The Graham Number Formula
The Graham Number Formula
Quick definition: The Graham Number is a mathematical formula that calculates a fair value ceiling for stocks by combining earnings yield and book value multiples, providing defensive investors with a quantitative threshold for maximum reasonable purchase prices based on Graham's valuation principles.
One of the most practical tools Benjamin Graham provided to individual investors is the Graham Number, a formula for calculating the maximum price an investor should pay for a stock. Unlike sophisticated financial models requiring assumptions about future cash flows and terminal value, the Graham Number uses only two readily available figures: earnings per share and book value per share. This simplicity, combined with its grounding in Graham's core valuation philosophy, makes the Graham Number both accessible and useful for defensive investors.
The Graham Number represents an attempt to quantify the boundary between value and speculation. Graham believed that buying stocks at prices above the Graham Number exposed investors to unnecessary risk. Stocks trading below the Graham Number had better margins of safety. The formula doesn't identify the cheapest stocks or the greatest bargains; it identifies the maximum prices at which quality companies offer reasonable value.
The Formula and Its Components
The Graham Number formula is as follows:
<p>Graham Number = √(22.5 × EPS × Book Value per Share)</p>
This appears as a formula:
Graham Number = √(22.5 × Earnings Per Share × Book Value Per Share)
The square root symbol indicates that the formula takes the geometric mean of the product of earnings per share and book value per share, adjusted by a constant factor of 22.5. The components are:
- Earnings Per Share (EPS): The company's net income divided by the number of shares outstanding, representing the company's current annual earning power allocated to each share
- Book Value Per Share: The company's total assets minus liabilities, divided by shares outstanding, representing the net tangible value attributable to each share
- 22.5: A constant derived from Graham's belief that companies should trade at multiples around 15 times earnings and 1.5 times book value
Understanding the Constant Factor
The constant 22.5 deserves explanation as it contains Graham's specific valuation philosophy. Graham believed that reasonable maximum prices should reflect two valuation approaches: a price-to-earnings multiple and a price-to-book multiple. He suggested that quality stocks shouldn't trade above approximately 15 times earnings and shouldn't trade above approximately 1.5 times book value.
The formula combines these two approaches. If a company trades at exactly 15 times earnings but only 1 times book value, the Graham Number would generate a higher fair value. If the same company trades at 15 times earnings and 1.5 times book value, the formula would generate a lower fair value. By incorporating both metrics, the formula prevents investors from overpaying based on a single valuation approach.
The specific multipliers of 15 and 1.5 reflected Graham's views about reasonable valuations during the mid-twentieth century. In contemporary markets with different interest rate environments and different business models, investors might reasonably adjust these factors. A defensive investor might apply stricter multipliers (say, 10 times earnings and 1.2 times book value), creating a more conservative fair value ceiling. An investor in a different era with different interest rates might apply more generous multiples.
Calculating a Practical Example
Consider a hypothetical company with earnings per share of $3 and book value per share of $20. The Graham Number calculation would be:
Graham Number = √(22.5 × 3 × 20)
Graham Number = √(1,350)
Graham Number = approximately $36.74
According to this calculation, an investor should not pay more than approximately $37 per share for this company. If the stock trades at $30 per share, it offers margin of safety. If it trades at $40 per share, it's overpriced relative to Graham's framework.
This example illustrates the formula's practical utility. An investor examining a stock can quickly calculate whether it trades at reasonable prices relative to Graham's valuation framework without requiring sophisticated financial modeling or assumptions about future growth.
Strengths of the Graham Number Approach
The Graham Number formula has several advantages over more complex valuation methods. First, it requires only basic financial information available in any company's annual report or financial database. An investor doesn't need special expertise to find earnings per share or book value per share.
Second, the formula is mechanical and objective. Different investors applying the formula to the same company will reach identical conclusions. This objectivity eliminates the subjective judgment that leads some analysts to justify any price through favorable assumptions.
Third, the formula reflects Graham's actual investment philosophy. Rather than representing theoretical financial modeling, the Graham Number embodies Graham's beliefs about reasonable valuations for quality companies. It provides a concrete implementation of his principles.
Fourth, the formula provides a conservative approach to valuation. The multiples incorporated (15 times earnings and 1.5 times book value) are deliberately conservative for the era in which they were developed. Even adjusting for modern market conditions, they typically produce fair values lower than those generated by optimistic growth-based models.
Limitations and Contextual Factors
The Graham Number formula, despite its merits, has limitations that investors should understand. First, the formula incorporates fixed multipliers reflecting Graham's views about reasonable valuations during a particular era. Market conditions, interest rates, and inflation change over time. A constant multiplier of 15 times earnings might be reasonable in some interest rate environments but unreasonably conservative or generous in others.
Second, the formula makes no distinction between different types of companies. A low-growth utility company and a stable-growth technology company might generate identical Graham Numbers if they have similar earnings and book values, yet investors might reasonably accept different valuations for each. Graham Number doesn't adjust for business quality, competitive advantage, or growth prospects.
Third, book value per share can be misleading for certain types of companies. Companies with significant intangible assets (technology companies, consumer brands) might have book values far below their economic value. Service companies with few tangible assets might show low book values despite generating substantial earnings. The Graham Number formula, by incorporating book value heavily, can undervalue such companies.
Fourth, the formula focuses on current earnings without considering earnings growth. A company with strong earnings growth justified by underlying business characteristics might generate a Graham Number that undervalues it relative to more rapidly growing competitors.
Adapting the Formula for Contemporary Use
Modern investors applying Graham's framework might adjust the formula's constants to reflect contemporary market conditions and valuation norms. If one believes that interest rates and inflation justify slightly higher earnings multiples than Graham's original 15x figure, one might calculate a fair value using 18x earnings and 1.5x book value, adjusting the constant accordingly.
Similarly, investors might apply different constants for different company types. A mature, stable utility might be evaluated using conservative multiples similar to Graham's original figures. A company in a growing industry with strong competitive advantages might be evaluated using somewhat more generous multiples while still remaining significantly below market-derived valuations for speculative growth stocks.
The key is maintaining Graham's underlying philosophy while adjusting for changed market conditions. The Graham Number isn't sacred in its specific numerical form; it's valuable as an implementation of conservative valuation principles.
The Graham Number in Practice
A defensive investor using the Graham Number as part of their security selection process might follow a simple screening approach. Calculate the Graham Number for each company under consideration. If the stock trades below the Graham Number, it might be acceptable for purchase if it meets other criteria (dividend history, earnings stability, debt levels). If the stock trades above the Graham Number, exclude it from consideration.
This mechanical approach has advantages and disadvantages. The advantage is that it's objective and requires no subjective judgment about which stocks are attractive. The disadvantage is that it might exclude some attractively priced stocks and might include some that appear cheap only by the mechanical formula.
An enterprising investor might use the Graham Number as one factor in evaluation rather than as an absolute rule. A company trading 20 percent above the Graham Number but with exceptional competitive advantages and strong growth prospects might warrant purchase despite the formula's suggestion. Conversely, a company trading below the Graham Number but showing deteriorating competitive position might warrant avoidance despite appearing cheap.
Historical Performance and Modern Validation
Research examining Graham Number-based screening has produced mixed results. Some studies have shown that stocks trading below the Graham Number outperform those trading above it. Other studies have suggested that the Graham Number's specific numerical factors don't perform better than simpler approaches like purchasing based solely on P/E ratio.
The mixed evidence likely reflects changing market conditions and the evolution of business models. The Graham Number's specific constants reflected market conditions in the mid-twentieth century. Applied mechanically to contemporary markets with different business structures and valuation norms, the formula might be either too conservative or too generous depending on the market environment.
That said, the principle underlying the Graham Number remains sound. Combining earnings-based and asset-based valuation approaches captures two different dimensions of company value. Limiting prices to multiples that offer reasonable margin of safety protects against overpayment. Investors using Graham Number either directly or as inspiration for their own adjusted formulas can implement these sound principles.
Key Takeaways
- The Graham Number formula (√22.5 × EPS × Book Value) provides a quantitative fair value ceiling based on combining 15x earnings and 1.5x book value multiples, suitable for defensive investor stock selection
- The formula's strength lies in its simplicity, objectivity, and grounding in Graham's actual investment philosophy, requiring only publicly available data and mechanical calculation
- The specific constants in the formula reflected market conditions and interest rates during Graham's era; contemporary investors might reasonably adjust multipliers to reflect modern conditions while maintaining the underlying principle
- The formula has limitations including inability to distinguish between different business types, difficulty with intangible-asset-heavy companies, and lack of consideration for growth prospects and competitive advantages
- The Graham Number functions best as one screening tool among several rather than as an absolute rule, helping investors identify potentially overpriced stocks while recognizing exceptions based on specific circumstances
Beyond the Formula
The true value of the Graham Number lies not in the specific numerical result but in what it represents: a disciplined, systematic approach to determining reasonable valuations. Graham resisted the notion that valuation was an art requiring subjective judgment and intuition. Instead, he insisted that quantitative frameworks could guide investment decisions.
The Graham Number embodies this philosophy. It says: here is a formula, here are the numbers to plug in, here is the result. That result might be perfect for identifying which stocks to buy. Alternatively, it might serve as a starting point for deeper analysis, a trigger for investigating whether the formula's verdict aligns with detailed fundamental analysis.
Contemporary investors can benefit from the Graham Number whether they apply it mechanically or adapt it. The formula demonstrates that valuation need not be mysterious, that numerical guidance is possible, and that disciplined investors can avoid the extremes of both overvaluation and excessive caution. By quantifying reasonable prices, Graham provided a tool that democratized investment decision-making and remains useful today.