The Graham number or Benjamin Graham number is a figure used in securities investing that measures a stock's so-called fair value. Named after Benjamin Graham, the founder of value investing, the Graham number can be calculated as follows:
22.5 × ( earnings per share ) × ( book value per share ) {\displaystyle {\sqrt {22.5\times ({\text{earnings per share}})\times ({\text{book value per share}})}}}
The final number is, theoretically, the maximum price that a defensive investor should pay for the given stock. Put another way, a stock priced below the Graham number would be considered a good value, if it also meets a number of other criteria. The number represents the geometric mean of the maximum that one would pay based on earnings and based on book value. Graham writes:
Current price should not be more than 11⁄2 times the book value last reported. However a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets. As a rule of thumb we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5. (This figure corresponds to 15 times earnings and 11⁄2 times book value. It would admit an issue selling at only 9 times earnings and 2.5 times asset value, etc.)
Derivation The constant 22.5 in the formula is derived from Graham's two criteria for defensive stock selection:
The price-to-earnings ratio (P/E) should not exceed 15 The price-to-book ratio (P/B) should not exceed 1.5 The product of these two maximum multiples is 15 x 1.5 = 22.5. Since:
P/E × P/B = Price EPS × Price BVPS = Price 2 EPS × BVPS {\displaystyle {\text{P/E}}\times {\text{P/B}}={\frac {\text{Price}}{\text{EPS}}}\times {\frac {\text{Price}}{\text{BVPS}}}={\frac {{\text{Price}}^{2}}{{\text{EPS}}\times {\text{BVPS}}}}}
Setting this product equal to 22.5 and solving for Price yields the Graham number formula:
Price ≤ 22.5 × EPS × BVPS {\displaystyle {\text{Price}}\leq {\sqrt {22.5\times {\text{EPS}}\times {\text{BVPS}}}}}
This derivation shows that the Graham number simultaneously enforces both the P/E and P/B constraints in a single metric.
Alternative calculation Earnings per share is calculated by dividing net income by shares outstanding. Book value is another way of saying shareholders' equity. Therefore, book value per share is calculated by dividing equity by shares outstanding. Consequently, the formula for the Graham number can also be written as follows:
15 × 1.5 × ( net income shares outstanding ) × ( s h a r e h o l d e r s ′ e q u i t y shares outstanding ) {\displaystyle {\sqrt {15\times 1.5\times \left({\frac {\text{net income}}{\text{shares outstanding}}}\right)\times \left({\frac {\mathrm {shareholders'\ equity} }{\text{shares outstanding}}}\right)}}}
Practical example Consider a company with trailing twelve-month earnings per share of $5.00 and a book value per share of $30.00. The Graham number would be:
22.5 × 5.00 × 30.00 = 3375 ≈ 58.09 {\displaystyle {\sqrt {22.5\times 5.00\times 30.00}}={\sqrt {3375}}\approx 58.09}
Under Graham's framework, a defensive investor should consider paying no more than approximately $58.09 per share for this stock. If the stock is trading at $45, the stock would be trading below its Graham number, suggesting it may be undervalued by this metric. If it is trading at $75, it would exceed the Graham number, indicating the stock may be overvalued relative to its earnings and book value.
History The Graham number was first mentioned in Benjamin Graham's famous 1949 book, The Intelligent Investor. Graham's defensive investment strategy mainly focused on a "margin of safety" and reducing losses as opposed to maximizing gains. The Graham number was developed based on this concept to quickly value a stock. Graham himself never gave a specific formula or equation. The Graham number was derived from guidelines he laid down in the book. The formula has since become widely used by value investors as a quick screening tool to identify potentially undervalued stocks.
Limitations The Graham number has several limitations that investors should consider:
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