Using Rational Value to Judge a Stock's Worth

The range of valuations a stock has traded at over the past several years can be used to determine if the current price is high or low.

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Here is a proposed departure from conventional thinking about the way we, as individual investors, value our holdings.

Wouldn’t it be wonderful if we could shake loose the fetters that bind us to the unpredictable movement of the volatile market and serenely view our holdings as the assets they really are? I would submit that we can.

When a company issues and sells new stock, two things happen: The company receives the money agreed to from its underwriting investment banks, and the banks receive the issued shares.

The company will use its newly acquired funds for whatever purposes they were sought—such things as paying off its initial investors, reducing its debt or acquiring assets with which it can increase its revenue or reduce costs.

The investment banks will take the shares to market and start the game, hoping to sell all their shares at a higher price than they paid for them. And a game it surely is, for the buying and selling has just begun.

All prospective purchasers of that company’s stock go to the same marketplace to buy them. However, once there, they have the option to follow two paths. Let’s call them Door #1 and Door #2.

Behind Door #1, where the shares went, there is an atmosphere of excitement. Door #2, where the money went, offers no excitement at all. The atmosphere there is very businesslike, even boring.

Let’s take a closer look at why there is such a difference.

Door #1: Speculative Trading

Those selecting Door #1 opt for the games. They are the folks who buy a company’s shares to sell, hopefully at a profit. Some want to “get in on the ground floor.” Others simply like the appealing story they’ve been told about how great the products or services are, or how much of a demand there will be for them. Others simply take the advice of their brokers, the talking heads on the financial TV channels, or their “Uncle Charlie who knows the business,” and buy the stock because they hope they’ll be able to sell it to someone else for more.

Often referred to as “the herd,” this group is not restricted to amateurs. Some professionals are just as prone to buy on faith, or simply gamble for the love of the game. The common denominator is simply that the herd pays little or no attention to the actual operation of the company—its fundamentals.

How could they? Most companies—especially with an initial public offering (IPO)—don’t have enough of a track record on which to base judgment! Since most seasoned investors will want a company to have been publicly traded for at least five years and produce annual revenues of at least $50 million to $100 million before considering it a candidate for investment, the herd will have only itself to buy those shares from or sell them to for a good while.

Behind Door #1, there is a pervasive hope that one can make a killing, or at least get lucky enough to put his or her money on one or more winners that will finance an early and lavish retirement.

Those in this group are concerned with “playing the market” and actively—sometimes frenetically—trade in and out in the hope they will make a profit (or prevent catastrophic loss). They are typically content to focus on price movement and volume only and are proud of the fact that their methods require no fundamental knowledge about the companies they invest in.

Of the hundreds of such approaches to focusing solely on price movement with no regard to other factors—some with such imaginative names as “dead cat bounce” and “stick sandwich” and many propounded by some very bright people over more than a century—none has produced a result that has proven in academic research to beat the odds with any statistical significance.

The downside is that many who gamble with such high stakes feel obliged to watch the upticks and downticks almost every minute the exchanges are open. And the odds of “winning” are heavily against them.

The only upside is that many enjoy the rush that comes with risk. And there’s plenty of that when they have to depend upon being smarter (or luckier) than both those they buy the shares from and those they sell them to, in order to make money. Given that requirement, those odds are formidable!

Door #1 actually provides all the allure of a Las Vegas casino and shares many of its characteristics—even to the point where “the house” can’t lose because they receive a commission from both the buyer and the seller on every transaction. And because they do it without any risk, the buyers and sellers are assuming all the risk.

Door #2: Buying to Own

Those who opt for Door #2 are those who buy the shares to own. They want to become part-owners of the company that issued them, and to profit from its successful operation and the future appreciation of those shares. From Graham to Buffett, renowned and consistently successful investors have chosen Door #2. They are the “fundamental” investors and, unlike the traders, they do enough homework about the companies whose shares they buy to be able to determine—or at least approximate—an absolute value for those shares.

Their risk is never statistically driven by the odds; it’s always determined by skillfully weighing business risks and making reasoned decisions. This homework is, in the computer age, far easier and less time-consuming than it was back in the day—easier, by far, than many financial professionals and fundamental investment gurus might suggest. In fact, with the inexpensive software available to anyone today, an amateur investor can now do in minutes the fundamental analysis that professionals once took hours to complete.

To earn a place in the portfolio of such an investor, for example, a company might have to display strong and consistent sales and earnings growth over an extended period of time, show a healthy return on equity, and maintain strong and steady profit margins. These days, that information is easy enough to come by. [For example, AAII’s Stock Investor Pro fundamental stock screening and research database program is a perfect source.]

A More Rational Approach to Portfolio Valuation

There are also two ways to value a portfolio. The conventional way is to multiply the number of shares by the market price of each stock and aggregate those results. The other way is less well-known but is actually more realistic: Multiply the number of shares by the rational price of each and aggregate those.

Although those passing through Door #1 often don’t hold any stock long enough to think of it as a part of a “portfolio,” they still view their holdings in terms of the market value of all of their shares at any given moment. As does the market capitalization of their stocks, their portfolios change in value every minute the exchanges are open.

As we know and have recently seen, the market price can be extremely volatile. Buffeted by events and opinions—and even more by speculation having little or nothing at all to do with the company’s ability to earn money for its owners—what drives the market price of one’s stocks is grossly unpredictable.

Such swings up and down are sometimes extreme, having been described as “irrational exuberance” (by former Federal Reserve chairman Alan Greenspan in reference to the tech bubble) and “irrational despair” (by presidential candidate John McCain early in the 2008 financial crisis).

Those who pass through Door #2—the classic investors—need have little concern for the market price of their holdings. The “market price” is commonly viewed as the price at which there are willing buyers and willing sellers. So, unless compelled by some emergency to be a willing (though reluctant) seller, those prudent enough to plan and prepare for such emergencies are rarely, if ever, put in that position. Nor should they be, since such an investor, knowing the true value of his or her shares, would certainly not be a willing seller at an irrationally depressed price.

Valuing a Stock Rationally

The term rational value is a function of a stock’s rational price, a realistic approximation of what the stock would sell for if those buying and selling it were acting rationally. It is a price that a wise investor can justify by evaluating the total return the company might earn on his or her investment over time. And it’s based on the conventional view among fundamental investors that the price of a share, over the long term, generally tracks the underlying company’s earnings.

The rational price is simply the product of the current annual earnings per share of the company multiplied by its signature P/E—the mid-point (trailing mean or median) of a long-term (five- to 10-year) succession of closing price-earnings (P/E) ratios.

Does it make any sense to value one’s holdings at a price at which others would sell them when, at that moment in time, a rational investor wouldn’t? Of course not! As long as the company continues to operate profitably, an investor can expect, with reasonable certainty, that the price will at some point not only revert to the mean but likely exceed its rational price. After all, by definition, the price-earnings ratio employed to calculate the rational price is the midpoint of its historical multiples.

A typical example can be found in Table 1.

My preference is to use the median of seven years of price-earnings ratios, so the signature P/E of Cognizant Technologies (CTSH) would be the median of both high and low price-earnings ratios, or 20.8. Essentially, this would suggest that, over the past seven years, there were about as many transactions with a price-earnings ratio above that number as below. So, with a trailing 12 month’s earnings at $2.48, the rational price per share of Cognizant would thus be around $51.58 ($2.48 x 20.8).

Thus, a 1,000-share position in Cognizant Technologies would have a rational value of about $51,580; and, at the market close as of this writing, the herd valued that company at $61.75 per share, so its market value would be $61,750—a historical value ratio (HVR, or the market price ÷ the rational price) of 1.20.

Already the value of this metric commences to become apparent. With this calculation, the investor has just been made aware that those shares are selling 20% above their “normal” price and are therefore approaching a seriously overbought condition. (It might be a good idea to find some member of the herd who is willing to buy the stock before it reaches 1.5.)

How the Calculations Are Made

A closer look at Cognizant Technology Solutions can provide a clearer understanding of how the signature P/E, rational price and historical value ratio are calculated.

Signature P/E

Table 1 shows the highest and lowest price-earnings (P/E) ratios that Cognizant has traded at during each of the past seven years. The high ratios are calculated based on the highest price a stock has traded at during a calendar year divided by earnings per share for that particular year. The low ratios are calculated based on the lowest price a stock has traded at during a calendar year divided by earnings per share for that particular year.

AAII’s Stock Investor Pro fundamental stock screening and research database has pre-calculated high and low price-earnings ratios for each of the past five years. Custom fields for years six and seven can easily be created by using the following formulas (simply change “Y6” to “Y7” for year seven):

[Price—High Y6]/[EPS—Diluted Continuing Y6]

[Price—Low Y6]/[EPS—Diluted Continuing Y6]

The signature P/E is the median of all high and low price-earnings ratios. Group all 14 ratios—not just the high or low price-earnings ratios, but all of them—and then calculate the median.

Using the “=MEDIAN()” function in Microsoft Excel, the median of the high and low price-earnings ratios for Cognizant is calculated as 20.8, making the signature P/E 20.8.

Table 1. Historical P/Es for Cognizant Technology Solutions (CTSH)   

High Price-Earnings Ratios
Y1 Y2 Y3 Y4 Y5 Y6 Y7
23.36 25.03 22.67 29.39 31.42 26.19 25.76
Low Price-Earnings Ratios
Y1 Y2 Y3 Y4 Y5 Y6 Y7
17.66 15.08 15.67 18.85 17.68 9.7 9.99
Source: AAII’s Stock Investor Pro, data as of September 4, 2015.

Rational Price

The rational price is the signature P/E multiplied by reported earnings per share for the trailing 12 months (TTM).

Stock Investor Pro lists Cognizant as having earned $2.48 per share over the past 12 months. Multiplying the signature P/E of 20.8 by earnings per share of $2.48 results in a rational price of $51.58.

This is can be construed as the stock’s intrinsic, or fair, value based on the range of valuations investors have historically paid. A current share price below this number implies the stock is trading at a discount; a price above it implies the stock is trading at a premium.

Historical Value Ratio

The historical value ratio (HVR) is helpful for determining the valuation of an overall position in a certain stock.

It is calculated by dividing the current market value of the position (number of shares held times current price per share) by the rational price of the position (number of shares held times rational price per share).

Using Cognizant’s closing price of $61.75 on September 4, 2015, a 1,000 share position would have had a market value of $61,750. The rational price of the position ($51.58 times 1,000 shares) would have been $51,580. Dividing $61,750 by $51,580 equals a HVR of 1.20, or a 20% premium.

A Caveat

These calculations only work with stocks with enough data to calculate the ratios. The seven-year ratios cannot be calculated for companies with negative earnings during any of the past seven years or whose stocks have not traded publicly for seven years. A shorter time horizon can be used, but periods of less than five years may not as insightful as longer periods are.

 

The Advantages for Prudent Investors

Just consider the benefits of changing your mindset to regard the rational investor as the norm and the herd as deviating from the norm. Suddenly you’re viewing the market from the perspective of its deviation, rather than considering your holdings as a part of the unpredictable ebb and flow. You’re now sitting safely and securely ashore, watching the tide and the waves move up and down rather than bobbing in a small boat on the churning surface.

Prudent investors need not be concerned with the movement of the market, and this metric makes it clear why. When the herd is spooked and has driven the market to dismaying lows, rational investors can serenely keep their heads in the clouds and be content that their holdings, valued at their rational value, are still healthy and potentially profitable. Say, for example, that Cognizant were selling today at $40.00. While others were wringing their hands and worrying about whether or not they should sell, prudent investors would be content that it was still worth $51.48.

Conversely, when the herd has overpriced the market, you can keep your feet firmly on the ground and know that your holdings are worth only as much as their rational valuation says they are. More useful still: If your shares are way overvalued, and their anticipated appreciation is way ahead of schedule, it would be smart to replace them with companies of equal or better fundamental quality but with a better appreciation potential for the long term.

It must also be noted that, at some point, it’s likely that any company’s ability to operate as profitably as expected (measured by the fundamentals suggested above) could decline. At that point, the rational value of that company must revert to its market value, since such an instance calls for the immediate replacement of that investment with another whose fundamentals would make it a better candidate. While this will cause a temporary decline in the portfolio’s aggregate rational value, it will also provide a strong stimulus to lose no time in making that replacement to restore its rational value.

Another beneficial by-product is that prudent investors can sleep better. Since a company reports its fundamentals only four times a year, its rational value can’t very well change more often. Now the day’s upticks and downticks in the market become merely interesting rather than relevant, because portfolio changes based solely on changes in market value are unwise. But it is sometimes fascinating to watch just how foolish the herd can be.

On the other hand, the historical value ratio (HVR) offers diligent investors a new and occasionally useful alarm. Should a stock’s HVR fall below about 0.85, it could mean that the herd is aware of something that rational investors are not—especially if the movement of the stock’s price is in the opposite direction from that of the market. While investors should never sell a stock just because of a decline in its market price, they should be moved to investigate the reasons for such a decline. If an event has occurred that would be likely to adversely affect the fundamentals, rational investors should act accordingly. The historical value ratio can be a helpful alert to signal the occurrence of such an event between quarters and might trigger a timely investigation.

Conclusion

All in all, the concept of rational value restores some common sense to the term long-term investing. Where buy and hold has lost some of its credibility because the term doesn’t emphasize the necessity for watchfulness, those who use rational value to evaluate their holdings will be more likely to do the required due diligence four times a year when they check the fundamentals to be sure the company continues to operate as profitably as expected.

Providing a valid rationale for not having to hover over a portfolio on a daily basis makes it far easier to impose the required discipline; and being concerned only with the fundamentals (and only passively interested in the market price) helps to prevent an investor from yielding to the destructive temptation to make buy or sell decisions based on price movement.

“How long is long term?” is thus no longer a matter of time for the rational investor. The answer is simply, “until a company can no longer earn money for its owners as it was expected to.”

And all the time, the wise investor will have a far more realistic view of what he or she owns than do those whose very lack of wisdom determines what one would have to accept for those holdings when there’s no good reason to sell.

Discussion

Paul Stadnik from OR posted over 10 years ago:

The Table discusses using the Excel MEDIAN function to generate a Signature P/E of 20.8. Normally, medians are an actual value, but there is no '20.8' in this data series. It should be pointed out, however, that when there is an even number of values, the MEDIAN function averages between the two innermost values. Thus, the Signature P/E is closer to an average than a median.


Ellis Traub from FL posted over 10 years ago:

You're quite right, Paul, that the median is the midpoint between the two middle values, when the number of values is an even number——but it's not the same as the average of the entire series. Our goal is to approximate a number that has as many transactions above as below it; and the median serves that purpose well. (Try calculating the median and the average of the figures in the example if the highest PE were to be 60.50.) But let's not strain at gnats here. I use a Flair pen rather than a sharp pencil when I draw these lines; and an approximation is fine, so long as you're consistent with the way you calculate it. If you know approximately what a stock is worth, you're way ahead of the herd that doesn't have a clue.


John Barrow from IN posted over 10 years ago:

Thanks much, Ellis. Very rational and helpful.


D Strohminger from FL posted over 10 years ago:

Great article. Why not use Earnings Per Share Estimates, (either this year or next), multiplied by its signature P/E? Current EPS can be misleading if the company is having a difficult year because of something like a Stong Dollar for an example. You are investing in a company for its future earnings. Also Stock Investor Pro has 7-year average P/E High and Low data points already calculated.


M Theriault from Maine posted over 10 years ago:

Is there a current stock screen which uses this methodology as part of its screening process?


Bill Smith from AZ posted over 10 years ago:

The article really made sense to me particularly in light of Charles Rothblut's piece on our "Irrational Brains". Given the ability of companies to manipulate earnings numbers, is there a more accurate measure that could be used? Price to sales, price to book, free cash flow or using these in combination with P/E. Keeping the process relatively simple and easy to use is important too; avoid paralysis by analysis.


Fernando Robles from FL posted over 10 years ago:

Ah, no, I don't think so. Too much reliance on PE alone. And having to look up stuff four times a year? Nope. How about buy low (52-week low, or thereabout) and rebalance in a year's time, or at the 52-week high, if later (you don't want to pay taxes at ordinary income rates)? Much simpler, in my view. Of course, PE and other metrics would come into play before buying because that's when you make the money.


Perry from Michigan posted over 10 years ago:

I know of no quarrel with the proposition that past performance is no guarantee of future results. But most all attempts to analyze stock performance or value begin with historical data and assume that past performance will repeat itself. This one is no exception. At some level of abstraction, history does repeat itself and inductive reasoning is useful even if the deductive cause is not identified. But I find this one useless on both the analytical and practical levels. The notion of capturing data points over a 5-10 year period to establish a historical average is unobjectionable. But to assert that "the median of seven years of price-earnings ratios . . . suggest[s] that, over the past seven years, there were about as many transactions with a price-earnings ratio above that number as below" is not. I understand Mr. Traub's point that he tries to "approximate a number that has as many transactions above as below it" and does not use a sharp pencil, but with literally millions or even billions of trades in an issue over an annual period, I cannot accept without proof that the mean of the high and low for a year equals the median for that year and hence the median of the highs and lows for seven years taken independently equals the median of all transactions over that period. But more fundamentally flawed is his use of the last 12 months earning to determine rational price. In how many instances are even this year's earnings equal to the last 12 months', let alone earnings for the next 5, 10 or 20 years? Rational value to me is discounted value of a future stream of earnings, not a historical multiple of the latest 12 months' earnings. A concrete example: As of 2/18/16, the Signature P/E for Pfizer (PFE) is 13.59 and its Rational Price $16.85 based on latest 12 months earnings of $1.24. It closed at $29.55. Thus Traub would assert that PFE is 75 per cent overvalued. But if we applied the Signature P/E to the consensus forward 12 months earnings of seven analysts of $2.28, the rational price would be $30.99, indicating by the Traub formula that PFE was trading at a 4.6 per cent discount. Which is the rational value?


Ellis Traub from FL posted over 9 years ago:

I'm a year late with this comment and apologize for being negligent with responses. The point of my article was simply to recognize that, as Warren Buffet points out, the value of one's holdings are more important than the price——and they are not the same. Whatever means you choose to use to establish the real value of your holdings——and I would take a close look at the historical accuracy of concensus estimates before I relied too heavily on them——the important thing is to dissociate your perspective from the market and judge the prices of your shares by how they compares to their value rather than what the flaky herd says the price should be. As I point out, this is a rough approximation; and my method tends to be conservative; so, you're right about the trivial understatement; but do know it's deliberate.


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