The Graham Number Explained

Apply Benjamin Graham's own test to two companies and it will tell you to buy the worse one. That is not a trick of how the example was chosen — it falls directly out of what the formula measures, and understanding why is the difference between using the Graham Number as a screen and using it as an answer.

The test is a single line. The Graham Number is the square root of 22.5 times earnings per share times book value per share, and it represents the highest price a defensive investor should pay. Run it properly on two businesses in the same industry and the result needs explaining.

Two companies, one formula

Stetron and Kestrel are both fictional industrial suppliers, described elsewhere on this site. They share a sector and a customer base and almost nothing else.

The arithmetic is short. Stetron: 22.5 × $2.60 × $13.00 = $760.50, and the square root of that is $27.58. Kestrel: 22.5 × $2.20 × $20.00 = $990.00, root $31.46. At $37.60, Stetron trades well through its ceiling. At $24.20, Kestrel has room underneath it.

There is a second way to reach the same verdict that is easier to check by eye. Multiply the two multiples together and compare with 22.5, which is exactly what 15 × 1.5 comes to. Stetron's P/E of 14.5 × its P/B of 2.89 is 41.8, nearly double the limit. Kestrel's 11.0 × 1.21 is 13.3, comfortably inside it. The square root and the multiple product are the same test wearing different clothes: passing requires P/E × P/B ≤ 22.5.

The verdict that should make you pause

Kestrel passes and Stetron fails, and the company that passes earns 11.0% on equity against Stetron's 19.9%. The failure is not because Stetron is expensive on earnings — 14.5× against 11.0× is a 3.5-point gap, not a chasm. It is because Stetron earns nearly twice the return on each dollar of book value, so the market pays 2.89× book for it while Kestrel trades at 1.21×.

The formula is doing exactly what it was designed to do, and the design is the point. Graham's screen asks whether a business is cheap relative to both its earnings and its assets at once. Stetron is not cheap relative to its assets, because its assets are unusually productive — which is a good thing about Stetron that the formula registers as a warning. A screen optimised for balance-sheet protection will systematically under-rate businesses whose value sits in returns rather than in assets.

If that reads as a flaw, consider the alternative. A screen that ranked Stetron above Kestrel would be ranking a 19.9% ROE business above an 11.0% ROE business at a higher multiple, which is a growth argument, not a defensive one. Graham was explicit that he was writing for investors who wanted protection first and would happily give up upside to get it. The formula is faithful to that brief. What it is not is a general-purpose answer to whether a stock is good value.

What 22.5 really enforces

The constant is presented as two separate limits — never more than 15 times earnings, never more than 1.5 times book — but the square root does not enforce them separately. It enforces their product. A stock can trade above one limit as long as it is far enough below the other to compensate.

The frontier where P/E × P/B equals exactly 22.5 runs like this:

At Stetron's own Graham Number of $27.58, the implied multiples are a P/E of 10.6× and a P/B of 2.12×. That P/B is well above the 1.5× limit Graham is usually quoted as setting, and the stock still counts as passing, because 10.6 × 2.12 = 22.5. Anyone who reads the rule as "15× earnings and 1.5× book, both" is applying a stricter filter than the formula does.

The square root cuts in both directions

Value climbs with the square root of the inputs, which means improvement is heavily discounted. To double a Graham Number you need to quadruple earnings per share or book value per share — or quadruple the product of the two. Nothing in between gets you there.

The practical version of that for Stetron: at $37.60 it needs its ceiling to rise by 36.3% to meet the price. Because of the square root, that requires earnings or book value per share to rise by 85.9% — from $2.60 to $4.83 of EPS, or from $13.00 to $24.17 of book value. Not a year of decent growth. Nearly a doubling of either.

This cuts the other way too, and it is the quieter problem. A company whose earnings fall 30% does not see its Graham Number fall 30%; it falls about 16%, because the square root of 0.7 is 0.837. The ceiling is sluggish. A business whose earnings are sliding will keep appearing to pass for a while after it has stopped deserving to, and a business compounding fast will keep appearing to fail.

Three things the formula cannot see

Debt. This is the largest hole. Stetron carries net debt of $200m, which is 0.55× EBITDA and 9.8× covered by operating profit. Kestrel carries $2.40× EBITDA — roughly four and a half times the leverage. Graham's formula looks at neither figure. It passes Kestrel and fails Stetron, and it would do the same for a company carrying debt at eight times EBITDA if the earnings and book value fell out the right way. Book value itself is the reason: leverage raises the return on a given equity base, so a heavily indebted company can show a flattering book value per share while the assets behind it are pledged to lenders. Graham later added explicit debt and stability tests to his screening criteria for exactly this reason.

What book value is made of. The formula treats a dollar of book value as a dollar of protection, which only holds when the assets are tangible and marked near what they can be sold for. For a manufacturer that is roughly true. For a company whose assets are software, brands or acquired goodwill, book value understates the business badly and the Graham Number comes out artificially low. For a bank or insurer, most assets are financial and marked close to market, so book value is unusually meaningful — but the leverage the formula ignores is also unusually large. The input is not comparable across industries.

Growth, entirely. A business that compounds earnings at 15% a year and reinvests nothing will fail this screen while a business that earns the same amount forever from a standing start will pass. That is a deliberate trade, not an oversight. It is also why almost nothing in the modern market clears the bar, and why a screen returning no results is the normal outcome rather than a signal that you looked in the wrong place.

How to use it without being misled

Treat a pass as necessary and nowhere near sufficient: a stock that clears the Graham ceiling is cheap against earnings and assets, and that is all you have established. Then add the three questions the formula skipped.

• Can it service its debt? Interest cover and net debt to EBITDA, before anything else. A Graham pass at 6× leverage is not the same security as a Graham pass with no debt.
• Is the return on equity durable? A high ROE built on a thin margin in a competitive market does not persist, and neither does the book value it produced. This is where the Stetron-versus-Kestrel comparison lands: the business that fails the screen earns almost double, and whether that is worth paying for is a question the screen cannot answer.
• Is the earnings figure real? Cyclical earnings at a peak, or earnings supported by accounting rather than cash, will flatter the ceiling. Compare free cash flow with net income before trusting the EPS input.

Used this way the Graham Number earns its place as a first pass. It is fast, it needs two numbers, and it is hard to fool with a story — a company either clears the ceiling or it does not. What it will not do is tell you which of two businesses is better, and the two-company example above is the demonstration: the formula's preference and the quality ranking point in opposite directions, and only one of them is a judgement about the business.

Run your own inputs through the Graham Number calculator to see the ceiling and the implied multiples it assumes, then check the result against the P/B calculator for the asset side and the P/E calculator for the earnings side. Because the ceiling ignores debt and growth, a pass is the beginning of an argument about a stock rather than the end of one — and how much discount to demand on top of it is the subject of margin of safety.

Related guides

• What Is a Good P/E Ratio? — The arithmetic of a justified multiple, and the four ways a low P/E ratio lies to you
• How to Compare Two Stocks — A five-axis comparison, worked side by side, and why the cheaper multiple can be the dearer stock

More guides

• Margin of Safety — How big a discount a given business deserves, and why a low multiple is not the same as a discount
• Dividend Investing — Testing whether a dividend is actually safe, using payout, cash coverage and leverage
• How to Read a Cash Flow Statement — The three sections, the eight sign combinations, and what each one warns you about
• Intrinsic Value vs Market Price — Why the two diverge, when cheap is not cheap, and what should force your estimate downward
• How to Read a Balance Sheet — Reading the asset side properly: six ratios, the ROE decomposition, and four common traps
• Dividend Yield vs Total Return — Four ten-year scenarios showing why a high yield and a high return are different things
• WACC Explained — The discount rate built from five sourced inputs, on the same worked example
• The DCF Method Explained — The forecast half of the model, worked end to end on one cash flow
• How to Value a Stock — The full valuation sequence on one worked example, from choosing a method to setting a buy price
• Free Cash Flow: What It Is and Why It Matters — The input every valuation depends on, including a case where profit is positive and cash flow is not

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