Value Investing and Fundamental Analysis

/was especially smitten with WorldCom’s critical Internet division, UUNet. The Internet wasn’t going away, and so, I thought, neither was UUNet or WorldCom. During this time of enchantment my sensible wife would say “UUNet, UUNet” and roll her pretty eyes to mock my rhapsodizing about WorldCom’s global IP network and related capabilities. The repetition of the word gradually acquired a more general anti- Pollyannish meaning as well. “Maybe the bill is so exorbitant because the plumber ran into something he didn’t expect.” “Yeah, sure. UUNet, UUNet.”
“Smitten,” “rhapsodizing,” and “Pollyanna” are not words that come naturally to mind when discussing value investing, a major approach to the market that uses the tools of so-called fundamental analysis. Often associated with Warren Buffett’s gimlet-eyed no-nonsense approach to trading, fundamental analysis is described by some as the best, most sober strategy for investors to follow. Had I paid more attention to WorldCom fundamentals, particularly its $30 billion in debt, and less attention to WorldCom fairy tales, particularly its bright future role as a “dumb” network (better not to ask), I would no doubt have fared better. In the stock market’s enduring tug-of-war between statistics and stories, fundamental analysis is generally on the side of the numbers.
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Still, fundamental analysis has always seemed to me slightly at odds with the general ethic of the market, which is based on hope, dreams, vision, and a certain monetarily tinted yet genuine romanticism. I cite no studies or statistics to back up this contention, only my understanding of the investors I’ve known or read about and perhaps my own infatuation, quite atypical for this numbers man, with WorldCom.
Fundamentals are to investing what (stereotypically) marriage is to romance or what vegetables are to eating—healthful, but not always exciting. Some understanding of them, however, is essential for any investor and, to an extent, for any intelligent citizen. Everybody’s heard of people who refrain from buying a house, for example, because of the amount they would have paid in interest over the years. (“Oh my, don’t get a mortgage. You’ll end up paying four times as much.”) Also common are lottery players who insist that the worth of their possible winnings is really the advertised one million dollars. (“In only 20 years, I’ll have that million.”) And there are many investors who doubt that the opaque pronouncements of Alan Greenspan have anything to do with the stock or bond markets.
These and similar beliefs stem from misconceptions about compound interest, the bedrock of mathematical finance, which is in turn the foundation of fundamental analysis.
e is the Root of All Money
Speaking of bedrocks and foundations, I claim that e is the root of all money. That’s e as in ex as in exponential growth as in compound interest. An old adage (probably due to an old banker) has it that those who understand compound interest are more likely to collect it, those who don’t more likely to pay it. Indeed the formula for such growth is the basis for
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most financial calculations. Happily, the derivation of a related but simpler formula depends only on understanding percentages, powers, and multiplication—on knowing, for example, that 15 percent of 300 is .15 x 300 (or 300 x .15) and that 15 percent of 15 percent of 300 is 300 x (.15)2.
With these mathematical prerequisites stated, let’s begin the tutorial and assume that you deposit $1,429.73 into a bank account paying 6.9 percent interest compounded annually. No, let’s bow to the great Rotundia, god of round numbers, and assume instead that you deposit $1,000 at 10 percent. After one year, you’ll have 110 percent of your original deposit—$1,100. That is, you’ll have 1,000 x 1.10 dollars in your account. (The analysis is the same if you buy $1,000 worth of some stock and it returns 10 percent annually.)
Looking ahead, observe that after two years you’ll have 110 percent of your first-year balance—$1,211. That is, you’ll have ($1,000 x 1.10) x 1.10. Equivalently, that is $1,000 x
1.102. Note that the exponent is 2.
After three years you’ll have 110 percent of your second- year balance—$1,331. That is, you’ll have ($1,000 x 1.102) x 1.10. Equivalently, that is $1,000 x 1.103. Note the exponent is 3 this time.
The drill should be clear now. After four years you’ll have 110 percent of your third-year balance—$1,464.10. That is, you’ll have ($1,000 x 1.103) x 1.10. Equivalently, that is $1,000 x 1.104. Once again, note the exponent is 4.
Let me interrupt this relentless exposition with the story of a professor of mine long ago who, beginning at the left side of a very long blackboard in a large lecture hall, started writing 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! .... (Incidentally the expression 5! is read 5 factorial, not 5 with an exclamatory flair, and it is equal to5x4x3x2xl. For any whole number N, N! is defined similarly.) My fellow students initially laughed as this professor, slowly and seemingly in a trance,
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kept on adding terms to this series. The laughter died out, however, by the time he reached the middle of the board and was writing 1/44! + 1/45! + .... I liked him and remember a feeling of alarm as I saw him continue his senseless repetitions. When he came to the end of the board at 1/83!, he turned and faced the class. His hand shook, the chalk dropped to the floor, and he left the room and never returned.
Mindful thereafter of the risks of too many illustrative repetitions, especially when I’m standing at a blackboard in a classroom, I’ll end my example with the fourth year and simply note that the amount of money in your account after t years will be $1,000 x 1.10l. More generally, if you deposit P dollars into an account earning r percent interest annually, it will be worth A dollars after t years, where A = P(1 + r)c, the promised formula describing exponential growth of money.
You can adjust the formula for interest compounded semiannually or monthly or daily. If money is compounded four times per year, for example, then the amount you’ll have after t years is given by A = P(1 + r/4)4t. (The quarterly interest rate is r/4, one-fourth the annual rate of r, and the number of compoundings in t years is 4t, four per year for t years.)
If you compound very frequently (say n times per year for a large number n), the formula A = P(1 + r/n)M can be mathematically massaged and rewritten as A = Pert, where e, approximately 2.718, is the base of the natural logarithm. This variant of the formula is used for continuous compounding (and is, of course, the source of my comment that e is the root of all money).
The number e plays a critical role in higher mathematics, best exemplified perhaps by the formula eKl + 1 = 0, which packs the five arguably most important constants in mathematics into a single equation. The number e also arises if we’re simply choosing numbers between 0 and 1 at random. If we (or, more likely, our computer) pick these numbers until
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their sum exceeds 1, the average number of picks we’d need would be e, about 2.718. The ubiquitous e also happens to equal 1 + 1/1! + 1/2! + 1/3! + 1/4! + . .., the same expression my professor was writing on the board many years ago. (Inspired by a remark by stock speculator Ivan Boesky, Gordon Gecko in the 1987 movie Wall Street stated, “Greed is good.” He misspoke. He intended to say, “e is good.”)
Many of the formulas useful in finance are consequences of these two formulas: A = P(1 + r)( for annual compounding and, for continuous compounding, A = Pert. To illustrate how they’re used, note that if you deposit $5,000 and it’s compounded annually for 12 years at 8 percent, it will be worth $5,000(1.08)12 or $12,590.85. If this same $4,000 is compounded continuously, it will be worth $4,OOOe( 08 x 12) or $13,058.48.
Using this interest rate and time interval, we can say that the future value of the present $5,000 is $12,590.85 and that the present value of the future $12,590.85 is $5,000. (If the compounding is continuous, substitute $13,058.48 in the previous sentence.) The “present value” of a certain amount of future money is the amount we would have to deposit now so that the deposit would grow to the requisite amount in the allotted time. Alternatively stated (repetition may be an occupational hazard of professors; so may self-reference), the idea is that given an interest rate of 8 percent, you should be indifferent between receiving $5,000 now (the present value) and receiving something near $13,000 (the future value) in twelve years.
And just as “George is taller than Martha” and “Martha is shorter than George” are different ways to state the same relation, the interest formulas may be written to emphasize either present value, P, or future value, A. Instead of A = P(1 + r)1, we can write P = A/(l + r)*, and instead of A = Pe", we can write P = AJen. Thus, if the interest rate is 12 percent, the present value
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of $50,000 five years hence is given by P = $50,000/(1.12)5 or $28,371.34. This amount, $28,371.34, if deposited at 12 percent compounded annually for five years, has a future value of $50,000.
One consequence of these formulas is that the “doubling time,” the time it takes for a sum of money to double in value, is given by the so-called rule of 72: divide 72 by 100 times the interest rate. Thus, if you can get an 8 percent (.08) rate, it will take you 72/8 or nine years for a sum of money to double, eighteen years for it to quadruple, and twenty-seven years for it to grow to eight times its original size. If you’re lucky enough to have an investment that earns 14 percent, your money will double in a little more than five years (since 72/14 is a bit more than 5) and quadruple in a bit over ten years. For continuous compounding, you use 70 rather than 72.
These formulas can also be used to determine the so-called internal rate of return and to define other financial concepts. They provide as well the muscle behind common pleas to young people to begin saving and investing early in life if they wish to become the “millionaire next door.” (They don’t, however, tell the millionaire next door what he should do with his wealth.)
The Fundamentalists’
Creed: You Get What You Pay For
The notion of present value is crucial to understanding the fundamentalists’ approach to stock valuation. It should also be important to lottery players, mortgagors, and advertisers. That the present value of money in the future is less than its nominal value explains why a nominal $1,000,000 award for winning a lottery—say $50,000 per year at the end of each of the next
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twenty years—is worth considerably less than $1,000,000. If the interest rate is 10 percent annually, for example, the $1,000,000 has a present value of only about $426,000. You can obtain this value from tables, from financial calculators, or directly from the formulas above (supplemented by a formula for the sum of a so-called geometric series).
The process of determining the present value of future money is often referred to as “discounting.” Discounting is important because, once you assume an interest rate, it allows you to compare amounts of money received at different times. You can also use it to evaluate the present or future value of an income stream—different amounts of money coming into or going out of a bank or investment account on different dates. You simply “slide” the amounts forward or backward in time by multiplying or dividing by the appropriate power of (1 + r). This is done, for example, when you need to figure out a payment sufficient to pay off a mortgage in a specified amount of time or want to know how much to save each month to have sufficient funds for a child’s college education when he or she turns eighteen.
Discounting is also essential to defining what is often called a stock’s fundamental value. The stock’s price, say investing fundamentalists (fortunately not the sort who wish to impose their moral certitudes on others), should be roughly equal to the discounted stream of dividends you can expect to receive from holding onto it indefinitely. If the stock does not pay dividends or if you plan on selling it and thereby realizing capital gains, its price should be roughly equal to the discounted value of the price you can reasonably expect to receive when you sell the stock plus the discounted value of any dividends. It’s probably safe to say that most stock prices are higher than this. During the 1990 boom years, investors were much more concerned with capital gains than they were with
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dividends. To reverse this trend, finance professor Jeremy Siegel, author of Stocks for the Long Run, and two of his colleagues recently proposed eliminating the corporate dividend tax and making dividends deductible.
The bottom line of bottom-line investing is that you should pay for a stock an amount equal to (or no more than) the present value of all future gains from it. Although this sounds very hard-headed and far removed from psychological considerations, it is not. The discounting of future dividends and the future stock price is dependent on your estimate of future interest rates, dividend policies, and a host of other uncertain quantities, and calling them fundamentals does not make them immune to emotional and cognitive distortion. The tango of exuberance and despair can and does affect estimates of stock’s fundamental value. As the economist Robert Shiller has long argued quite persuasively, however, the fundamentals of a stock don’t change nearly as much or as rapidly as its price.
Ponzi and the Irrational Discounting of the Future
Before returning to other applications of these financial notions, it may be helpful to take a respite and examine an extreme case of undervaluing the future: pyramids, Ponzi schemes, and chain letters. These differ in their details and colorful storylines. A recent example in California took the form of all-women dinner parties whose new members contributed cash appetizers. Whatever their outward appearance, however, almost all these scams involve collecting money from an initial group of “investors” by promising them quick and extraordinary returns. The returns come from money contributed by a larger group of people. A still larger group of people contributes to both of the smaller earlier groups.
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This burgeoning process continues for a while. But the number of people needed to keep the pyramid growing and the money coming in increases exponentially and soon becomes difficult to maintain. People drop out, and the easy marks become scarcer. Participants usually lack a feel for how many people are required to keep the scheme going. If each of the initial group of ten recruits ten more people, for example, the secondary group numbers 100. If each of these 100 recruit ten people, the tertiary group numbers 1,000. Later groups number 10,000, then 100,000, then 1,000,000. The system collapses under its own weight when enough new people can no longer be found. If you enter the scheme early, however, you can make extraordinarily quick returns (or could if such schemes were not illegal).
The logic of pyramid schemes is clear, but people generally worry only about what happens one or two steps ahead and anticipate being able to get out before a collapse. It’s not irrational to get involved if you are confident of recruiting a “bigger sucker” to replace you. Some would say that the dot-coms’ meteoric stock price rises in the late ’90s and their subsequent precipitous declines in 2000 and 2001 were attenuated versions of the same general sort of scam. Get in on the initial public offering, hold on as the stock rockets upward, and jump off before it plummets.
Although not a dot-com, WorldCom achieved its all-too- fleeting dominance by buying up, often for absurdly inflated prices, many companies that were (and a good number that weren’t). MCI, MFS, ANS Communication, CAI Wireless, Rhythms, Wireless One, Prime One Cable, Digex, and dozens more companies were acquired by Bernie Ebbers, a pied piper whose song seemed to consist of only one entrancing and repetitive note: acquire, acquire, acquire. The regular drumbeat of WorldCom acquisitions had the hypnotic quality of the tinkling bells that accompany the tiniest wins at casino
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slot machines. As the stock began its slow descent, I’d check the business news every morning and was tranquilized by news of yet another purchase, web hosting agreement, or extension of services.
While corporate venality and fraud played a role in (some of) their falls, the collapses of the dot-coms and WorldCom were not the brainchilds of con artists. Even when entrepreneurs and investors recognized the bubble for what it was, most figured incorrectly that they’d be able to find a chair when the mania-inducing IPO/acquisition music stopped. Alas, the journey from “have-lots” to “have-nots” was all too frequently by way of “have-dots.”
Maybe our genes are to blame. (They always seem to get the rap.) Natural selection probably favors organisms that respond to local or near-term events and ignore distant or future ones, which are discounted in somewhat the same way that future money is. Even the ravaging of the environment may be seen as a kind of global Ponzi scheme, the early “investors” doing well, later ones less well, until a catastrophe wipes out all gains.
A quite different illustration of our short-sightedness comes courtesy of Robert Louis Stevenson’s “The Imp in the Bottle.” The story tells of a genie in a bottle able and willing to satisfy your every romantic whim and financial desire. You’re offered the opportunity to buy this bottle and its amazing denizen at a price of your choice. There is a serious limitation, however. When you’ve finished with the bottle, you have to sell it to someone else at a price strictly less than what you paid for it. If you don’t sell it to someone for a lower price, you will lose everything and will suffer excruciating and unrelenting torment. What would you pay for such a bottle?
Certainly you wouldn’t pay 1 cent because then you wouldn’t be able to sell it for a lower price. You wouldn’t pay
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2 cents for it either since no one would buy it from you for 1 cent since everyone knows that it must be sold for a price less than the price at which it is bought. The same reasoning shows that you wouldn’t pay 3 cents for it since the person to whom you would have to sell it for 2 cents would object to buying it at that price since he wouldn’t be able to sell it for 1 cent. Likewise for prices of 4 cents, 5 cents, 6 cents, and so on. We can use mathematical induction to formalize this argument, which proves conclusively that you wouldn’t buy the genie in the bottle for any amount of money. Yet you would almost certainly buy it for $1,000. I know I would. At what point does the argument against buying the bottle cease to be compelling? (I’m ignoring the possibility of foreign currencies that have coins worth less than a penny. This is an American genie.)
The question is more than academic since in countless situations people prepare exclusively for near-term outcomes and don’t look very far ahead. They myopically discount the future at an absurdly steep rate.
Average Riches, Likely Poverty
Combining time and money can yield unexpected results in a rather different way. Think back again to the incandescent stock market of the late 1990s and the envious feeling many had that everyone else was making money. You might easily have developed that impression from reading about investing in those halcyon days. In every magazine or newspaper you picked up, you were apt to read about IPOs, the initial public offerings of new companies, and the investment gurus who claimed that they could make your $10,000 grow to more than a million in a year’s time. (All right, I’m exaggerating their exaggerations.) But in those same periodicals, even then,
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you also would have read stories about new companies that were stillborn and naysayers’ claims that most investors would lose their $10,000 as well as their shirts by investing in such volatile offerings.
Here’s a scenario that helps to illuminate and reconcile such seemingly contradictory claims. Hang on for the math that follows. It may be a bit counterintuitive, but it’s not difficult to follow and it illustrates the crucial difference between the arithmetic mean and the geometric mean of a set of returns. (For the record: The arithmetic mean of N different rates of return is what we normally think of as their average; that is, their sum divided by N. The geometric mean of N different rates of return is equal to that rate of return that, if received N times in succession, would be equivalent to receiving the N different rates of return in succession. We can use the formula for compound interest to derive the technical definition. Doing so, we would find that the geometric mean is equal to the Nth root of the product [(1 + first return) x (1 + second return) x (1 + third return) x ... (1 + Nth return)] - 1.)
Hundreds of IPOs used to come out each year. (Pity that this is only an illustrative flashback.) Let’s assume that the first week after the stock comes out, its price is usually extremely volatile. It’s impossible to predict which way the price will move, but we’ll assume that for half of the companies’ offerings the price will rise 80 percent during the first week and for half of the offerings the price will fall 60 percent during this period.
The investing scheme is simple: Buy an IPO each Monday morning and sell it the following Friday afternoon. About half the time you’ll earn 80 percent in a week and half the time you’ll lose 60 percent in a week for an average gain of 10 percent per week: [(80%) + (—60%)]/2, the arithmetic mean.
Ten percent a week is an amazing average gain, and it’s not difficult to determine that after a year of following this strategy,
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the average worth of an initial $10,000 investment is more than $1.4 million! (Calculation below.) Imagine the newspaper profiles of happy day traders, or week traders in this case, who sold their old cars and turned the proceeds into almost a million and a half dollars in a year.
But what is the most likely outcome if you were to adopt this scheme and the assumptions above held? The answer is that your $10,000 would likely be worth all of $1.95 at the end of a year! Half of all investors adopting such a scheme would have less than $1.95 remaining of their $10,000 nest egg. This same $1.95 is the result of your money growing at a rate equal to the geometric mean of 80 percent and -60 percent over the 52 weeks. (In this case that’s equal to the square root (the Nth root for N = 2) of the product [(1 + 80%) x (1 + (-60%))] minus 1, which is the square root of [1.8 x .4] minus 1, which is .85 minus 1, or -.15, a loss of approximately 15 percent each week.)
Before walking through this calculation, let’s ask for the intuitive reason for the huge disparity between $1.4 million and $1.95. The answer is that the typical investor will see his investment rise by 80 percent for approximately 26 weeks and decline by 60 percent for 26 weeks. As shown below, it’s not difficult to calculate that this results in $1.95 of your money remaining after one year.
The lucky investor, by contrast, will see his investment rise by 80 percent for considerably more than 26 weeks. This will result in astronomical returns that pull the average up. The investments of the unlucky investors will decline by 60 percent for considerably more than 26 weeks, but their losses cannot exceed the original $10,000.
In other words, the enormous returns associated with disproportionately many weeks of 80 percent growth skew the average way up, while even many weeks of 60 percent shrinkage can’t drive an investment’s value below $0.
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In this scenario the stock gurus and the naysayers are both right. The average worth of your $10,000 investment after one year is $1.4 million, but its most likely worth is $1.95.
Which results are the media likely to focus on?
The following example may help clarify matters. Let’s examine what happens to the $10,000 in the first two weeks. There are four equally likely possibilities. The investment can increase both weeks, increase the first week and decrease the second, decrease the first week and increase the second, or decrease both weeks. (As we saw in the section on interest theory, an increase of 80 percent is equivalent to multiplying by 1.8. A 60 percent fall is equivalent to multiplying by 0.4.) One-quarter of investors will see their investment increase by a factor of 1.8 x 1.8, or 3.24. Having increased by 80 percent two weeks in a row, their $10,000 will be worth $10,000 x 1.8 x 1.8, or $32,400 in two weeks. One-quarter of investors will see their investment rise by 80 percent the first week and decline by 60 percent the second week. Their investment changes by a factor of 1.8 x 0.4, or 0.72, and will be worth $7,200 after two weeks. Similarly, $7,200 will be the outcome for one-quarter of investors who will see their investment decline the first week and rise the second week, since 0.4 x 1.8 is the same as 1.8 x 0.4. Finally, the unlucky one-quarter of investors whose investment loses 60 percent of its worth for two weeks in a row will have 0.4 x 0.4 x $10,000, or $1,600 after two weeks.
Adding $32,400, $7,200, $7,200, and $1,600 and dividing by 4, we get $12,100 as the average worth of the investments after the first two weeks. That’s an average return of 10 percent weekly, since $10,000 x 1.1 x 1.1 = $12,100. More generally, the stock rises an average of 10 percent every week (the average of an 80 percent gain and a 60 percent loss, remember). Thus after 52 weeks, the average value of the investment is $10,000 x (1.10)52, which is $1,420,000.
The most likely result is that the companies’ stock offerings will rise during 26 weeks and fall during 26 weeks. This means
that the most likely worth of the investment is $10,000 x (1.8)26 x (A)26, which is only $1.95. And the geometric mean of 80 percent and -60 percent? Once again, it is the square root of the product of [(1 + .8) x (1 - .6)] minus 1, which equals approximately -.15. Every week, on average, your portfolio loses 15 percent of its value, and $10,000 x (1 - .15)S2 equals approximately $1.95.
Of course, by varying these percentages and time frames, we can get different results, but the principle holds true: The arithmetic mean of the returns far outstrips the geometric mean of the returns, which is also the median (middle) return as well as the most common return. Another example: If half of the time your investment doubles in a week, and half of the time it loses half its value in a week, the most likely outcome is that you’ll break even. But the arithmetic mean of your returns is 25 percent per week—[100% + (-50%)]/2, which means that your initial stake will be worth $10,000 x 1.2552, or more than a billion dollars! The geometric mean of your returns is the square root of (1 + 1) x (1 - .5) minus 1, which is a 0 percent rate of return, indicating that you’ll probably end up with the $10,000 with which you began.
Although these are extreme and unrealistic rates of return, these example have much more general importance than it might appear. They explain why a majority of investors receive worse-than-average returns and why some mutual fund companies misleadingly stress their average returns. Once again, the reason is that the average or arithmetic mean of different rates of return is always greater than the geometric mean of these rates of return, which is also the median rate of return.
Fat Stocks, Fat People, and P/E
You get what you pay for. As noted, fundamentalists believe that this maxim extends to stock valuation. They argue that a
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company’s stock is worth only what it returns to its holder in dividends and price increases. To determine what that value is, they try to make reasonable estimates of the amount of cash the stock will generate over its lifetime, and then they discount this stream of payments to the present. And how do they estimate these dividends and stock price increases? Value investors tend to use the company’s stream of earnings as a reasonable substitute for the stream of dividends paid to them since, the reasoning goes, the earnings are, or eventually will be, paid out in dividends. In the meantime, earnings may be used to grow the company or retire debt, which also increases the company’s value. If the earnings of the company are good and promise to get better, and if the economy is growing and interest rates stay low, then high earnings justify paying a lot for a stock. And if not, not.
Thus we have a shortcut for determining a reasonable price for a stock that avoids complicated estimations and calculations: the stock’s so-called P/E ratio. You can’t look at the business section of a newspaper or watch a business show on TV without hearing constant references to it. The ratio is just that—a ratio or fraction. It’s determined by dividing the price P of a share of the company’s stock by the company’s earnings per share E (usually over the past year). Stock analysts discuss countless ratios, but the P/E ratio, sometimes called simply the multiple, is the most common.
The share price, P, is discovered simply by looking in a newspaper or online, and the earnings per share, E, is obtained by taking the company’s total earnings over the past year and dividing it by the number of shares outstanding. (Unfortunately, earnings are not nearly as cut-and-dried as many once thought. All sorts of dodges, equivocations, and outright lies make it a rather plastic notion.)
So how does one use this information? One very common way to interpret the P/E ratio is as a measure of investors’
expectations of future earnings. A high P/E indicates high expectations about the company’s future earnings, and a low one low expectations. A second way to think of the ratio is simply as the price you must pay to receive (indirectly via dividends and price appreciation) the company’s earnings. The P/E ratio is thus both a sort of prediction and an appraisal of the company.
A company with a high P/E must perform to maintain its high ratio. If its earnings don’t continue to grow, its price will decline. Consider Microsoft, whose P/E was somewhere north of 100 a few years ago. Today its P/E is under 50, although it’s one of the larger companies in Redmond, Washington. Still a goliath, it’s nevertheless growing more slowly than it did in its early days. This shrinking of the P/E ratio occurs naturally as start-ups become blue-chip pillars of the business community.
(The pattern of change in a company’s growth rate brings to mind a mathematical curve—the S-shaped or logistic curve. This curve seems to characterize a wide variety of phenomena, including the demand for new items of all sorts. Its shape can most easily be explained by imagining a few bacteria in a petri dish. At first the number of bacteria will increase slowly, then at a more rapid exponential rate because of the rich nutrient broth and the ample space in which to expand. Gradually, however, as the bacteria crowd each other, their rate of increase slows and their number stabilizes, at least until the dish is enlarged.
The curve appears to describe the growth of entities as disparate as a composer’s symphony production, the rise of airline traffic, highway construction, mainframe computer installations, television ownership, even the building of Gothic cathedrals. Some have speculated that there is a kind of universal principle governing many natural and human phenomena, including the growth of successful businesses.)
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Of course, the P/E ratio by itself does not prove anything. A high P/E does not necessarily indicate that a stock is overvalued (too expensive for the cash flow it’s likely to generate) and a candidate for selling, nor does a low one indicate that a stock is undervalued and a candidate for buying. A low P/E might mean that a company is in financial hot water despite its earnings.
As WorldCom approached bankruptcy, for example, it had an extremely low P/E ratio. A constant stream of postings in the chatrooms compared it to the P/Es of SBC, AT&T, Deutsche Telekom, Bell South, Verizon, and other comparable companies, which were considerably higher. The stridency of the postings increased when they failed to have their desired effect: Investors hitting their foreheads with the sudden realization that WCOM was a great buy. The posters did have a point, however. One should compare a company’s P/E to its value in the past, to that of similar companies, and to the ratios for the sector and the market as a whole. The average P/E for the entire market ranges somewhere between 15 and 25, although there are difficulties with computing such an average. Companies that are losing money, for example, have negative P/Es although they’re generally not reported as such; they probably should be. Despite the recent market sell-offs in 2001-2002, some analysts believe that stocks are still too expensive for the cash flow they’re likely to generate.
Like other tools that fundamental analysts employ, the P/E ratio seems to be precise, objective, and quasi-mathematical. But, as noted, it too is subject to events in the economy as a whole, strong economies generally supporting higher P/Es. As bears reiteration (verb appropriate), the P in the numerator is not invulnerable to psychological factors nor is the E in the denominator invulnerable to accountants’ creativity.
The P/E ratio does provide a better measure of a company’s financial health than does stock price alone, just as,
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for example, the BMI or body mass index (equal to your weight divided by the square of your height in appropriate units) gives a better measure of somatic health than does weight alone. The BMI also suggests other ratios, such as the P/E2 or, in general, the P/Ex, whose study might exercise analysts to such a degree that their BMIs would fall.
(The parallel between diet and investment regimens is not that far-fetched. There are a bewildering variety of diets and market strategies, and with discipline you can lose weight or make money on most of them. You can diet or invest on your own or pay a counselor who charges a fee and offers no guarantee. Whether the diet or strategy is optimal or not is another matter, as is whether the theory behind the diet or strategy makes sense. Does the diet result in faster, more easily sustained weight loss than the conventional counsel of more exercise and a smaller but balanced intake? Does the market strategy make any excess returns, over and above what you would earn with a blind index fund? Unfortunately, most Americans’ waistlines in recent years have been expanding, while their portfolios have been getting slimmer.
Numerical comparisons of the American economy to the world economy are common, but comparisons of our collective weight to that of others are usually just anecdotal. Although we constitute a bit under 5 percent of the world’s population, we make up, I suspect, a significantly greater percentage of the world’s human biomass.)
There is one refinement of the P/E ratio that some find very helpful. It’s called the PEG ratio and it is the P/E ratio divided by (100 times) the expected annual growth rate of earnings. A low PEG is usually taken to mean that the stock is undervalued, since the growth rate of earnings is high relative to the P/E. High P/E ratios are fine if the rate of growth of the company is sufficiently rapid. A high-tech company with a P/E ratio of 80 and annual growth of 40 percent will have a PEG of
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2 and may sound promising, but a stodgier manufacturing company with a P/E of 7 and an earnings growth rate of 14 percent will have a more attractive PEG of .5. (Once again, negative values are excluded.)
Some investors, including the Motley Fool and Peter Lynch, recommend buying stocks with a PEG of .5 or lower and selling stocks with PEG of 1.50 or higher, although with a number of exceptions. Of course, finding stocks having such a low PEG is no easy task.
Contrarian Investing and the Sports Illustrated Cover Jinx
As with technical analysis, the question arises: Does it work? Does using the ideas of fundamental analysis enable you to do better than you would by investing in a broad-gauged index fund? Do stocks deemed undervalued by value investors constitute an exception to the efficiency of the markets? (Note that the term “undervalued” itself contests the efficient market hypothesis, which maintains that all stocks are always valued just right.)
The evidence in favor of fundamental analysis is a bit more compelling than that supporting technical analysis. Value investing does seem to yield moderately better rates of return. A number of studies have suggested, for example, that stocks with low P/E ratios (undervalued, that is) yield better returns than do those with high P/E ratios, the effect’s strength varying with the type and size of the company. The notion of risk, discussed in chapter 6, complicates the issue.
Value investing is frequently contrasted with growth investing, the chasing of fast-growing companies with high P/Es. It brings better returns, according to some of its supporters, because it benefits from investors’ overreactions. Investors sign
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on too quickly to the hype surrounding fast-growing companies and underestimate the prospects of solid, if humdrum companies of the type that Warren Buffett likes—Coca-Cola, for instance. (I write this in a study littered with empty cans of Diet Coke.)
The appeal of value investing tends to be contrarian, and many of the strategies derived from fundamental analysis reflect this. The “dogs of the Dow” strategy counsels investors to buy the ten Dow stocks (among the thirty stocks that go into the Dow-Jones Industrial Average) whose price-to- dividend, P/D, ratios are the lowest. Dividends are not earnings, but the strategy corresponds very loosely to buying the ten stocks with the lowest P/E ratios. Since the companies are established organizations, the thinking goes, they’re unlikely to go bankrupt and thus their relatively poor performance probably indicates that they’re temporarily undervalued. This strategy, again similar to one promoted by the Motley Fool, became popular in the late ’80s and early ’90s and did result in greater gains than those achieved by, say, the broad-gauged S8cP 500 average. As with all such strategies, however, the increased returns tended to shrink as more people adopted it.
A ratio that seems to be more strongly related to increased returns than price-to-dividends or price-to-earnings is the price-to-book ratio, P/B. The denominator B is the company’s book value per share—its total assets minus the sum of total liabilities and intangible assets. The P/B ratio changes less over time than does the P/E ratio and has the further virtue of almost always being positive. Book value is meant to capture something basic about a company, but like earnings it can be a rather malleable number.
Nevertheless, a well-known and influential study by the economists Eugene Fama and Ken French has shown P/B to be a useful diagnostic device. The authors focused on the period from 1963 to 1990 and divided almost all the stocks on the
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New York Stock Exchange and the Nasdaq into ten groups: the 10 percent of the companies with the highest P/B ratios, the 10 percent with the next highest, on down to the 10 percent with the lowest P/B ratios. (These divisions are called deciles.) Once again a contrarian strategy achieved better than average rates of return. Without exception, every decile with lower P/B ratios outperformed the deciles with higher P/B ratios. The decile with lowest P/B ratios had an average return of
21.4 percent versus 8 percent for the decile with the highest P/B ratios. Other studies’ findings have been similar, although less pronounced. Some economists, notably James O’Shaugh- nessy, claim that a low price to sales ratio, P/S, is an even stronger predictor of better-than-average returns.
Concern with the fundamental ratios of a company is not new. Finance icons Benjamin Graham and David Dodd, in their canonical 1934 text Security Analysis, stressed the importance of low P/E and P/B ratios in selecting stocks to buy. Some even stipulate that low ratios constitute the definition of “value stocks” and that high ratios define “growth stocks.” There are more nuanced definitions, but there is a consensus that value stocks typically include most of those in oil, finance, utilities, and manufacturing, while growth stocks typically include most of those in computers, telecommunications, pharmaceuticals, and high technology.
Foreign markets seem to deliver value investors the same excessive returns. Studies that divide a country’s stocks into fifths according to the value of their P/E and P/B ratios, for example, have generally found that companies with low ratios had higher returns than those with high ratios. Once again, over the next few years, the undervalued, unpopular stocks performed better.
There are other sorts of contrarian anomalies. Richard Thaler and Werner DeBondt examined the thirty-five stocks on the New York Stock Exchange with the highest rates of
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returns and the thirty-five with the lowest rates for each year from the 1930s until the 1970s. Three to five years later, the best performers had average returns lower than those of the NYSE, while the worst performers had averages considerably higher than the index. Andrew Lo and Craig MacKinlay, as mentioned earlier, came to similar contrarian conclusions more recently, but theirs were significantly weaker, reflecting perhaps the increasing popularity and hence decreasing effectiveness of contrarian strategies.
Another result with a contrarian feel derives from management guru Tom Peters’s book In Search of Excellence, in which he deemed a number of companies “excellent” based on various fundamental measures and ratios. Using these same measures a few years after Peters’s book, Michelle Clay- man compiled a list of “execrable” companies (my word, not hers) and compared the fates of the two groups of companies. Once again there was a regression to the mean, with the execrable companies doing considerably better than the excellent ones five years after being so designated.
All these contrarian findings underline the psychological importance of a phenomenon I’ve only briefly mentioned: regression to the mean. Is the decline of Peters’s excellent companies, or of other companies with good P/E and P/B ratios the business analogue of the Sports Illustrated cover jinx?
For those who don’t follow sports (a field of endeavor where the numbers are usually more trustworthy than in business), a black cat stared out from the cover of the January 2002 issue of Sports Illustrated signaling that the lead article was about the magazine’s infamous cover jinx. Many fans swear that getting on the cover of the magazine is a prelude to a fall from grace, and much of the article detailed instances of an athlete’s or a team’s sudden decline after appearing on the cover.
There were reports that St. Louis Rams quarterback Kurt Warner turned down an offer to pose with the black cat on
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the issue’s cover. He wears No. 13 on his back, so maybe there’s a limit to how much bad luck he can withstand. Besides, a couple of weeks after gracing the cover in October 2000, Warner broke his little finger and was sidelined for five games.
The sheer number of cases of less than stellar performance or worse following a cover appearance is impressive at first. The author of the jinx story, Alexander Wolff, directed a team of researchers who examined almost all of the magazine’s nearly 2,500 covers dating back to the first one, featuring Milwaukee Braves third baseman Eddie Mathews in August 1954. Mathews was injured shortly after that. In October 1982, Penn State was unbeaten and the cover featured its quarterback, Todd Blackledge. The next week Blackledge threw four interceptions against Alabama and Penn State lost big. The jinx struck Barry Bonds in late May 1993, seeming to knock him into a dry spell that reduced his batting average forty points in just two weeks.
I’ll stop. The article cited case after case. More generally, the researchers found that within two weeks of a cover appearance, over a third of the honorees suffered injuries, slumps, or other misfortunes. Theories abound on the cause of the cover jinx, many having to do with players or teams choking under the added performance pressure.
A much better explanation is that no explanation is needed. It’s what you would expect. People often attribute meaning to phenomena governed only by a regression to the mean, the mathematical tendency for an extreme value of an at least partially chance-dependent quantity to be followed by a value closer to the average. Sports and business are certainly chancy enterprises and thus subject to regression. So is genetics to an extent, and so very tall parents can be expected to have offspring who are tall, but probably not as tall as they are. A similar tendency holds for the children of very short parents.
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If I were a professional darts player and threw one hundred darts at a target (or a list of companies in a newspaper’s business section) during a tournament and managed to hit the bull’s-eye (or a rising stock) a record-breaking eighty-three times, the next time I threw one hundred darts, I probably wouldn’t do nearly as well. If featured on a magazine cover (Sports Illustrated or Barron’s) for the eighty-three hits, I’d probably be adjudged a casualty of the jinx too.
Regression to the mean is widespread. The sequel to a great CD is usually not as good as the original. The same can be said of the novel after the best-seller, the proverbial sophomore slump, Tom Peters’s excellent companies faring relatively badly after a few good years, and, perhaps, the fates of Bernie Ebbers of WorldCom, John Rigas of Adelphia, Ken Lay of Enron, Gary Winnick of Global Crossing, Jean-Marie Messier of Vivendi (to throw in a European), Joseph Nacchio of Qwest, and Dennis Kozlowski of Tyco—all CEOs of large companies who received adulatory coverage before their recent plunges from grace. (Satirewire.com refers to these publicity-fleeing, company-draining executives as the CEOnistas.)
There is a more optimistic side to regression. I suggest that Sports Illustrated consider featuring an established player who has had a particularly bad couple of months on its back cover. Then they could run feature stories on the boost associated with such appearances. Barron’s could do the same thing with its back cover.
An expectation of a regression to the mean is not the whole story, of course, but there are dozens of studies suggesting that value investing, generally over a three-to-five year period, does result in better rates of return than, say, growth investing. It’s important to remember, however, that the size of the effect varies with the study (not surprisingly, some studies find zero or a negative effect), transaction costs can eat up some or all of it, and competing investors tend to shrink it over time.
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In chapter 6 I’ll consider the notion of risk in general, but there is a particular sort of risk that may be relevant to value stocks. Invoking the truism that higher risks bring greater returns even in an efficient market, some have argued that value companies are risky because they’re so colorless and easily ignored that their stock prices must be lower to compensate! Using “risky” in this way is risky, however, since it seems to explain too much and hence nothing at all.
Accounting Practices, WorldCom’s Problems
Even if value investing made better sense than investing in broad-gauged index funds (and that is certainly not proved) a big problem remains. Many investors lack a clear understanding of the narrow meanings of the denominators in the P/E, P/B, and P/D ratios, and an uncritical use of these ratios can be costly.
People are easily bamboozled about numbers and money even in everyday circumstances. Consider the well-known story of the three men attending a convention at a hotel. They rent a booth for $30, and after they go to their booth, the manager realizes that it costs only $25 and that he’s overcharged them. He gives $5 to the bellhop and directs him to give it back to the three men. Not knowing how to divide the $5 evenly, the bellhop decides to give $1 to each of the three men and pockets the remaining $2 for himself. Later that night the bellhop realizes that the men each paid $9 ($10 minus the $1 they received from him). Thus, since the $27 the men paid (3 x $9 = $27) plus the $2 that he took for himself sums to $29, the bellhop wonders what happened to the missing dollar. What did happen to it?
The answer, of course, is that there is no missing dollar. You can see this more easily if we assume that the manager
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originally made a bigger mistake, realizing after charging the men $30 that the booth costs only $20 and that he’s overcharged them $10. He gives $10 to the bellhop and directs him to give it back to the three men. Not knowing how to divide the $10 evenly, the bellhop decides to give $3 to each of the three men and pockets the remaining $1 for himself. Later that night the bellhop realizes that the men each paid $7 ($10 minus the $3 they received from him). Thus, since the $21 the men paid (3 x $7 = $21) plus the $1 he took for himself sums to $22, the bellhop wonders what happened to the missing $8. In this case there’s less temptation to think that there’s any reason the sum should be $30.
If people are baffled by these “disappearances,” and many are, what makes us so confident that they understand the accounting intricacies on the basis of which they may be planning to invest their hard-earned (or even easily earned) dollars? As the recent accounting scandals make clear, even a good understanding of these notions is sometimes of little help in deciphering the condition of a company’s finances. Making sense of accounting documents and seeing how balance sheets, cash flow statements, and income statements feed into each other is not something investors often do. They rely instead on analysts and auditors, and this is why conflating the latter roles with those of investment bankers and consultants causes such concern.
If an accounting firm auditing a company also serves as a consultant to the company, there is a troubling conflict of interest. (A similar crossing of professional lines that is more upsetting to me has been curtailed by Eliot Spitzer, New York attorney general. One typical instance involved Jack Grub- man, arguably the most influential analyst of telecommunications companies such as WorldCom, who was incestually entangled in the investments and underwriting of the very companies he was supposed to be dispassionately analyzing.)
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A student’s personal tutor who is paid to improve his or her performance should not also be responsible for grading the student’s exams. Nor should an athlete’s personal coach be the referee in a game in which the athlete competes. The situation may not be exactly the same since, as accounting firms have argued, different departments are involved in auditing and consulting. Nevertheless, there is at least the appearance of impropriety, and often enough the reality too.
Such improprieties come in many flavors. Enron’s accounting feints and misdirections involving off-shore entities and complicated derivatives trading were at least subtle and almost elegant. WorldCom’s moves, by contrast, were so simple and blunt that Arthur Andersen’s seeming blindness is jawdropping. Somehow Andersen’s auditors failed to note that WorldCom had classified $3.8 billion in corporate expenses as capital investments. Since expenses are charged against profits as they are incurred, while capital investments are spread out over many years, this accounting “mistake” allowed WorldCom to report profits instead of losses for at least two years and probably longer. After this revelation, investigators learned that earnings were increased another $3.3 billion by some combination of the same ruse and the shifting of funds from exaggerated one-time charges against earnings (bad debts and the like) back into earnings as the need arose, creating, in effect, a huge slush fund. Finally (almost finally?) in November 2002 the SEC charged WorldCom with inflating earnings by an additional $2 billion, bringing the total financial misstatements to over $9 billion! (Many comparisons with this sum are possible; one is that $9 billion is more than twice the gross domestic product of Somalia.)
WorldCom’s accounting fraud first came to light in June 2002, long after I had invested a lot of money in the company and passively watched as its value shriveled to almost nothing. Bernie Ebbers and company had not merely made $1 disappear
as in the puzzle above, but had presided over the vanishing of approximately $190 billion, the value of WorldCom’s market capitalization in 1999—$64 a share times 3 billion shares. For this and many other reasons it might be argued that both the multi-trillion-dollar boom of the ’90s and the comparably sized bust of the early ’00s were largely driven by telecommunications. (With such gargantuan numbers it’s important to remember the fundamental laws of financial estimation: A trillion dollars plus or minus a few dozen billion is still a trillion, just as a billion dollars plus or minus a few dozen million is still a billion.)
I was a victim, but the primary victimizer, I’m sorry to say, was not WorldCom management but myself. Putting so much money into one stock, failing to place stop-loss orders or to buy insurance puts, and investing on margin (puts and margin will be discussed in chapter 6) were foolhardy and certainly not based by the company’s fundamentals. Besides, these fundamentals and other warning signs should have been visible even through the accounting smoke screen.
The primary indication of trouble was the developing glut in the telecommunications industry. Several commentators have observed that the industry’s trajectory over the last decade resembled that of the railroad industry after the Civil War. The opening of the West, governmental inducements, and new technology led the railroads to build thousands of miles of unneeded track. They borrowed heavily, each company attempting to be the dominant player; their revenue couldn’t keep pace with the rising debt; and the resulting collapse brought on an economic depression in 1873.
Substitute fiber-optic cable for railroad tracks, the opening of global markets for the opening of the West, the Internet for the intercontinental railroad network, and governmental inducements for governmental inducements, and there you have it. Millions of miles of unused fiber-optic cable costing billions
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of dollars were laid to capture the insufficiently burgeoning demand for online music and pet stores. In a nutshell: Debts increased, competition grew keener, revenue declined, and bankruptcies loomed. Happily, however, no depression, at least as of this writing.
In retrospect, it’s clear that the situation was untenable and that WorldCom’s accounting tricks and deceptions (as well as Global Crossing’s and others’) merely papered over what would soon have come to light anyway: These companies were losing a lot of money. Still, anyone can be forgiven for not recognizing the problem of overcapacity or for not seeing through the hype and fraudulent accounting. (Far less blameless, if I may self-flagellate again, were my dumb investing practices, for which WorldCom management and accountants certainly weren’t responsible.) The real source of most people’s dismay and apprehension, I suspect, derives less from accountants’ malfeasance than from the market’s continuing to flounder. If it were rising, interest in the various accounting reforms that have been proposed and enacted would rival the public’s keen fascination with partial differential equations or Cantor’s continuum hypothesis.
Reforms can only accomplish so much. There are countless ways for accountants to dissemble, many of which shade into legitimate moves, and this highlights a different tension running through the accounting profession. The precision and objectivity of its bookkeeping fit uncomfortably alongside the vagueness and subjectivity of many of its practices. Every day accountants must make judgments and determinations that are debatable—about the way to value inventory, the burdens of pensions and health care, the quantification of goodwill, the cost of warranties, or the classification of expenses—but once made, these judgments result in numbers, exact to the nearest penny, that seem indubitable.
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The situation is analogous to that in applied mathematics where the appropriateness of a mathematical model is always vulnerable to criticism. Is this model the right one for this situation? Are these assumptions warranted? Once the assumptions are made and the model is adopted, however, the numbers and organizational clarity that result have an irresistible appeal. Responding to this appeal two hundred years ago, the German poet Goethe rapturously described accounting this way: “Double entry bookkeeping is one of the most beautiful discoveries of the human spirit.”
Focusing only on the bookkeeping and the numerical output, however, and refusing to examine the legitimacy of the assumptions made, can be disastrous, both in mathematics and accounting. Recall the tribe of bear hunters who became extinct once they became expert in the complex calculations of vector analysis. Before they encountered mathematics, the tribesmen killed, with their bows and arrows, all the bears they could eat. After mastering vector analysis, they starved. Whenever they spotted a bear to the northeast, for example, they would fire, as vector analysis suggested, one arrow to the north and one to the east.
Even more important than the appropriateness of accounting rules and models is the transparency of these practices. It makes compelling sense, for example, for companies to count the stock options given to executives and employees as expenses. Very few do so, but as long as everyone knows this, the damage is not as great as it could be. Everyone knows what’s going on and can adapt to it.
If an accounting practice is transparent, then an outside auditor who is independent and trusted can, when necessary, issue a statement analogous to the warning made by the independent and trusted matriarch from chapter 1. By making a bit of information common knowledge, an auditor (or
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the SEC) can alert everyone involved to a violation and stimulate remedial action. If the auditor is not independent or not trusted (as Harvey Pitt, the recently departed chairman of the SEC, was not), then he is simply another player and violations, although perhaps widely and mutually known, will not become commonly known (everyone knowing that everyone else knows it and knowing that everyone else knows they know it and so on), and no action will result. In a similar way, family secrets take on a different character and have some hope of being resolved when they become common knowledge rather than merely mutual knowledge. Family and corporate “secrets” (such as WorldCom’s misclassification of expenses) are often widely known, just not talked about.
Transparency, trust, independence, and authority are all needed to make the accounting system work. They are all in great demand, but sometimes in short supply.