gather Data: Obtain the latest diluted trailing twelve-month EPS and BVPS from audited financial statements or reliable databases.
2. Check Validity: Ensure both EPS and BVPS are positive, and refer to the same fiscal period and currency.
3. Apply Formula: Multiply EPS by BVPS, then by 22.5. Take the square root of the product.
4. Interpretation: Compare the result to the current market price. A price below the Graham Number may indicate possible undervaluation, but this is not a standalone buy signal.

Example Application (Fictional Case)
Suppose a fictional company, “Acme Manufacturing,” has an EPS of USD 4.00 and a BVPS of USD 20.00:

22.5 × 4 × 20 = 1,800
sqrt(1,800) = USD 42.43

If the current market price is USD 35.00, the stock may appear undervalued based on the Graham Number. However, it is necessary to further analyze earnings quality, leverage, and business stability.

Sector Suitability and Data Adjustments

• Use multi-year average or normalized EPS for cyclical companies to avoid over-reliance on peak or trough performance.
• Use tangible book value (excluding goodwill/intangibles) in asset-heavy industries.
• Do not apply this screen to financials, REITs, or asset-light technology firms without making industry-specific adjustments.

Data Source Quality

• Use audited reports (annual and quarterly filings) for EPS and BVPS.
• Normalize for one-off items, such as asset write-downs or major legal expenses.
• Adjust for stock splits, buybacks, or share-based compensation, as these impact per-share figures.

Comparison, Advantages, and Common Misconceptions

Comparison with Other Valuation Approaches

Primary Advantages

• Simplicity and Transparency: Can be calculated using standard financial statements, and is easy to explain.
• Discipline: Establishes an upper boundary, reducing the risk of paying too much.
• Anchored in Fundamentals: Considers both profitability and balance sheet strength.

Common Misconceptions

• Not a Target Price: The Graham Number is an upper threshold, not a suggested buy price. Investors should seek to purchase well below this figure to maintain a margin of safety.
• Not an Intrinsic Value: This is a screening tool based on conservative estimates, not a precise valuation.
• Sector Blindness: Applying this metric without sector or accounting context may give misleading outcomes, especially for financial firms, asset-light businesses, or those with significant intangible assets.
• Reliance on Non-Normalized Earnings: Using unadjusted or one-off EPS or BVPS figures can distort results. Always adjust for sustainable earning power and clean book value.

Practical Guide

Implementing the Graham Number in Investment Research

How to Use Effectively

1. Initial Screening
   Employ the Graham Number to filter out stocks trading at elevated valuations—those well above their historical earning power or asset base.

2. Data Preparation

   • Use diluted, normalized, trailing twelve-month earnings and book values.
   • Adjust for exceptional or non-recurring items, especially in cyclical sectors.

3. Interpret & Validate

   • A stock trading well below its Graham Number deserves further review but is not automatically a value opportunity.
   • Investigate the reliability and sustainability of both profits and assets.

4. Apply Margin of Safety

   • Consider purchasing only when the stock trades at a meaningful discount (for example, 30 percent below the Graham Number), taking into account overall quality, sector, and accounting conservativeness.

5. Cross-Verification

   • Use in conjunction with DCF analysis, peer group multiples, and qualitative reviews of the business.
   • Avoid purely mechanical use—independent analysis is essential.

Virtual Case Study (Fictional Scenario)

Suppose a hypothetical company, “Summit Tools,” an industrial manufacturer, reports:

• EPS (TTM): USD 6.00
• BVPS: USD 25.00

Calculation:

6 × 25 × 22.5 = 3,375
sqrt(3,375) ≈ USD 58.09

If the stock trades at USD 40 and passes key quality checks—such as steady cash flows and manageable debt—it warrants additional research. If, however, book value contains large amounts of goodwill from earlier acquisitions that have subsequently been impaired, or if EPS is temporarily elevated due to the economic cycle, recalculate using adjusted figures.

Warnings and Edge Case Management

• Do not use this metric for companies with negative EPS or BVPS; such cases indicate financial distress, and the Graham Number does not apply.
• For financials, REITs, and asset-light businesses, use relevant industry valuation metrics such as NAV, FFO, or cash flow multiples instead of the Graham Number.

Resources for Learning and Improvement

• Classic Texts

  • The Intelligent Investor – Benjamin Graham (Commentary by Jason Zweig)
  • Security Analysis – Benjamin Graham & David Dodd
  • Value Investing: From Graham to Buffett and Beyond – Bruce Greenwald

• Academic Research

  • SSRN and JSTOR for empirical research on Graham-style screening compared with multifactor models.
  • Studies discussing survivorship bias, accounting practices, and factor-based performance.

• Case Studies and Investor Letters

  • Berkshire Hathaway Shareholder Letters for discussion on “margin of safety”
  • Tweedy, Browne’s What Has Worked in Investing

• Online Tools and Calculators

  • Yahoo! Finance, Value Line, and similar platforms for financial statement data.
  • Online calculators for inputting EPS and BVPS.

• Courses and Lectures

  • MIT OpenCourseWare and Columbia University lectures on valuation fundamentals.
  • Online webinars and MOOC platforms focusing on financial statement analysis.

• Communities and Forums

  • r/ValueInvesting (Reddit) and The Motley Fool for community discussion and Q&A.
  • Analyst and CFA forums for advanced analysis and sector discussion.

• Glossaries and FAQ Archives

  • Investopedia for key terms and concepts.
  • Research notes from brokers for screening methodology and live examples.

FAQs

What is the Graham Number?

The Graham Number is a metric created by Benjamin Graham to estimate the maximum fair purchase price for a stock from a defensive investor’s perspective. It blends earnings and tangible asset value to set a conservative valuation ceiling.

How is the Graham Number calculated?

It is calculated using the formula sqrt(22.5 × EPS × BVPS), based on trailing twelve-month, diluted earnings per share and (preferably tangible) book value per share. Both figures must be positive and up to date.

Why is it important for defensive investors?

The Graham Number fosters valuation discipline, discourages overpayment, and requires that investments have both profits and solid assets backing them. It is straightforward to calculate and reduces reliance on projections.

Can I use forward or adjusted EPS in the formula?

No. Use trailing and normalized figures, reflecting actual, sustainable performance rather than optimistic forecasts or “adjusted” earnings omitting ongoing expenses.

Is the Graham Number suitable for all industries?

No. It is most effective for mature, asset-heavy businesses such as industrial, utility, or select consumer staple companies. The Graham Number is less applicable to sectors built on intangible assets or rapid growth, or those with complex financial statements (e.g., technology, biotech, or financial services).

How does the Graham Number compare to DCF or multiples?

The Graham Number is a quick, conservative screening measure. Discounted Cash Flow (DCF) modeling calculates intrinsic value from forecasted future cash flows, while multiples (e.g., P/E, EV/EBITDA) compare companies to peers. Sound practice is to use multiple methods together.

What should I do if EPS or BVPS is negative?

Do not use the Graham Number if either input is negative; such cases typically signal financial distress or unusual accounting circumstances. Investigate the underlying causes before proceeding.

Where should I obtain EPS and BVPS data?

Refer to audited company reports (annual and quarterly) and credible data sources. Be sure to account for one-time or non-recurring events, and check that reporting periods and per-share measurements are consistent.

Does a price below the Graham Number mean a stock is a buy?

Not necessarily. A price below the Graham Number suggests potential undervaluation, but further investigation into earnings quality, industry context, future prospects, and risk factors is essential before making any investment decisions.

Conclusion

The Graham Number stands as a persistent conservative screen for stock selection, particularly suited for value investors who value downside protection and straightforward metrics. Its blend of earnings per share and book value per share directly expresses Benjamin Graham’s fundamental principle: sound investments should possess both demonstrated earning power and tangible asset backing. However, the Graham Number should be treated as an initial filter rather than a definitive valuation tool.

To apply the Graham Number effectively:

• Ensure strict vetting and normalization of financial input data.
• Consider sector, business model, and market cycle context.
• Incorporate it alongside additional valuation techniques and in-depth qualitative assessment for comprehensive decision-making.

Ultimately, the value of Graham’s approach lies in the disciplined, evidence-based practice of investing with a margin of safety, for which the Graham Number can serve as a valuable component in the research process.