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A multifaceted approach to value investing with stock valuation based on intrinsic value estimated from cash returns, appraised value of assets, and other facets of value.



Stock Screening


Screening   |   Bargain Issues   |   Three-Factor Screen   |   Unit Pricing   |   Grail


Screening versus Valuation

Absolute investment valuation independent of the stock market pricing process is not the same as mechanical stock screening and relative rank-ordering. Such screens or filters are usually financial ratios that include price and other accounting measures of value. The table below demonstrates the double-trap of mere screening without investment valuation. The hypothetical numbers in the table are chosen so as to better illustrate the phenomenon for ten randomly-chosen stocks.

Stock No.

$ Value

$ Price

$ Book

MM Shares

P/B Ratio


Cum $ MC

Cum % MC



























































































In the table, MM is millions, P/B Ratio is price-to-book ratio, MC is market capitalization, and Cum is cumulative. In the second column, the < symbol indicates a share value that is over-priced by a small margin, and the >> symbol indicates a share value that is under-priced by a large margin. The estimated intrinsic economic value of a company is a probabilistic range based on spreadsheet net cash flow analysis and formulas, and the judgment reached is independent of the market quotations for its common stock. The precision of a single appraisal number such as the mean of the probabilistic range is consistent with the essential precision of the concept of intrinsic value but is also potentially misleading. The upper and lower bounds of the probabilistic range are also useful in making investing decisions.

The first five stocks are punished with P/B Ratios less than 1 for some good reason that is not important for this argument. Only one stock, number 8, is under-priced at this time, and it has a large margin of safety. Yet, the important point is that stock #8 would be classified as a growth stock and not as a value stock by the criterion of either P/B Ratio, or half the number of stocks, or fifty percentage of the total market capitalization.

Improper finds (false positives) and overlooked opportunities (false negatives) are the
two traps or double-trap that can result from any mechanical stock screening. Investment ideas will not come from screening. The sources of good ideas include the business and financial press and rigorous, systematic, scientifically-valid, economic research.

Because screens are superficial and mask underlying meaningful distinctions among stocks and companies, due to the operation of
double-traps there will be no significant difference in long-term total return between the group of stocks included by a screen and the remaining group of stocks excluded by the screen. It makes as much or as little sense to screen the S&P 500 or any other universe of stocks by their ticker symbol and rank them in alphabetical order from A to Z, then divide them into two equal size groups, place any odd median stock in either A or Z by convention, and call them the Alpha and Omega portfolios that track the corresponding investment styles. In the short run, Alpha and Omega will alternate being first and last. The last will be first, and the first will be last. In the long run, Alpha and Omega will have total returns that are not significantly different, and comparisons between their performance over arbitrary periods of time such as one or more calendar quarters or years will prove nothing. Academicians, financial journalists, investment managers and mutual fund brochures can be expected to argue the relative advantages of Alpha style or Omega style during different phases of the stock market cycle.

Bargain Issues

Bargain issues are discussed by Graham and Dodd in every edition of Security Analysis and by Graham in The Intelligent Investor. A bargain issue is detected by one of two tests. The first test is the method of appraisal using a P/E ratio. The second test is the value of the business to a private owner where more attention is likely to be paid to the realizable value of the assets, with particular emphasis on the net current assets or working capital, i.e., a P/NCA ratio or P/WC ratio. The pawnbroker's version of the second test emphasizes quickly realizable assets such as cash and near cash or P/C ratio. These two tests are not estimates of intrinsic value. The first test is a screen based on unit pricing. The second test is a screen based on a very conservative estimate of breakup value.

Three-Factor Screen

Phil Graham sought the cheapest stocks, and Warren Buffett sought stocks in great companies at bargain prices. A three-factor screen is being touted to pick so-called good cheap stocks, but it is old wine in a new bottle.

An article entitled "Magic Formula Of Little Book Just May Work" by Jesse Eisinger on pages C1 and C5 in the 9 November 2005 Wall Street Journal discusses a method of picking stocks that is essentially a screen. The source of the magic formula is a 2005 book entitled The Little Book That Beats the Market by Joel Greenblatt, who is also the author of a 1997 book entitled You Can Be a Stock Market Genius (Even If You're Not Too Smart). Eisinger reports that the "Little Book is one of the best, clearest guides to [so-called] value investing. ... in a world where individual-investor advice is dominated by jargon-filled short-termism on the one hand and oversimplified [slice and dice] indexing on the other. ... He [Mr. Greenblatt] writes ... with the fervor of a true believer." The following is a paraphrase of selected excerpts from the article, followed by a cautionary comment.

The magic formula is to invest in good companies when they are cheap. Good companies earn high returns on their investments. Cheap companies have share prices that are low based on past earnings. The proxies for these two criteria are accounting return on capital and market earnings yield. Accounting return on capital is here defined as operating profit as a percentage of net working capital and net fixed assets. Market earnings yield is here defined as pretax operating earnings compared with enterprise value, which is the market capitalization of the stock plus the net debt.

Mr. Greenblatt advises individual investors to buy a basket of top stocks and turn them over on a strict schedule, depending on how they perform. For maximum tax advantage, sell losers just before a year is up, and winners just after a year.

Looked at in hindsight, the returns of the magic-formula method allegedly beat the market. From 1988 through 2004 (7 years), according to Mr. Greenblatt's book, the (1) high-book-return and (2) low-price stocks of (3) the largest 1,000 companies had (4) stock market returns of 22.9% annually, compared to 12.4% for the S&P 500. When (1) 2,500 companies [one-half of U.S. industrial stocks; probably the largest] are ranked for (2) price and (3) book returns (based on the formula), then in terms of (4) stock market returns, the top 10% outperformed the second 10%, which outperformed the third 10%, and so on. It works in order.

The approach is difficult not because it is hard to understand, but because it requires patience and trust that you are right when the market is indicating that you are wrong. Some limitations to the approach include the tendency to choose stocks whose high book returns and growth in size or market capitalization may be in the past. Some of the magic-formula stocks with more than $1 billion in stock-market capitalization include many fast-growing specialty retailers and niche pharmaceutical companies, some of which will burn out.

That is why Mr. Greenblatt argues that novice investors buy at least 20 to 30 of them. For himself, he buys a smaller number that he can know deeply. But that requires something not easily taught in a book: good instincts and judgment to distinguish true cheap gems from one-hit wonders.

COMMENT: There are two problems with this magic formula investing three-factor screen of (1) market size, (2) book return on capital, and (3) combination market-and-book earnings/size yield, to maximize (4) stock market return. The current values of the magic formula investing criteria are available from S&P Compustat that provides financial and other information on more than 5,000 U.S. industrial stocks and from other commercial databases, but their use as a stock picking method is dubious.

Neither Mr. Eisinger nor Mr. Greenblatt holds a Ph.D. degree in financial economics, and this might explain their silence about the first problem. Two of the three screens or factors are not independent of stock market return. The market capitalization of a company's total stock, a k a size, as here defined, is not independent of stock market return. Earnings/size yield, as here defined, is not independent of stock market return, because earnings/size yield entails size. Only return on capital, as here defined, is independent of stock market return.

Size is logically circular as an explanatory factor in any econometric model of stock market return, because both size and market return entail stock price. An econometric model with size as a factor, or with size as part of a factor, is not scientifically valid. Therefore, back-testing the magic formula investing three-factor screen is vicious circular reasoning, fatally fallacious, meaningless, and non-interpretable. The magic formula investing three-factor screening method for picking stocks is fatally flawed and disguised market timing.

When being back-tested for (4) stock market return, and compared to benchmarks such as the S&P 500 Index of common stocks, the magic formula investing three-factor screening method is essentially and effectively an asset pricing model of return; and as such, it is a variation of the pseudo-scientific Three-Factor Model of return for stock portfolio pricing. Both return models have three factors, each of which entails one of three variables: (1) size, defined as market capitalization; (2) a variable that does not entail price; and (3) a yield on price, defined in various ways, such as earnings/price, earnings/size, or earnings/enterprise value. For both return models, the factors related to the size and yield-on-price variables are logically circular.

Both Mr. Eisinger and Mr. Greenblatt have reason to know about the second problem with this magic formula investing three-factor screen. An investor can choose to ignore the first problem, which involves theory, and believe in magic. But an investor cannot ignore the second problem, which is practical implementation of the theory behind the magic formula investing three-factor screen.

The Greenblattt Magic Cube of three dimensions is a black box, and the details of sorting, ranking, and picking individual stocks are proprietary. And the devil is in the details. More transparency is needed for fuller accountability. The Greenblattt universe of investment opportunities is already screened for (1) publicly traded common stocks, (2) U.S. based companies, and (3) industrial firms. This universe of U.S. industrial common stocks is sorted by the three screens in some order, and the order is arbitrarily chosen. A different order results in a different selection of stocks if the net remaining universe is used instead of the gross beginning universe of investment opportunities to determine averages or cut-off points. The gross cheapest stocks that are the net best are not the same as the gross best stocks that are the ne cheapest.

In addition, each screen or dimension is a continuum that is partitioned into categories, and the number of categories is arbitrarily chosen. If each of the three dimensions is split into two parts, then 1/8 of the universe is selected; and if each dimension is split into ten parts, then 1/1000 of the universe is selected. For the universe of U.S. industrial stocks of about 5,000 companies, this ranges from 625 to 5 stocks selected.

Furthermore, there must be breakpoints between the adjacent categories, and the breakpoint values and/or the method of determining the breakpoint values is arbitrarily chosen. The categories might be deciles, for example, and the breakpoint values would follow this choice of relative comparative values. Or the categories might be simply pass or no pass, depending on the absolute minimum acceptable value of each criteria. For an example of such absolute minimums, "large" might be more than $1 billion in market capitalization; "good" might be higher than the risk-free rate on U.S. Treasury bonds, adjusted for price-level inflation, plus an equity risk premium; and "cheap" might be higher than the earnings/price ratio on the S&P 500 index of common stocks.

In summary, the magic formula investing three-factor screen will continue to work even after everyone "knows" it, because mathematics will continue to work even after everyone "knows" it. Logically circular back-testing is purely mathematical. Vicious circular reasoning can be subtle to detect, even for intellectuals with doctoral degrees and for practitioners who have made fortunes in the stock market. It is a familiar phenomenon for someone who has successfully invested in the stock market to believe he has a magic touch and then write a book about his alleged method, leaving readers to discover that there is no magic or science about his stock-picking success.

Unit Pricing

Price is not value, and unit pricing is not valuation. Unit pricing in this context does refer to market price per share of stock but rather to what the investor gets by owning that share of stock. A unit price may be useful for comparison shopping, but how many people buy even their commodity groceries strictly on the basis of calculated unit prices? That is how many value and growth investors unwittingly buy their stocks and mutual funds. Are common stocks fungible?

Unit prices are expressed either in number of units per dollar or other currency or in dollars or other currency per unit. Unit prices for common stocks are expressed as price ratios such as the P/E ratio (the dollar market price per unit of earnings), the P/BV ratio (the dollar market price per unit of book value), and the dividend yield or D/P ratio (the number of dividend units per dollar market price).

The fact that unit prices are quantifiable, monetizable and easy to calculate explains their attraction. They are also superficial in the sense that no judgment or expertise or even experience is needed to calculate them. They have the advantage of convenience. Screens based on external financial accounting data bring to mind the Sufi story about the man searching at night under a lamp post for his lost house keys. When asked by a passerby where he was when he last had the keys, he said it was near his house. When then asked why he was searching so far away from his house, he said because this is where the light is.


There is a perennial search for a screen that is a good proxy for investment value. Such a screen is a grail for some so-called value investors. Various screens have been proposed over the years. Some questions come to mind concerning such a grail screen.

First, how high is the correlation between any given screen and investment value, in terms of the stocks selected? If a particular screen results in selecting the same stocks as estimates of investment value, then the correlation between the screen and the investment value estimate is perfect and the coefficient of correlation between them is one hundred percent. What is the minimum acceptable correlation coefficient to justify use of a screen in lieu of estimates of investment value?

Second, since correlation is a statistical concept based on a group of stock selections as opposed to a single stock selection, would it be necessary to have a minimum number of stock selections in order to realize the validity of the correlation? If so, what is the minimum number of selected stocks in the portfolio?

Third, correlation is calculated between a sample of a sufficient number of pairs of points. Each pair consists of a point for the screen value for a particular stock and a point for investment value of that same stock. As a practical matter, the concept of investment value is operationalized as a range of values and not as a single point estimate, and sometimes to select or deselect a stock, this investment value range is unbounded on either the upper tail or the lower tail, respectively. In other circumstances, to select or deselect a stock, a margin of safety is calculated from the estimated investment value mean and the quoted market price, and the size of this margin can vary subjectively from stock to stock depending on the size and shape (moments) of the distribution of investment value and other considerations. Without losing information for informed rational decisions about selecting or deselecting a stock, how can a simple correlation coefficient be calculated from a distribution of investment value, an unbounded distribution of investment value, or a fuzzy distribution of the margin of safety of a stock?

Fourth, before calculating correlation coefficients, someone with an appropriate circle of competence would need to estimate investment value of the company and its common stock. Such expertise is idiosyncratic and constitutes a valuable person-specific monopoly of knowledge. Setting aside for the time being the practical difficulties of finding such qualified persons, how would you operationally define and grade the circle of competence of the expert appraisers?

Fifth, assuming that we have the results of such a correlation analysis with assessments of statistical reliability, is this correlation that is calculated using in part historical data and 20/20 hindsight expected to hold beyond the fiscal periods on which the screen data are based? For example, assume the screen is the Price to Book Value ratio (P/BV). If the correlation between P/BV and investment value turns out to have the highest coefficient in the empirical study, will P/BV remain the single best proxy of investment value both for all stocks in all markets and for all future stock market cycles?

Sixth, assuming that we have access to estimates of investment value of a sufficient number of stocks within the circles of competence of the associated expert appraisers, what would be the purpose of calculating the statistical correlation coefficients between the investment value selections and the selections by various screens? Would it be done for an academic paper? Would the authors of the paper estimate investment values?

It is clear that screening, regardless of the number or sophistication of the screens used, is not a reliable substitute for valuation. Screening is superficial, and valuation is deep. Screening is an efficient way to reduce a universe of stocks within an already circumscribed circle of competence to a short list of stocks for in-depth study. Valuation is an independent process that has no necessary relation to screening and can be done without any screening whatsoever. Screening is more useful in a top-down approach that begins with a universe of stocks than in a bottom-up approach that begins with a single stock idea.

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