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:
<math>\sqrt{22.5\times(\text{earnings per share})\times(\text{book value per share})}</math>
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:
Derivation
The constant 22.5 in the formula is derived from Graham's two criteria for defensive stock selection:
:<math>\text{Price} \leq \sqrt{22.5 \times \text{EPS} \times \text{BVPS</math>
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:
<math>\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)}</math>
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:
:<math>\sqrt{22.5 \times 5.00 \times 30.00} = \sqrt{3375} \approx 58.09</math>
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. The formula has since become widely used by value investors as a quick screening tool to identify potentially undervalued stocks.