Using The Graham Number Correctly

√[22.5 x EPS x BVPS] is an Intrinsic Value investing formula that Benjamin Graham — Warren Buffett's mentor — did recommend, but with conditions.


Benjamin Graham did recommend the Intrinsic Value calculation known today as the Graham Number. But as with most things related to Graham today, there's a big difference between how this calculation was recommended and how it's being used.

The Number

The Graham Number itself is simple enough, and can be derived from rule #6 and #7 of Graham's rules for Defensive stocks.

1. Not less than $100 million of annual sales.
2-A. Current assets should be at least twice current liabilities.
2-B. Long-term debt should not exceed the net current assets.
3. Some earnings for the common stock in each of the past 10 years.
4. Uninterrupted [dividend] payments for at least the past 20 years.
5. A minimum increase of at least one-third in per-share earnings in the past 10 years.
6. Current price should not be more than 15 times average earnings of the past three years.
7. Current price should not be more than 1½ times the book value.
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.

Chapter 14: Stock Selection for the Defensive Investor, The Intelligent Investor.

Note: The "multiplier" Graham refers to is simply another term for the P/E Ratio. Criterion #1 works out to $500 million today based on the increase in CPI / Inflation.

Mathematical Derivation

The optimum price for a Defensive grade stock can easily be derived from the last three lines above, and this price is known as the Graham Number.

P/E < 15

P/B < 1.5

P/E * P/B < 22.5

P * P < [22.5 * EPS * BVPS]

Final Result

Graham Number = √[22.5 x EPS x BVPS]

Note: EPS(avg) is used here instead of plain EPS to indicate that the average of the past three years has been used, just as Graham required.


The Graham Number is designed to assess stocks regardless of sector. Companies from low-earning industries such as Utilities will need higher asset figures, and those from low-asset ones such as Financial Services will need higher earning figures.

"It has long been the prevalent view that the art of successful investment lies first in the choice of those industries that are most likely to grow in the future and then in identifying the most promising companies in these industries... The author did not follow this approach in his financial career as fund manager, and he cannot offer either specific counsel or much encouragement to those who may wish to try it."

Benjamin Graham, Introduction: The Intelligent Investor.

Common Misuses

The most common misuse of the Graham Number today is that it's used in isolation almost everywhere, while the five other supporting criteria for Defensive stock selection are completely ignored.

An online search for Graham Number will bring up dozens of analyst reports recommending stocks based on the Graham Number alone.

Graham Numbers are also rarely calculated using the average earnings of the past three years now, even though Graham gave detailed explanations of how easy it was to manipulate a single year's earnings figure and why such averaging was essential.

"The more seriously investors take the per-share earnings figures as published, the more necessary it is for them to be on their guard against accounting factors of one kind and another that may impair the true comparability of the numbers. We have mentioned three sorts of these factors: the use of special charges, which may never be reflected in the per-share earnings, the reduction in the normal income-tax deduction by reason of past losses, and the dilution factor implicit in the existence of substantial amounts of convertible securities or warrants... One important advantage of such an averaging process is that it will solve the problem of what to do about nearly all the special charges and credits."

Chapter 12: Things to Consider About Per-Share Earnings, The Intelligent Investor.

Further Reading

For a complete understanding of stocks and investing, a reading of The Intelligent Investor by Benjamin Graham is highly recommended. This is the book that Warren Buffett himself describes — in his 1986 preface to it — as "by far the best book about investing ever written".


Graham's various sets of criteria are a fine balance of checks. There's no point if a stock meets just some of the criteria in a group and doesn't meet others. For example, it may be possible for a stock to show great Earnings figures while having too much Debt.

Using just a single year's Graham Number — which barely covers two of the seven Defensive criteria — is not only excessively simplistic, but also potentially dangerous.

Choosing stocks that completely meet one of Graham's other sets of criteria is a far better approach; rather than investing in stocks that incompletely meet the Defensive criteria. Graham did allow for individual exceptions though, if the portfolio as a whole cleared all criteria for Defensive investment.

Due to omissions in recent editions of The Intelligent Investor, a technique called the Benjamin Graham Formula is also often mistakenly used for stock valuation today.

Video: Graham Number

Buffett Likes Dividends

In the below clip from his address at the Berkshire Hathaway Annual Shareholders Meeting, Warren Buffett explains why he likes the stocks he owns to pay dividends and why Berkshire Hathaway hasn't paid any as yet.

Facebook Likes and Comments


HI there. Thanks for all the information your provide in your site. I have a question. I have an investor account in Australia´s stock exchange.
I wonder if Graham methods are valid as-is in this (or any other) stock exchange. Of course, his philosophy and ideas will stand in any country, but my question is if the specific mathematics would work the same or will need some adjustment.
Regards, Carlos

Hello Carlos,

The only one of Graham's criteria that seems region-specific is #5 of the defensive criteria - a minimum increase of one third in per share earnings over the past 10 years.

The rate of inflation in the United States when these criteria were published was about 5% annually. If the rate of inflation and the market cycle in Australia over the last 10 years was significantly different from the late 60s and early 70s in the United States, this criteria may need some slight adjustment.

The other Defensive, Enterprising and NCAV criteria should not require any adjustment if applied in USD.

Number 4 above says:
4. Uninterrupted payments for at least the past 20 years.

Does this mean dividends for the past 20 years? What is payments referring to?


#4 refers to uninterrupted dividend payments for at least the past 20 years.

Thank you!

Hi there, Just wanted to send you a note of approval as I find your website quite informative. I am working through The Intelligent Investor at the moment and am writing chapter summaries as I do so. Your website has been a great resource throughout this process. Thanks!

There are going to be some enhancements this quarter to Serenity's final analysis of stocks.
Do keep checking in.

can you use the Graham original formula for private company with $15M annual revenue, $50M enterprise value?

Hello SK,

Yes, you can. But you would need to use Book Value instead of Enterprise Value, as well as the 6 other supporting qualitative criteria.

Thank you for your comment!

Hi, everyone,
Thank you very much for this site! My question is related to the difference between Enterprising and Defensive prices. My intuition suggests that Enterprising investor would accept higher risk and therefore higher price than Defensive investor (all other things equal). However, in all stocks I see the opposite, defensive price (Graham number) is always higher than enterprising price (Serenity number). This suggests that defensive investor would find certain stocks fairly (or bargain) priced which enterprising investor would consider over-priced. For example, DRW8.DE has Graham number = 98% of its current price ("fairly" priced), but Serenity number = 52% ("overpriced"). Am I missing something obvious here?

"There has developed the general notion that the rate of return which the investor should aim for is more or less proportionate to the degree of risk he is ready to run. Our view is different. The rate of return sought should be dependent, rather, on the amount of intelligent effort the investor is willing and able to bring to bear on his task."
Benjamin Graham, Chapter 4: General Portfolio Policy, The Intelligent Investor.
"The determining trait of the enterprising (or active, or aggressive) investor is his willingness to devote time and care to the selection of securities that are both sound and more attractive than the average. Over many decades an enterprising investor of this sort could expect a worthwhile reward for his extra skill and effort, in the form of a better average return than that realized by the passive investor."
Benjamin Graham, Introduction, The Intelligent Investor.

Dear nvladimus,

Thank you for your comment!

As can be inferred from the above quotes, Graham taught that returns were proportional to the "intelligent effort" one put into one's investments, and not the risk one undertook.

The Enterprising Price (Serenity №) in Graham's framework is therefore lower than the Defensive Price (Graham №) because such stocks are harder to find; such a portfolio requires more diversification as well.