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Analysts Continue To Use Wrong Benjamin Graham Formula

Sep. 23, 2013 3:53 PM ETBVN, GFI, DINO, HNRG14 Comments
GrahamValue profile picture

Benjamin Graham was Warren Buffett's professor and mentor at Columbia Business School. Buffett even named his son - Howard Graham Buffett - after Graham. In the preface to Graham's book - "The Intelligent Investor" - Buffett calls it "by far the best book about investing ever written."

Serenity's Benjamin Graham Screener applies Graham's 16 financial criteria to 4500 NYSE and NASDAQ stocks to find Defensive, Enterprising and NCAV grade Graham stocks today.

Last year, we briefly saw a formula that Graham actually warned against, but is widely used as "The Benjamin Graham Formula". Today, we will look in greater depth into how this confusion came about, what Graham actually wrote and finally, some stocks that meet the more complex formulas that Graham actually did recommend.

The Wrong Intrinsic Value Formula

The formula itself is mentioned in "Chapter 11: Security Analysis for the Lay Investor" of Graham's seminal book "The Intelligent Investor" as:

Value = Current (Normal) Earnings X (8.5 plus twice the expected annual growth rate)

As shown in the scan above, Graham intended this formula to produce figures close to formal appraisals related to the valuation of growth stocks.

He then uses this formula to make the converse calculation of determining what rates of growth are anticipated by the current market price of a given stock, and then explains why such expectations are almost always unrealistic.

The Cause of the Confusion

What seems to have started the confusion is that the most commonly available edition of the book today is not the one originally written by Graham, but the new version with commentary by Jason Zweig.

In this edition, all the Foot Notes from the original book have been moved to the end of the book to make place for Zweig's commentary. For example, if we look at the same page with

This article was written by

GrahamValue profile picture
Value Investing Software True To Benjamin Graham. Apply the complete Stock Selection Framework for Intelligent Investors — that Warren Buffett recommends — optionally adjusting for Interest Rates and Inflation. Free! SerenityStocks is now GrahamValue.com #intelligentinvestor #warrenbuffett #valueinvesting Recommended Articles: 1. How To Build A Complete Benjamin Graham Portfolio (2012)  2. Using The Graham Number Correctly (2012)  3. Understanding The Benjamin Graham Formula Correctly (2015)

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Comments (35)

This formula useful for approx the value of growth stock if the future of the company perform as assumption you make (or figure you put in). More about this formula and how this formula was derived, do more on research on paper written by Benjamin Graham.
Thanks Serenity highlight the footnote been shifted for new edition of the book. That formula not indicate true value of stock but helping approximate estimate the value if the future business factor support what figure you put in.
GrahamValue profile picture
Hello Kent_Soon,

Thank you for you comment!
As mentioned, the formula also comes with a detailed and very clearly labelled warning.

Unfortunately, the warning is a given couple of pages later and is easily missed. In fact, that's possibly why Graham added the footnote in the first place.
I find it hard to believe that someone would not bother to read the foot/end notes, and then make a tool for other people to use that they themselves do not understand. But there it is, those links you provided. Unbelievable!
GrahamValue profile picture
Thank you, Panphobia!

As mentioned, the footnote was misplaced in newer editions and that probably led to the confusion.
The warning is present in both old and new editions, but on the next page.

However, a Graham valuation method with no mention of assets and based on a predictive "expected growth rate" should set off alarm bells for any student of Graham.
Ján Mazák profile picture
There are two main points of The intelligent investor: First, do not take the market price as a correct estimate of intrinsic value, and second, insist on a margin of safety.

Note that Graham explicitly mentions an 'inescapable necessity' to estimate some future growth rate for most companies. After making that estimate, the formula approximates the results you would get by multiple-stage DCF or other more elaborate valuation methods. Of course, the formula cannot replace thinking about the business itself and the reliability of its future earnings.

You can be conservative with growth estimates and insist on a large margin of safety in case your assumptions prove to be off the mark. That is what Graham suggests instead of relying just on formulas. It does not mean that the formula is of no use -- after all, it seem to be the best simple formula he could come up with.

The Graham's formula mentioned in the article could provide a good starting point, it allows to roughly screen stocks: if one finds a stock selling at, say, 80% of the price calculated by the formula, it is much more promising than one selling at 150% of the price. That's why it is used in Fast graphs etc.

Finally, asset-based valuation methods have their limitations, too; there are much more services and other asset-light businesses nowadays. Also, corporate repurchases of the last few decades have often reduced equity (i.e., net assets) to a meaningless amount.
GrahamValue profile picture
Hello Ján Mazák,

Thank you for your comment!

Given below is the reply to your comment, as well as a summary of the replies given to Jae Jun and James Allen, Sr:

1. Graham dedicates two entire, clearly-named chapters of The Intelligent Investor to stock selection. The 17 rules in these chapters are designed to ensure both a qualitative and quantitative Margin of Safety. No assumptions are required.

2. On the other hand, this formula is only mentioned briefly in an unrelated chapter, with two clear warnings.

The first is a footnote that says that this formula does not really provide any true value.

Also, Graham's actual methods always use figures from the past, including checks for past growth rate. Past figures are objective and require no assumptions. Predictions of the future are subjective. This formula uncharacteristically requires a predicted "expected growth rate" - a subjective number - to arrive at an intrinsic value.

Graham actually uses this formula to calculate the "expected growth rate" from the current price, as can be seen in the scans above. The second warning - clearly labelled as such - then says that the formula is only intended as an illustration and such projections are never reliable.

The stock selection chapters have no such warnings.

3. Recent editions of The Intelligent Investor have had the footnote moved to an obscure location, at the end of the book.

4. The full warning is only given a couple of pages later, and is easy to miss. This probably was the reason Graham included the footnote in the first place.

5. Graham's true methods always include checks for assets. This formula has no such checks. Services and other asset-light companies are nothing new. In Graham's real framework, low assets can be offset by high earnings and vice versa. Graham designed a well balanced framework that could assess all types of companies.

So while it's true that nothing is black and white - and an intrinsic value is an estimate at best - one also needs to be able to avoid mistakes and make sound decisions, based on facts. It's easy to get lost in a world of grays.

George Soros' theory of reflexivity states that our view of the world is inherently flawed. But those who have a marginally clearer view of reality tend to make slightly better decisions and over time, the slightly better decisions can snowball into significant differences in gains.

It always helps to remember Buffett's "Keep It Simple" principle.

The facts are all laid out in plain view.
What we choose to believe is up to each one of us.
James Allen, Sr. profile picture
You said:

"1. It uses subjective future estimates rather than objective past figures
2. It makes no allowance for a Margin of Safety in terms of Assets; only Earnings. "

That's where judgment and experience come into play, and programmers and high end mathematicians run into foul territory.

You run the formula, see what results, apply the sniff test, compare to other estimates of value based on other criteria, like assets, evaluate the financial statements for liquidity and other signs of impermanence, perhaps with other formulas, add in a Margin of Safety and decide what to do.

A bomb disposal officer in the British Army was asked once about how he would handle a bomb type he had never seen before. He advised to examine it very carefully, take his most experienced guess and hope for the best. It's like that in investing, except the only loud noises are the wailing when you mess up.

Warren Buffet, who was intimately familiar with Graham's teachings, observed that it is preferable to be vaguely right than precisely wrong. IOW, you don't need the formulas to be precise, only to keep you out of trouble. This is hard to accept in this age of computerization of everything, where we have come to expect a program, formula or checklist to be objective, precise, resulting in The Right Answer [tm], "buy at $14.38!"

My reading of Graham's warning is not that the formula is wrong, or should not be used, but that projections often don't come to pass, and even when they do, the value represented in the answer does not come to pass in the price.

Relying on projections into the future is always fraught with difficulties, uncertainties, doubt and fear.
GrahamValue profile picture
Hello Jim Allen,

As mentioned, Graham gives a footnote as well as a warning that such growth projections are unreliable. Even a stock with absolutely no tangible assets can clear this formula just by having a high "expected" growth rate.

On the other hand, two entire chapters of The Intelligent Investor are dedicated to methods that Graham actually recommends for investors:

1. Chapter 14: Stock Selection for the Defensive Investor, and
2. Chapter 15: Stock Selection for the Enterprising Investor

The sixteen criteria mentioned in those chapters are designed to verify all aspects of a stock before investment. http://seekingalpha.co... lists all sixteen criteria, and gives step-by-step instructions on how to find stocks that meet them.

Thank you for your comment.
James Allen, Sr. profile picture
The sense I have from years of reading and thinking and trying Graham's teachings was that valuation of a stock is not unlike appraising real estate. Real estate appraisers use several different approaches in arriving at an opinion of value. The most common are the income approach, the replacement cost approach and the comparative market approach.

This last is merely looking to see what other similar properties in the area have recently sold for, making adjustments to account for factors that seem to reflect a difference in value, like views, upgrades, quality of construction, differences in room count, zoning, etc.

The income approach tries to arrive at a value by assigning an appropriate capitalization rate to the stream of income from the property, with some regard for uncertainty, risks etc. The replacement cost approach tries to estimate what it would cost to replace the property in its present condition.

These computations are not "fixed in stone" numbers, but rather usually form a band of figures from which the appraiser can use experience and judgment in arriving at an opinion of value. The numbers support, justify, that opinion, hopefully.

The most important concept to internalize is that the valuation, however derived, is an opinion. These values are not facts but opinions, formed hopefully with due regard for the facts of income, comparative prices, etc. tempered by experience and judgment.

In real estate, you wouldn't buy a property for $1 million if the appraisal came in at half that. You hunt for properties that have a value of $1 million which you can buy for half that. In hunting for stocks, we know the price but often stumble in figuring the value.

Salesmen will often tout "potential" as a substitute for "value" and they get away with it just often enough to keep on trying it. Potential, however impressive, should not be an element of valuation for an investor. Maybe Disney will come along in 6 months, buy that big property down the road and all these properties nearby will shoot up in price. Maybe not.

The end purpose of all of this effort is to satisfy yourself that you didn't pay too much.
GrahamValue profile picture
That's a very nice analogy, Jim Allen!

When done for the purpose of investment, buying real estate is really no different from buying stocks. The old misconception that real estate prices only go up will find fewer takers after the crash of 2008. In fact, stocks have quite a few advantages over real estate - better liquidity, more historical performance data, better overall performance, and more formally documented approaches to analysis.

You're right in that the general idea is to ensure you're not paying too much (keeping a "Margin of Safety") and there are multiple ways to calculate the value of a stock.

The purpose of the article was only to point out that - if you're following Graham's approaches to investing - Graham had very specifically warned against using this formula, or any other such growth stock valuation.

The other major arguments against this formula - other than the fact that Graham warned against it - are that

1. It uses subjective future estimates rather than objective past figures
2. It makes no allowance for a Margin of Safety in terms of Assets; only Earnings.
James Allen, Sr. profile picture
I'm not sure I would characterize Graham's "formula" as incorrect or being used incorrectly. Formulae in financial analysis, especially valuation ones, are not like formulae in physics or geometry. They can be regarded as guesstimates at best, not precise, unyielding, immovable declarations. Right, Long Term Capital Management?

I have always thought of these formulae more as "Rules of Thumb," comparative tools, not precise Excel spread sheet "take it to the bank" formulae, guidelines only to compare similar, or different, investments with each other.

Towards the end of his life, Graham became more and more interested in simple methods which could be used in place of the complex analyses which he and the financial analysts had developed over a few decades, simple rules of thumb that would give respectable results, always with a margin of safety.

I'm not sure Graham would have been happy with the so-called "Graham Number" or its usage, "if the price is less than the Graham Number it's a buy, if not, it isn't." Graham had not been that mechanical in his career. Buffett and Schloss complained that they would spend hours gathering and working up the figures on a stock, get all the formulae all figured out, and Graham wouldn't jump on it. None of them had the benefit of computers and the internet to help gather and interpret. That is part of what is lacking in so many of our efforts now. We have numbers, formulae, computers to correlate every number with every other number and more people doing it, in a hurry. No time is lost in thinking, just number crunching. Judgment, founded upon knowledge and experience of what the numbers mean in a given context, is still essential to avoid spectacular failures, or try to.

I remember reading that Christopher Browne of Tweedy Browne complained gently he had spent one summer early in his career computing the book value of every bank stock in the entire country, thousands of them. I'm sure that experience paid off handsomely as he proceeded through a wonderfully successful career, much more so than for the poor bloke now who writes up a program to crunch all those numbers pulled out of a database, rank all the "betas", untouched by human brains.
GrahamValue profile picture
Thank you, Jim Allen!

The purpose of the article was not to evaluate the formula itself, but to simply point out that Graham had very specifically warned against using this formula, or any other such growth stock valuation.

Over time, Graham did move away from the in-depth methods detailed in "Security Analysis" to the more large-scale methods in "The Intelligent Investor".

But all the methods actually recommended by Graham have at least one requirement for Earnings, and one for Assets; at a minimum.

http://seekingalpha.co... lists all sixteen of the criteria Benjamin Graham recommended in The Intelligent Investor, and gives step-by-step instructions on how to build a stock portfolio that meets them.
ArtfulDodger profile picture
Good piece, Serenity. Excellent catch. Will put you on my read list. Thanks much.

Odd is it not that WB touts BG so often and so much, but from as far back as I've studied WB's techniques has not followed BG's methods, except perhaps at the very first of his investing career?

Obviously, CM has affected WB more than BG. If I had to analyze CM's method, which strongly contrasts with BG's, it would be focusing on investing in high-quality businesses with essential products/services over raw, fundamental numbers investing.

CM certainly has caused WB to focus more on qualifying a company than quantifying it. Personally, I try to do a little of both, as I'm sure WB & CM do, too.

Please keep up the good work, Serenity. Thanks again.
GrahamValue profile picture
Thank you very much, ArtfulDodger!

Replying to your observation about Buffett and Graham will require including a few quotes that are lengthy, but insightful.

Buffett himself says he's 85% Graham and 15% Phil Fisher.
In his 1984 speech "The Superinvestors of Graham-and-Doddsville", he says:

"In this group of successful investors that I want to consider, there has been a common intellectual patriarch, Ben Graham.... They have gone to different places and bought and sold different stocks and companies ... I should add that in the records we’ve looked at so far, through- out this whole period there was practically no duplication in these portfolios."

Also, in the "Legacy of Benjamin Graham" video released by the Heilbrunn Center, Buffett explains that Graham was focussed on refining a method that ordinary investors - without specialized knowledge or access - could apply to achieve the same results as himself.

Regarding the possibility that Buffett may tout Graham without following him, given below is part of the conclusion from the study "The Evolution of the Idea of Value Investing: From Benjamin Graham to Warren Buffett" by Robert F. Bierig, Duke University:

"A [casual] observer of Buffett today would find it difficult to see the Ben Graham influence in many of his activities. However, that influence remains at the core of Buffett’s investment model. Buffett continues to think about stocks as fractional ownership interests in underlying businesses, he continues to operate under the assumption that there is a distinction between price and value, and he continues to search for the largest discrepancy between those two items. In other words, he continues to be a value investor."

The difference between Graham and Buffett is simply that of principle and application.

All of Graham's students follow the same principles, they just apply them in their own way. Buffett is simply the most visible of them because he's the wealthiest.

But large portfolios are simply not a priority to some people.
Graham himself said in 1976:

"About six years later, we decided to liquidate Graham-Newman Corporation-to end it primarily because the succession of management had not been satisfactorily established. We felt we had nothing special to look forward to that interested us. We could have built up an enormous business had we wanted to, but we limited ourselves to a maximum of $15 million of capital-only a drop in the bucket these days. The question of whether we could earn the maximum percentage per year was what interested us. It was not the question of total sums, but annual rates of return that we were able to accomplish."
ArtfulDodger profile picture

Thank you for that reply. I just caught it today, 5-13,14. Sorry I have not replied sooner.

I would agree on this point: there is often a difference between method and practice, which is one thing I think you're saying. And there can be a difference in definition among people who say they are value investors, because people look at value differently.

Buffett is a slick customer; he often speaks of a method he does not now practice, and has been moving away from since the 1960s. Indeed, he does love giving Graham a lot a credit. But I believe he should say, From the late `50s to 1967 I followed the Graham-method of investing. After that I moved to the Munger-method, that is, qualifying companies over quantifying them.

For years Buffett & Munger have been looking at buying companies they believe will be here and be needed 100-years from now. In so doing, they've paid some premium prices for these companies, the railroad they bought for one. But they believed that they bought in the best area of the country a business that would still be here and be needed in 100-years.

They bought an insurance company because they wanted the float so they would have a continuous flow of cash to re-invest. They certainly did not steal it, as Buffett was trying to do back in the `60s, until he met Munger who much more strongly pushes to buy companies with great products and management — even if they have to pay a premium for them, though he may say they're paying a fair price for a great company. Neither Graham nor Fisher would have done that at any time in their careers. Neither would Fisher have owned a whole host of companies as Berkshire does.

As for quotations, one of Munger's goes something like this: I would rather buy a great company at a premium price than a not-so-great company at a cheap price. (that's by memory and paraphrasing; but it's his thinking, which has moved directly into Buffett's)

To me that is buying companies by qualifying them to a much greater degree than quantifying them, as Graham and Fisher emphasized.

I'm a don't show me — tell me type of person. And what Buffett says goes in one side and out the other, because he has at times, over the years, knocked stocks as expensive and claimed there wasn't enough potential return to buy them. Meanwhile, it comes out a few weeks later he's been buying with both hands (making such a statements can get you strung up in certain parts of the country). He did this 40-years ago when he was gobbling up Washington Post shares for under $5.00.

Serenity, I have tried to learn from all of these successful investors, plus a few others, such as David Dreman and Philip Carret. Toward the end of carrying out what I have learned, I want to both qualify and quantify an investment by a criteria I myself am comfortable with. I can't, for example, pay a premium for companies — looking out 100-years, because I don't have a continuous float to keep buying with. And I can't buy companies simply because they have great products and excellent management.

As a couple of examples, I have to use quite a bit of discretion. I have to look for quality and value where no one else wants to go.

Again, good piece and excellent reply. The best to you and your investing.
GrahamValue profile picture
Thank you for that very informative comment, ArtfulDodger!

NCAV stocks are Graham's most popular investment model, and possibly the reason for the common belief that he only recommended cheap stocks. But Graham actually recommended Defensive and Enterprising stocks before NCAV stocks and both were allowed higher quantitative evaluations and required greater qualitative checks. Graham did advocate paying more for quality. His only prerequisite was that there be the margin of safety between price and value, whether the value be qualitative or quantitative.

In fact, the last of the Graham strategies mentioned in http://seekingalpha.co... is "Special Situations", which is precisely the type of investment you speak of. But he did not recommend it for the ordinary investor as it supposedly required a high degree of skill, experience and resources. As Buffett said, Graham was more focussed on developing an investment model with which the ordinary investor - with his ordinary resources - could use to get results similar to his own.

But Buffett being Buffett has the skill, experience and resources; and yes, almost all his investments do fall in Graham's "Special Situations" category.

Thank you again for a very informative comment!
Jae Jun profile picture
@ varan and serenity.
Not unreliable. All valuation purposes are designed to give the user an approximation of value. There is no such thing as a concrete, absolute method for valuation. Investing is an art as well as science.

The point is that Graham's intention was not to say "I'm just writing this formula for illustration purposes" and forget about it, it's his disclaimer from back in the day saying that valuation should be used with caution instead of blindly applying.

If Graham just wanted to use it as an example with no intention of using, why would he bother to research how it works, the effects, and the results?

Use with caution is what he is saying, not, don't use it at all.

Anyways, thanks for the discussion.
GrahamValue profile picture
Hello Jae Jun,

As mentioned, Graham gives a footnote as well as a warning that such growth projections are unreliable. Even a stock with absolutely no tangible assets can clear this formula just by having a high "expected" growth rate.

On the other hand, two entire chapters of The Intelligent Investor are dedicated to methods that Graham actually recommends for investors:

1. Chapter 14: Stock Selection for the Defensive Investor, and
2. Chapter 15: Stock Selection for the Enterprising Investor

The sixteen criteria mentioned in those chapters are designed to verify all aspects of a stock before investment. http://seekingalpha.co... lists all sixteen criteria, and gives step-by-step instructions on how to find stocks that meet them.

Thank you for your comment.
Jae Jun profile picture
Hello Serenity.

The point is that Graham's intention was not to say "I'm just writing this formula for illustration purposes" and forget about it, it's his disclaimer from back in the day saying that valuation should be used with caution instead of blindly applying.

Entire shelves of textbooks written by valuation masters that I respect like Prof Damodaran, Prof Greenwald also include methods of calculating stocks with growth.

Value and growth are joined at the hip. Please read Buffett's 1992 letter.

"In our opinion, the two approaches are joined at the hip: Growth is always a component in the calculation of value, constituting a variable whose importance can range from negligible to enormous and whose impact can be negative as well as positive." - Buffett

The word I've used over and over again is that valuation requires a range.
You even highlighted that Graham said to it as an approximation and range.
GrahamValue profile picture
Thank you for your comment, Jae Jun.

This debate has become quite academic. The Graham references cited in the Serenity's articles are all publicly available. Interested readers are encouraged to look them up and decide on the facts for themselves.

Thank you.
Jae Jun profile picture
Yes. All three can be applied to any valuation method.
Varan profile picture
really? then why go through the exercise of computing numbers that may be unreliable for the purposes for which they are intended? if it is just a question of faith, you are talking about religion rather than anything else.
GrahamValue profile picture
Graham only gives these warnings for this formula, Jae Jun.
He strongly recommends the formulas in the Stock Selection chapters: http://seekingalpha.co...

Thank you!
GrahamValue profile picture
Also Jae Jun,

Even though it's mentioned on your profile, it should perhaps be noted here for the benefit of casual readers that you run "Old School Value"; a valuation tool that uses this formula to analyze stocks.
Jae Jun profile picture
Thanks for the link Serenity.
Think there is some serious incorrect assumptions here. The most important topic is not the formula being used incorrectly (which it isnt), it's that valuation is an art and should always be taken as a range. That is what Graham is saying. Not the formula being incorrect.
GrahamValue profile picture
Thank you for your comment, Jae Jun.

The phrases "for illustrative purposes only" and "Let the reader not be misled into thinking that such projections have any high degree of reliability" are from the Warning note.
The phrase "we do not suggest that this formula gives the true value of a growth stock" is from the Foot Note.

All 3 are quite unambiguous.
Varan profile picture
ha! but they [abusers of Graham formula] also say that the intrinsic value "need not be precisely defined." So you can never prove them wrong.
GrahamValue profile picture
Thank you, Varan.
The intent was not to prove anyone wrong anyway.

But vague definitions are dangerous territory. Success, Failure, Profits, Losses and Bankruptcy are all terms that need not be precisely defined.
I tried the Serenity Screen on one of Buffet's holdings, a megacap stock, symbol IBM. Far from unknown or opaque financially. There was no graded value. End of that resource for me.
GrahamValue profile picture
As far as Buffett's holdings go, wdjax0n:

Most of Buffett's operations come under what Graham classified as "Special Situations", advanced investments not suitable for the ordinary investor. Buffett makes institutional deals with prices and benefits that most people cannot.
GrahamValue profile picture
Also, not all stocks failing Graham's rules are necessarily bad investments. Graham's rules are just extremely selective. Graham designed and backtested his framework for over 50 years, to deliver the best possible long-term results.

Even when stocks don't clear them completely, Graham's rules give a clear quantifiable frame of reference for comparison.
Great article and a good quick reference for authors who want to avoid invoking Graham's name & methods incorrectly (which is all too common, it seems).
GrahamValue profile picture
Thank you, WallStreetDebunker!
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