36
The Pyramid of Numbers Firm Size, Growth Rates, and Valuation
Growth is important because companies create shareholder value through profitable growth. Yet there is powerful evidence that once a company’s core business has matured, the pursuit of new platforms for growth entails daunting risk. Roughly one company in ten is able to sustain the kind of growth that translates into an above-average increase in shareholder returns over more than a few years. . . . Consequently, most executives are in a no-win situation: equity markets demand that they grow, but it’s hard to know how to grow.
—Clayton M. Christensen and Michael E. Raynor, The Innovator’s Solution
Analysts and investors seem to believe that many firms’ earnings can consistently grow at high rates for quite a few years. The evidence suggests instead that the number of such occur- rences is not much different from what might be expected from sheer chance.
—Louis K. C. Chan, Jason Karceski, and Josef Lakonishok, “The Level and Persistence of Growth Rates”
Why Big Fierce Animals Are Rare
On the surface, the size and frequency distribution for species, cities, and company sizes may not seem like they would have a lot in common. Yet each follows a power law, which looks like a straight line when plotted on a log-log scale. Power laws indicate that there are lots of small occurrences and very few large ones.1 In nature, there are lots of ants—the combined weight of ants is larger than the combined weight of humans—but very few elephants. Similarly, we have many small companies and a modest number of huge ones. Exhibit 36.1 shows examples of these distributions side by side.
Take species for a moment. Why are large carnivorous animals, like tigers, relatively rare, while small animals, like termites, are so abundant? Ecologists answer by pointing out that all animals have a niche—not just a physical location, but a real place in the grand scheme of things. A species must not only survive in its home; it must successfully interact with the other plant and animal species that share that home.
The niche idea, though, still doesn’t explain why the distribution of species looks the way it does. That insight came from Oxford’s Charles Elton, who noted that larger animals need smaller animals to sustain them. (Animals rarely prey on larger animals.) So, Elton reasoned, with every increment in body size, there should be an associated loss in numbers. He called this fact of life the “Pyramid of Numbers.” Big fierce animals are rare because they have fewer sources of energy than smaller animals.2 The species power law distribution is a natural outcome of interacting animals constrained by the laws of physics.3
What does this have to do with the stock market? Investors should pay attention to these distributions for three reasons. First, companies, like species, fit into niches. Thinking about these niches and how they change can provide some insight into a company’s growth potential.
EXHIBIT 36.1 Distribution for Species, City, and Company Sizes
Source: Marquet et al., “Lifespan, Reproduction, and Ecology”; van Marrewijk, “International Trade and the World Economy,” http://www.few.eur.nl/few/people/vanmarrewijk/international/zipf.htm; Axtell, “Zipf Distributions,” 1819. Reproduced with permission.
Second, a strong body of evidence shows that the variance of growth rates is smaller for large firms than for small firms (even though the median growth rate is fairly stable across the population). Further, growth for large companies often stalls, leading to marked share-price underperformance as investors recalibrate their expectations.
Finally, investors often extrapolate past growth rates into the future, leading to disappointing shareholder returns for companies that cannot meet those expectations. Investors who are aware of patterns of growth may be able to avoid unfavorable expectations gaps.
Find Your Niche
The idea that companies find niches is certainly not new. For example, many aspects of competitive-strategy literature in general, and game theory in particular, address how and why companies should seek profitable niches. The main message here is that environments, and hence niches, change over time as the result of technological developments, regulatory shifts, and industry entry and exit.
Think of mini-mills versus integrated steel companies, or Internet-based retailers compared to brick-and-mortar competitors. New niches open, and new companies exploit them. A company’s ability to adapt to a changing environment is critical—and the number of companies that can do so is small.
As a result, optimal firm size may not be fixed for a particular industry, and comparing the valuations of companies with different economic models doesn’t make sense.
Dear CEO: We’ve Made It to the Fortune 50! You’re Fired
Studies of firm size distributions and growth rates reveal four stylized facts:1. Firm-size distributions follow Zipf’s law (a specific class of power law).4 What is crucial for investors is that this distribution is very robust in the face of significant economic change. This means that the proportion of very large companies to smaller companies is unlikely to vary much in the future.
2. Variances of firm-growth rates decrease with size.5 My analysis suggests that median growth rates are stable across a large sample of U.S. public companies (sales of $100 million or more) but that the variance in growth narrows substantially (see exhibit 36.2). On one level, this observation is common sense—large companies represent a substantial percentage of the GDP, so it’s unlikely that they will outstrip it to any meaningful degree. (The Fortune 50 represent about 35 percent of the GDP.) Yet companies that launch into the Fortune 50 are often those that have realized strong past growth, setting up a potential investor-expectations mismatch.This empirical finding is consistent with stochastic models similar to Gibrat’s law. This law, also known as the law of proportionate effect, says that a firm’s growth rate is independent of its size. With some modifications, applying Gibrat’s law to a sample of companies generates a Zipf distribution. Classical microeconomics has no satisfactory models to explain these findings.6
EXHIBIT 36.2 Shrinking Variance of Sales Growth in Relation to Sales Base
Source: FactSet, author analysis.
3. The growth for large companies often stalls. This was the conclusion of a detailed study by the Corporate Strategy Board.7 The research argued that once companies reach a sufficient sales level, they see their growth rate stall. That stall level has risen over the decades but looked to be in the $20 to $30 billion area in the late 1990s.Exhibit 36.3 shows the average annual growth rate for companies entering into the Fortune 50 (a ranking based on sales). The data show that companies often enjoy strong growth rates before making the top fifty but tend to have rather anemic growth once they attain that group. The high growth rate in the first year suggests that acquisitions catapult many companies into the Fortune 50.
4. Most industries follow an identifiable life cycle.8 Early on, an industry tends to see substantial growth and entry, then meaningful exit and high economic returns (for the survivors), followed by gradual growth deceleration. In mature stages, companies have muted growth and economic returns close to competitive equilibrium. Large companies tend to be mature companies.
EXHIBIT 36.3 Average Annual Growth Rate for Companies Entering the Fortune 50
Source: Reprinted with permission from Corporate Strategy Board, “Stall Points,” 15. Copyright 1998 AAAS.
Advising companies what to do in the face of slowing growth is an industry in and of itself. It is true that large companies have a difficult time innovating as successfully as smaller companies for a host of reasons. I enthusiastically recommend a book by Clayton Christensen and Michael Raynor, The Innovator’s Solution, which provides managers with a useful innovation framework. But the truth is that not all companies can grow rapidly forever.
Extrapolative Expectations
A review of the evidence on firm size and growth rates suggests that investors should temper their growth expectations as companies get larger. But the reality is that investors tend to extrapolate
from the recent past and hence miss declining growth rates. According to Chan, Karceski, and Lakonishok:Market valuation ratios have little ability to sort out firms with high future growth from firms with low growth. Instead, in line with the extrapolative expectations hypothesis, investors tend to key on past growth. Firms that have achieved high growth in the past fetch high valuations, while firms with low past growth are penalized with poor valuations.9
Data from the Corporate Strategy Board support this point. Its multidecade study shows that roughly two-thirds of the companies that hit the stall point lose 50 percent or more of their market value (relative to the Dow Jones Industrial Average) within a decade. Ninety-five percent underperform the DJIA by 25 percent or more.
EXHIBIT 36.4 Total Shareholder Return—Largest 50 Versus S&P 500
Source: FactSet, Ibbotson, author analysis.
EXHIBIT 36.5 Large Companies: Present Value of Cash Flows from Existing Assets Versus Future Investments
Source: FactSet, HOLT.
I asked a similar, simple question: How would an equal-weighted portfolio of the largest fifty companies in market capitalization, purchased at year end, fare versus the S&P 500 in the subsequent one-, three-, and five-year periods? I ran the numbers from 1980 through 2006 and found that for each holding period, the S&P 500 outperformed the large cap portfolio (see exhibit 36.4). Again, it’s hard for the largest companies to meaningfully outperform the market because they are such a large percentage of the market.10
Another way to look at expectations is to break down the percentage of shareholder value that comes from assets in place versus the value attributable to future investments. In early 2007, 30 percent of the value of the twenty largest U.S. companies was expected to come in the future (see exhibit 36.5).11
Economies and markets are certainly vibrant. But underneath the constant change lurk robust patterns of growth and firm-size distributions. Mindful investors should take these patterns into account as they assess the growth prospects of companies—especially large ones.
37
Turn Tale
Exploring the Market’s Mood Swings
The conviction that the party is far from over is part of the reason . . . technology stocks soar ever higher. “I don’t think anything could shake my confidence in this market,” Mr. Allen says. Mr. O’Keefe adds: “Even if we do go down 30%, we’ll just come right back.”
“There was that bad stretch a little while back,” he says. “Guys called me up and said, ‘What do I do?’ I told them, ‘Buy more.’ ”
—“Tech-Stock Chit-Chat Enriches Many Cape Cod Locals” The Wall Street Journal, March 13, 2000
“All they ever say is, ‘Buy, buy, buy,’ all the way down from $100 a share to bankruptcy,” the burly 63-year-old barber said . . . Now, they give a stock tip and I stay as far away from it as I can. Nobody trusts anyone any more.”
Indeed, while mostly avoiding investments in more stocks, Mr. Flynn has been driving to a casino in nearby Connecticut every Monday to play blackjack and poker. “I do better there than I do in the market,” notes Mr. Flynn.
—“At Cape Cod Barber Shop, Slumping Stocks Clip Buzz,” The Wall Street Journal, July 8, 2002
Hush Puppies and Dogs of the Dow
Sales of Hush Puppies, the nerdish suede shoes with crepe soles, hovered around 30,000 pairs in 1994. Indeed, the manufacturer of the once-popular shoes was considering phasing them out. But then, something remarkable happened: Hush Puppies suddenly became hip in downtown Manhattan. Sales of classic Hush Puppies reached 430,000 pairs in 1995 and over 1.7 million in 1996. Within a couple of years, Hush Puppies shook off their label as the dog of the footwear world and became a must-have item for the fashion cognoscenti.1
What does the story about Hush Puppies have to do with the stock market? In both cases, sentiment is a critical determinant of performance. The mechanism that made Hush Puppies hot is the same as what causes investors to go back and forth from extreme optimism to extreme pessimism.
I extracted the above quotations from two articles in The Wall Street Journal about a small-town barber, written less than two-and-one-half years apart. In the first article, the barber’s faith in the market is unshakeable—his portfolio is approaching seven figures, he’s doling out advice, and he’s contemplating early retirement. In the second article, he’s lost all faith in the stock market and investment professionals, and prefers casino gambling over investing. The barber’s swing from manic to depressed resonates with us precisely because it reflects the change in sentiment among many investment professionals—those who are supposed to know better.
Ah Choo
If you want to understand how broadscale sentiment shifts occur, you can start by thinking about the flu—well, actually, how the flu spreads. There are two key dimensions, both intuitive. The first is the degree of contagiousness—how easily an idea spreads. The second is the degree of interaction—how much people bump into one another. If the flu is very contagious but carriers don’t interact with others, it will not take off. If there’s a lot of interaction but the flu strand is not contagious, it will not take off. But combine interaction with contagiousness and you’ve got an epidemic.2
As it turns out, the graphs of idea and disease propagation look the same. They both follow an S-curve (see exhibit 37.1). Not surprisingly, our biological analogy points to business world parallels. We can understand susceptibility, or contagiousness, as adoption thresholds. And we can model the degree of interaction with a “small-world” framework.
EXHIBIT 37.1 Disease Propagation
Source: Mark E. Newman and Duncan J. Watts, Scaling and Percolation in Small World Networks.
Ben Graham once said, “In the stock market, value standards don’t determine prices; prices determine value standards.”3 Individuals don’t construct value standards based on intrinsic principles but rather are influenced by what other people do. Stock prices reflect the collective actions of others. But we all don’t have equal potential to be influenced. We all have what’s called an adoption threshold, which is defined by how many other people must engage in an activity before we join in. Market extremes push the sentiment beyond the adoption threshold of nearly all investors. Such extremes can create, by definition, the conditions for a sentiment reversal.
Also, we interact more than ever. Scientists have made significant strides in understanding the small-world effect—colloquially known as six degrees of separation—in recent years.4 One of the central ideas in the small-world model is clustering, or the degree to which connections to one node connect to another. For example, clustering expresses the likelihood that your friends are likely to know one another.
When modeling these networks, researchers discovered that just a few random links between local, clustered networks dramatically reduce the degrees of separation. Because of our modern, low-cost communications network, ideas can cascade through social clusters faster than ever. The mass media further reinforce our interconnectedness.
This biological analogy reveals that almost all investors succumb to strong sentiment—either bullish or bearish—sooner or later. Further, interaction is almost assured because of our ability to communicate. Sentiment swings are age old and there are no modern inoculations.
Economists, Meet Mr. Market
Economists have long understood the role of expectations in shaping economic outcomes, including the performance of the stock market and the robustness of capital spending. Yet most economic models presume rational agents, a convenient modeling assumption that also happens to be safely removed from reality. An agent-based model of markets not only offers results consistent with the empirical facts but also accommodates periodic deviations between price and value.5
Practitioners spanning the centuries have documented the role of sentiment in investing and speculation.6 Perhaps the best way to think about sentiment is Ben Graham’s Mr. Market metaphor. Graham suggested imagining market quotes coming from an accommodating fellow named Mr.
Market, who never fails to show up and offer you a price to either buy or sell your interest in a business.
Warren Buffett describes Mr. Market’s most important characteristic:Even though the business that the two of you own may have economic characteristics that are stable, Mr. Market’s quotations will be anything but. For, sad to say, the poor fellow has incurable emotional problems. At times he feels euphoric and can only see the favorable factors favoring the business. When in that mood, he names a very high buy-sell price because he fears you will snap up his interest and rob him of imminent gains. At other times he is depressed and can see nothing but trouble ahead for both the business and the world. On these occasions he will name a very low price, since he is terrified that you will unload your interest on him. 7
Buffett underscores that since Mr. Market does not mind if you ignore him, you should never fall under his influence. The message is that price and value may diverge from one another, but investors who focus too much on price may have an emotionally difficult time distinguishing between the two.
More Than You Know Page 22
