What is the Graham Number and how do I calculate it for bank stocks?
The Graham Number estimates the most you should pay for a stock using the formula: square root of (22.5 multiplied by EPS multiplied by book value per share). The 22.5 represents Benjamin Graham's combined value ceilings of 15 times earnings and 1.5 times book value (15 multiplied by 1.5 equals 22.5). Bank stocks are a natural fit for this formula because both inputs, earnings per share and book value per share, are central to how banks are analyzed.
The Graham Number is a formula created by Benjamin Graham, often called the father of value investing. It calculates a maximum price you should pay for a stock by combining two numbers: the company's earnings per share (EPS) and the company's net worth per share (book value per share, or BVPS). Bank stocks are a natural fit for the Graham Number because earnings and book value are already the two most important numbers in bank analysis.
The formula: Graham Number = square root of (22.5 multiplied by EPS multiplied by BVPS)
The constant 22.5 has a specific origin. Graham set two ceilings: a stock should not trade above 15 times earnings (a P/E ratio of 15), and it should not trade above 1.5 times book value (a P/B ratio of 1.5). Multiply those two limits and you get 22.5. The square root converts the result back into a dollar-per-share figure you can compare directly to the stock's market price.
Finding the Right Inputs
Two numbers feed into the formula, and getting them right matters.
For EPS, use diluted trailing twelve-month (TTM) earnings per share. "Diluted" means the figure accounts for stock options and other securities that could convert into additional shares, giving you a more conservative earnings number. You can find diluted EPS in the bank's most recent 10-K (annual filing) or 10-Q (quarterly filing) with the SEC. If you're pulling from a quarterly report, add up the four most recent quarters to get the TTM figure.
For BVPS, take total shareholders' equity from the balance sheet, subtract any preferred stock, and divide by diluted shares outstanding. This gives you common shareholders' net asset value on a per-share basis. The same SEC filings that provide EPS will have the balance sheet data you need.
Worked Example
Consider a bank reporting TTM diluted EPS of $3.50 and BVPS of $28.00.
Graham Number = square root of (22.5 multiplied by 3.50 multiplied by 28.00)= square root of 2,205 = approximately$46.96
If this bank's stock trades at $38, the price sits about 19% below the Graham Number, suggesting the stock may be undervalued by this measure. That 19% gap also represents a margin of safety. If the stock instead trades at $52, it exceeds the Graham Number and fails Graham's combined earnings-and-book-value test.
Adjusting the Calculation for Banks
The standard formula works for most banks, but a few common situations call for modifications.
- One-time earnings distortions: If the bank's recent EPS was inflated by securities gains, unusual tax benefits, or a legal settlement recovery (or depressed by a large one-time charge), the Graham Number won't reflect normal earning power. Using average EPS over three to five years, or stripping out clearly nonrecurring items, produces a more reliable result.
- Goodwill on the balance sheet: Banks that have grown through acquisitions often carry significant goodwill, which inflates BVPS above the tangible asset backing. Substituting tangible book value per share (TBVPS) for BVPS yields a more conservative Graham Number. This adjustment matters most for serial acquirers where goodwill makes up 10% or more of total equity.
- Negative or near-zero earnings: When a bank is losing money or barely breaking even, which can happen during severe credit cycles, the formula either produces a meaningless result or breaks entirely (you can't take the square root of a negative number). Skip the Graham Number in those periods and rely on asset-based valuation approaches instead.
What the Graham Number Won't Tell You
The Graham Number is a screening tool, not a complete valuation. It identifies stocks trading below a conservative price ceiling, but it treats all banks with the same EPS and BVPS as identical.
In practice, that's a real limitation. A bank earning a 12% return on equity (ROE) with clean asset quality deserves a higher price than one earning 6% ROE with rising problem loans, even if their per-share numbers happen to match. The formula says nothing about profitability differences, asset quality, capital strength, or growth prospects. It answers one narrow question: is the price below Graham's combined earnings-and-book-value threshold?
The practical takeaway: use the Graham Number to narrow a large universe of bank stocks to a shortlist of candidates that pass the basic value test. Then dig deeper into each one. Check whether earnings are sustainable, whether book value is overstated by goodwill or understated by unrealized securities losses, and whether the bank's ROE justifies its current P/B multiple. Banks that look attractive on the Graham Number and hold up under further scrutiny are the ones worth serious attention.
Related Metrics
- Earnings Per Share (EPS)
- Book Value Per Share (BVPS)
- Price to Book (P/B) Ratio
- Price to Earnings (P/E) Ratio
- Return on Equity (ROE)
- Tangible Book Value Per Share (TBVPS)
Related Valuation Methods
Related Questions
- How do I use the Graham Number to find undervalued bank stocks?
- What is margin of safety and how do I apply it to bank stocks?
- What is a good price-to-book ratio for a bank stock?
- What filters should I set to find undervalued bank stocks?
Key terms: Tangible Book Value Per Share, Goodwill — see the Financial Glossary for full definitions.