Graham Number
Type: Intrinsic Value Method
Overview
The Graham Number tells you the highest price you should pay for a stock if you want to invest conservatively. It uses two pieces of information: how much the company earns per share and how much the company is worth on its books per share. If the stock price is below this number, the stock might be a bargain.
The formula comes from Benjamin Graham, widely regarded as the father of value investing and a major influence on Warren Buffett. Graham believed a stock should not trade at more than 15 times its earnings or more than 1.5 times its book value. The Graham Number rolls both of those limits into one calculation that produces a single dollar figure.
For bank stock investors, the Graham Number is a particularly useful starting point. Banks are routinely evaluated on both earnings multiples and book value multiples, because a bank's book value represents the net worth of its lending and deposit-taking operations. The assets and liabilities on a bank's balance sheet are predominantly financial instruments carried close to their actual value, which makes book value a more meaningful anchor than it would be for, say, a software company. The formula's reliance on both earnings per share (EPS) and book value per share (BVPS) fits the way banks are already analyzed.
The result is a conservative ceiling. When a bank's share price sits below its Graham Number, the stock may warrant closer examination as a potential value opportunity. When the share price exceeds the Graham Number, the stock is trading above what Graham considered appropriate for a cautious buyer. That alone does not make it overvalued, since the formula intentionally sets a high bar for entry, but it does mean the stock would need to justify its premium through above-average profitability, growth prospects, or franchise quality.
Formula
Graham Number = √(22.5 × EPS × BVPS)
The constant 22.5 comes from multiplying Graham's maximum acceptable price-to-earnings (P/E) ratio of 15 by his maximum acceptable price-to-book (P/B) ratio of 1.5 (15 × 1.5 = 22.5). EPS is earnings per share, typically using diluted trailing twelve-month figures. BVPS is book value per share, calculated as total shareholders' equity divided by shares outstanding.
The square root converts the product back into a per-share price figure. You can think of the math this way: if a stock traded at exactly 15× earnings and exactly 1.5× book value, its price would equal the Graham Number. The formula finds the price where both constraints are satisfied simultaneously.
If either EPS or BVPS is negative, the formula cannot produce a meaningful result because you cannot take the square root of a negative number in this context.
How to Apply
- Determine the trailing twelve-month diluted earnings per share (EPS). Use diluted EPS rather than basic EPS to account for stock options, convertible securities, and other potential dilution. For banks, check whether the EPS figure is distorted by large one-time items such as securities gains, restructuring charges, or unusually high provision expenses. If it is, consider using a normalized or multi-year average EPS instead.
- Calculate the book value per share (BVPS) from the most recent balance sheet. Divide total shareholders' equity by the number of diluted shares outstanding. For banks with significant goodwill from acquisitions, also note the tangible book value per share (TBVPS) as a cross-check, since goodwill can meaningfully inflate the BVPS figure.
- Multiply EPS by BVPS, then multiply that result by 22.5. This produces the value under the square root sign in the formula. For example, if EPS is $4.00 and BVPS is $40.00, this step yields 22.5 × $4.00 × $40.00 = $3,600.
- Take the square root of the result to arrive at the Graham Number. Continuing the example above, the square root of $3,600 is $60.00. This figure represents the maximum price Graham's framework considers appropriate for a conservative buyer.
- Compare the Graham Number to the current stock price. If the stock trades below the Graham Number, it passes Graham's initial screen and may deserve a closer look. If it trades above, the stock does not meet the criteria for a conservative purchase at the current price, though other valuation methods may still find it reasonably priced.
Example Calculation
Consider a regional bank with diluted EPS of $4.00 and BVPS of $40.00. The Graham Number calculation works out to: 22.5 × $4.00 × $40.00 = $3,600, and the square root of $3,600 = $60.00. If this bank's stock trades at $48 per share, the Graham Number exceeds the market price by $12, suggesting the stock passes Graham's initial value screen. The margin of safety in this case would be ($60 - $48) / $60 = 20%, which falls within the range most value investors consider adequate.
Now consider what happens if that same bank had a difficult year with elevated loan loss provisions that pushed EPS down to $2.50 while BVPS remained at $40.00. The Graham Number drops to the square root of (22.5 × $2.50 × $40.00) = the square root of $2,250 = approximately$47.43. At a $48 share price, the stock now fails the Graham Number test. The bank did not necessarily become less valuable; the formula is simply responding to temporarily depressed earnings. This is exactly why the Graham Number works best with normalized or sustainable earnings rather than a single quarter or year that may not represent the bank's true earning power.
For comparison, a highly profitable bank with EPS of $6.00 and BVPS of $45.00 would produce a Graham Number of approximately $77.94 (the square root of 22.5 × $6.00 × $45.00 = $6,075). The higher result reflects both stronger earnings and a larger asset base. The formula naturally rewards banks that score well on both dimensions simultaneously.
It is also worth running the calculation with tangible book value. If that first bank's $40.00 BVPS includes $8.00 of goodwill per share, its tangible BVPS would be $32.00. Using that figure instead: 22.5 × $4.00 × $32.00 = $2,880, and the square root of $2,880 = approximately$53.67. The gap between $60.00 (using total book value) and $53.67 (using tangible book value) shows how much goodwill inflates the result for banks that have grown through acquisitions.
Strengths
- Produces a single, objective price threshold that removes emotional judgment from the initial screening decision. The result is either above or below the current stock price, giving investors a clear pass/fail signal for a first look.
- Combines both earnings power and asset value into one calculation, which aligns well with how bank stocks are evaluated. Most bank valuation methods focus on either P/E or P/B in isolation. The Graham Number requires that a stock look reasonable on both measures simultaneously, catching situations where a stock might appear cheap on one metric but expensive on the other.
- The calculation is straightforward and requires only two inputs (EPS and BVPS), both of which are readily available in bank financial statements and earnings releases. No subjective assumptions about growth rates, discount rates, or terminal values are required. This makes the formula easy to apply across dozens of bank stocks quickly when screening for candidates.
- Rooted in Benjamin Graham's investment philosophy, which emphasizes paying a conservative price for demonstrable value. The framework has survived decades of market cycles, and its conservative orientation suits the banking sector well, where downside protection and balance sheet stability matter more than rapid growth.
- Particularly effective as a first-pass filter when combined with other screens. An investor can quickly identify banks trading below their Graham Number and then apply more detailed analysis (P/B versus ROE analysis, asset quality review, capital adequacy checks) to the smaller list of candidates that passed.
Limitations
- Does not account for growth prospects, management quality, or franchise value. A well-managed bank with strong growth potential and a highly profitable deposit franchise will produce the same Graham Number as a poorly managed bank with identical EPS and BVPS figures. The formula treats two banks as equivalent if their current numbers match, regardless of trajectory.
- May systematically undervalue high-quality banks that deserve premium valuations. Banks with consistently high returns on equity, strong fee income, and durable competitive advantages often trade above their Graham Number for good reason. Filtering them out as too expensive means missing some of the best-performing stocks in the sector.
- Requires both positive earnings and positive book value to function. Banks experiencing losses or with negative tangible equity (rare but possible after large write-downs) cannot be evaluated with this formula, which means the tool goes blank precisely when scrutiny is most needed.
- Does not distinguish between reported book value and tangible book value. Banks carrying substantial goodwill from acquisitions will show a higher BVPS and therefore a higher Graham Number than their tangible asset base justifies. This can make an acquisition-heavy bank appear cheaper than it actually is relative to its hard assets.
- The 22.5 constant reflects Graham's mid-twentieth-century assumptions about maximum reasonable multiples. In prolonged low-interest-rate environments, average bank multiples may run higher than 15x earnings or 1.5x book value, making the constant overly restrictive. In stressed credit environments, even these multiples may prove generous. The constant does not adjust to market conditions.
- Uses a point-in-time EPS figure that may not represent the bank's normalized earning power. During credit cycle peaks, low provision expense inflates EPS and makes the Graham Number look generous. During troughs, elevated provisions depress EPS and pull the Graham Number down, potentially flagging a temporarily struggling but fundamentally sound bank as overpriced.
Bank-Specific Considerations
The Graham Number fits bank stock screening well because its two inputs, earnings per share and book value per share, are the same fundamental measures that drive most bank valuations. Banks are balance-sheet-intensive businesses whose assets and liabilities are predominantly financial instruments carried near fair value. That makes book value a more meaningful anchor for banks than for asset-light industries like technology or services, where most of the business's worth comes from intangible assets that never appear on the balance sheet.
Several bank-specific factors affect how investors should interpret the result:
Asset Quality Is Invisible to the Formula
A bank with a clean loan portfolio and a bank with rising delinquencies will produce identical Graham Numbers if their EPS and BVPS happen to match. The formula cannot tell the difference between high-quality earnings backed by sound credit and earnings that are about to be eroded by deteriorating loans. Investors should always check asset quality metrics (non-performing assets, charge-off rates, reserve coverage) alongside the Graham Number to understand whether the earnings input is sustainable.
Goodwill Inflates the Result
Banks that have grown through acquisitions carry goodwill on their balance sheets, and this goodwill gets included in BVPS. Because the Graham Number uses total book value rather than tangible book value, acquisition-heavy banks may show a Graham Number that overstates what a conservative buyer should pay. Running the calculation a second time with tangible book value per share reveals how much goodwill is affecting the result. If the two Graham Numbers diverge significantly, the tangible version is generally the more cautious reference point.
Regulatory Capital Creates a Separate Floor
Bank valuations have a floor that the Graham Number does not account for: regulatory capital requirements. A bank trading below book value but well above its minimum capital requirements occupies a very different risk position than one trading below book value with thin capital buffers. The Graham Number does not incorporate capital ratios, so a stock might pass the Graham Number screen while still carrying meaningful regulatory risk (or, conversely, fail the screen while being exceptionally well-capitalized).
Earnings Cyclicality Distorts the Input
Bank earnings are cyclical. Credit quality, interest rate movements, and provision expense timing all push EPS around from year to year. The Graham Number is only as reliable as its EPS input. During benign credit conditions, provision expense stays low and EPS runs high, producing a generous Graham Number. During stress periods, provisions spike and EPS drops, pulling the Graham Number down and making otherwise solid banks look expensive. Using a multi-year average EPS or pre-provision earnings per share can partially address this, though neither adjustment is perfect.
When to Use This Method
The Graham Number works best as a quick screening filter rather than a standalone valuation conclusion. It is well-suited for narrowing a large universe of bank stocks down to a smaller list that deserves deeper analysis.
The calculation is most reliable when applied to banks with stable, repeatable earnings and a book value that closely approximates tangible net asset value. Community banks with straightforward lending operations and limited goodwill tend to produce the most meaningful Graham Number results. These banks have the kind of predictable, balance-sheet-driven business model that Graham's formula was designed for.
When the Graham Number Is Less Appropriate
The method is less reliable in several situations:
- Banks with highly volatile earnings, particularly those experiencing a credit cycle spike in provision expense or benefiting from unusually large reserve releases. The EPS input in these cases does not reflect sustainable profitability.
- Banks with significant goodwill on the balance sheet, which inflates BVPS and pushes the Graham Number higher than the tangible asset base supports. Running a parallel calculation with tangible book value is the simplest fix.
- Banks with negative or near-zero EPS, where the formula produces artificially low or undefined results. The Graham Number goes silent exactly when you might want it most.
- Banks undergoing restructuring, strategic transformation, or regulatory remediation, where current financials may not represent future earning power. The formula has no way to anticipate improvement or deterioration.
Pairing with Other Methods
The Graham Number should not serve as the sole basis for any investment decision. It is most effective when used alongside price-to-book analysis, price-to-earnings comparisons, and the ROE-P/B valuation framework. Applying a margin of safety assessment on top of the Graham Number adds another layer of discipline. Together, these approaches build a more complete picture of whether a bank stock is reasonably priced or whether an apparent bargain has a catch that the Graham Number alone cannot detect.
Method Connections
The Graham Number pulls from both the price-to-earnings (P/E) and price-to-book (P/B) valuation frameworks. The formula implicitly assumes a maximum P/E of 15 and a maximum P/B of 1.5 (since 15 × 1.5 = 22.5). Mathematically, the Graham Number is the geometric mean of two independent price ceilings: 15 times EPS and 1.5 times BVPS. If a stock traded at exactly those multiples, its share price would equal the Graham Number.
Comparing the Graham Number to the current share price produces a margin of safety estimate. If the Graham Number exceeds the share price, the percentage difference represents the available margin of safety. A stock with a Graham Number of $60 and a share price of $48 has a 20% margin of safety by this measure. This directly connects the formula to the margin of safety concept, which quantifies the discount between market price and estimated intrinsic value.
Because the Graham Number uses BVPS rather than tangible book value per share (TBVPS), banks with substantial goodwill from acquisitions may show an inflated result. The price-to-tangible-book valuation method addresses this limitation by stripping out intangible assets. Running both calculations side by side (the standard Graham Number using BVPS and a modified version using TBVPS) reveals how much goodwill is distorting the output.
The ROE-P/B framework offers a complementary perspective. The Graham Number sets a static ceiling based on Graham's original multiples, while the ROE-P/B framework derives a justified P/B multiple from the bank's actual profitability. A bank earning 15% ROE may deserve a P/B multiple well above 1.5×, which means it could trade above its Graham Number and still be reasonably valued. Using the two methods together helps separate stocks that are genuinely cheap from those that trade at low multiples for justifiable reasons.
The price-to-earnings valuation method also overlaps with the Graham Number, since both rely on EPS as a core input. Where they differ is scope: the P/E valuation method compares a bank's earnings multiple to its peers and historical averages, while the Graham Number applies a fixed maximum multiple regardless of context. A bank trading at 12x earnings might pass the Graham Number screen (since 12 is below 15) while still looking expensive relative to its peer group if similar banks trade at 9x.
Common Mistakes
Using Abnormal Earnings
The most frequent mistake is applying the Graham Number to banks with temporarily abnormal earnings. Using EPS from a year with elevated provision expense (due to a credit downturn or large individual loan charge-offs) produces an artificially low Graham Number that understates fair value. The reverse is equally misleading: applying EPS from a year with large reserve releases or one-time gains overstates what the bank is sustainably worth. Where possible, using a normalized or multi-year average EPS produces a more representative result. Some investors prefer to use pre-provision net revenue (PPNR) per share as a proxy for core earning power, though this requires adjusting the 22.5 constant since PPNR runs higher than net income.
Choosing the Wrong EPS Figure
Using basic EPS rather than diluted EPS inflates the Graham Number by ignoring the dilutive effect of stock options, warrants, and convertible instruments. Diluted EPS is the more conservative and appropriate input. The difference between basic and diluted EPS is usually small for banks, but it can be meaningful for banks with large outstanding option grants or convertible preferred stock.
Ignoring Goodwill in Book Value
Failing to account for goodwill in the BVPS input overstates the Graham Number for acquisition-heavy banks. A bank with $50 in BVPS but $15 in goodwill per share has a tangible book value of only $35 per share. Running the calculation with both figures reveals how sensitive the result is to intangible assets. When the two Graham Numbers diverge by more than 10-15%, the goodwill effect is significant enough to warrant using the tangible version as the primary reference.
Treating the Result as a Price Target
The Graham Number is a screening threshold, not a precise fair value target. The formula produces a single number, but that number is only as accurate as its two inputs and the assumption that Graham's original multiples (15x earnings, 1.5x book) are appropriate for the current environment. Stocks below the Graham Number warrant further analysis. Stocks above it simply did not pass this particular screen. Treating the Graham Number as the stock's true value leads to false confidence and poor decisions in both directions.
Not Asking Why a Stock Is Cheap
Some investors apply the Graham Number in isolation without considering why a bank trades below it. A low share price relative to the Graham Number may reflect legitimate concerns about asset quality, management, regulatory issues, or structural challenges that the formula cannot capture. A stock trading at 60% of its Graham Number is not automatically a great buy if the bank is under a consent order, losing deposits, or facing deteriorating credit quality in its loan portfolio.
Across Bank Types
Community Banks
The Graham Number tends to be most reliable for community banks and smaller regional banks. These institutions typically have straightforward balance sheets built on deposits and loans, stable earnings driven primarily by net interest income, and limited goodwill. Their book value closely approximates tangible net asset value, and their earnings tend to be less volatile than those of larger, more complex institutions. The formula's assumptions about reasonable multiples (15x earnings, 1.5x book) align well with how the market typically values these banks.
Mid-Size Regional Banks
Mid-size regional banks present a mixed picture. Many have grown through acquisitions, carrying meaningful goodwill that inflates BVPS. Their earnings may include a larger share of fee income from wealth management, mortgage banking, or capital markets activities, which adds variability that the Graham Number does not account for. The formula still provides a useful reference point for these banks, but investors should run a parallel calculation with tangible book value per share to strip out the goodwill effect. The gap between the standard Graham Number and the tangible version often runs 5-15% for acquisition-active regionals.
Large Money Center Banks
For large money center banks with complex balance sheets, significant trading operations, and diverse revenue streams, the Graham Number is a less reliable indicator. BVPS for these banks includes substantial intangible assets, and EPS is influenced by businesses (investment banking, trading, asset management) that are inherently more volatile than traditional lending. The formula's simplicity becomes a drawback when applied to institutions whose value drivers extend well beyond net interest income and tangible equity. Most professional analysts evaluating these banks rely on more granular, segment-by-segment valuation rather than a single formula.
Mutual-to-Stock Conversions
Banks that have recently completed mutual-to-stock conversions represent a special case. These banks typically carry excess capital because the conversion proceeds sit on the balance sheet as equity that has not yet been deployed into earning assets. BVPS is high relative to current earnings capacity. This results in an unusually high Graham Number relative to the share price, which can make the stock appear deeply undervalued. In reality, the market is pricing the time it will take for the bank to deploy that capital productively. The earnings input (EPS) is temporarily depressed not because the bank is performing poorly, but because the equity base is oversized relative to the loan portfolio. As these banks put the conversion capital to work over several years, EPS should rise and the Graham Number will become a more meaningful reference point.
Related Valuation Methods
- Margin of Safety — Apply a margin of safety to the Graham Number for additional downside protection.
- Price to Book Valuation — P/B valuation provides a market-based complement to the Graham Number's formula-based approach.
- Price to Earnings Valuation — A method for estimating what a bank stock should be worth by comparing its share price to the earnings it generates per share.
- ROE-P/B Valuation Framework — A valuation framework that calculates what price-to-book multiple a bank deserves based on its return on equity, cost of equity, and growth rate.
- Price to Tangible Book Valuation — Values a bank stock by comparing its market price to tangible book value per share, which strips goodwill and intangible assets from the equation. This produces a more conservative, asset-focused valuation than standard price-to-book and serves as the standard pricing metric in bank mergers and acquisitions.
Related Metrics
- Earnings Per Share (EPS) — EPS is one of two required inputs to the Graham Number formula, representing the earnings power component of Graham's dual-factor intrinsic value estimate.
- Book Value Per Share (BVPS) — BVPS is one of two required inputs to the Graham Number formula, representing the asset backing component that reflects the bank's tangible and intangible net worth per share.
- Price to Book (P/B) Ratio — The Graham Number implicitly caps the acceptable P/B at 1.5x, connecting the Graham framework to price-to-book valuation analysis.
- Price to Earnings (P/E) Ratio — The Graham Number implicitly caps the acceptable P/E at 15x, making the current P/E ratio a useful cross-check on whether the Graham Number estimate is reasonable.
- Tangible Book Value Per Share (TBVPS) — Tells you how much tangible (real, hard) net asset value backs each share of a bank's stock, after removing goodwill and other intangible assets from equity
- Return on Equity (ROE) — Measures how much profit a bank earns for each dollar of shareholder equity. One of banking's most watched profitability metrics because it captures both operating performance and the effect of leverage in a single number.
- Price to Tangible Book Value (P/TBV) — Compares a bank's stock price to the value of its tangible assets per share. Because it strips out goodwill and other intangible assets, P/TBV gives a more conservative picture of what investors are paying for each dollar of hard asset value.
Frequently Asked Questions
What is the Graham Number and how do I calculate it for bank stocks?
The Graham Number estimates a maximum fair price using both EPS and BVPS, applying Benjamin Graham's criteria that a stock should not trade above 15x earnings or 1.5x book value Read more →
How do I use the Graham Number to find undervalued bank stocks?
Banks trading below their Graham Number may represent value opportunities, though the calculation should be verified with stable earnings and adjusted for goodwill Read more →
What is margin of safety and how do I apply it to bank stocks?
Margin of safety measures the discount between a bank's market price and its estimated intrinsic value, with the Graham Number providing one approach to estimating that intrinsic value Read more →
What is intrinsic value and how do I estimate it for a bank?
The Graham Number offers one formula-based approach to estimating intrinsic value for bank stocks, combining earnings power and book value into a single conservative price ceiling Read more →
How do I tell if a bank stock is overvalued or undervalued?
Comparing a bank's share price to its Graham Number provides a quick initial screen, though a complete assessment requires multiple valuation approaches used together Read more →
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