Island of Foxes and Hares: How the S-Curve Forecasts Stock Behavior

In the early days of biological field research, scientists discovered a small island off the coast of Alaska that contained effectively three species: grass, arctic hares and arctic foxes. (There were some birds and insects flying around as well.) The scientists set up a field station to monitor the populations of the hares and foxes and, seeing a relatively simple ecosystem, assumed the head count of animals on the island would remain constant from season to season.

In fact, they were wrong. The population waxed and waned according to a predictable pattern. As we'll see, this phenomenon that occurs in nature also occurs in economic markets and can be used to forecast stock and commodity prices, among other things.

Back to the biology lesson: The researchers discovered that every couple of years, the populations of foxes and hares would soar wildly, only to crash to the point where the animals practically disappeared. For several seasons, both foxes and hares were scarce, only to soar and crash again. On a chart, the population cycle looked like an S-curve: Low numbers in the first few years, a sharp rise for one or two years, a brief period where the population was stable, followed by a crash back to low numbers again.

Fox and Hare Census

What could account for this cycle? As it turned out, the acreage and density of grass on the island were the key elements. When hare populations were low, the grass spread across the island. As density increased, the better-fed hares started having larger families, more of which survived to adulthood to propagate more hares. As the number of hares increased, foxes had better luck hunting, leading to better-fed foxes with their own larger families. Populations of both animals swung up. Eventually, there were so many rabbits that they overgrazed, chewing the grass down to the roots and leaving little vegetation behind. Starvation and disease soon decimated the hare population, leaving less food for the fox population, which in turn experienced sharp declines.

Why didn't the supply of grass and the number of animals settle into a steady state? The answer was that grass grew at an arithmetic rate (i.e., so many inches per year) and was limited to the available open land on the island. The animal population, however, grew at a geometric rate (i.e., two hares bore 10 offspring, six of which survived to adulthood to bear 30 offspring, etc.). It was even possible to predict when a crash would occur: When the rate of growth in the hare population leveled off after a sharp spike, it meant the grass supply was failing. (Less food reduced the hares' fertility.) When the grass supply failed completely, the hares died off and subsequently so did the foxes.

In the life cycle of companies, markets are analogous to the grass supply.

For example, the personal computer market, while huge, is finite. When every man, woman and child on the planet has a PC, future sales will be limited to replacements. Companies, on the other hand, are required by investors to grow revenue (the top line, analogous to the hares) and earnings (the bottom line, analogous to the foxes) every year.

To support a growth rate of 24% in revenue, a company must double sales every three years. A company can easily maintain this geometric growth in a rapidly expanding market. In slowly expanding or flat markets, high growth in revenue is achieved with great difficulty, usually by taking market share away from competitors. Alternatively, a company can jump to a new, rapidly expanding market. Companies that can do this successfully are terrific investments. It's comparable to a starving hare swimming to an adjoining island.

Let's consider General Electric GE, a high-performing company, No. 2 in the world in terms of market capitalization.

From 1997 to 1998, overall revenue was up 10.6%, earnings were up 13.3%, earnings per share were up 13.8%, and the stock price gained 39.5%. Revenue growth in the GE Capital subsidiary was 22%; growth in manufacturing divisions was only 7%.

Now look at a page from GE's 1998 annual report detailing the performance of its segments.

Below is GE's revenue growth over the past seven years:

GE Revenue Growth
Year	% increase in revenue
1993	5%
1994	7.9
1995	16.5
1996	13
1997	14.7
1998	10.6
1999*	9.9
*Estimated. Source: General Electric.

What does this tell us? Having dominated the slow-growth markets on the manufacturing side, GE pushed aggressively into financial services. Revenue growth overall was flat in the early 1990s, accelerated sharply in the mid-1990s as the financial services unit kicked into high gear, and now shows signs of leveling off.

If we graphed the revenue data, we would see an S-curve. Unfortunately, GE revenue is at the top, flattening part, not the bottom, accelerating part. This implies that after last year's 39% gain in the stock price and this year's 44% gain, we may be in for a flat spell (or worse).

By comparison, Cisco's CSCO recent and forward revenue growth remain high, ranging between 86.5% and 31.6% over the past four years. Zack's estimates it will be 30% annually over the next five years.

Graphically, Cisco's growth of revenue is perhaps halfway up the S-curve. Even with a price-to-earnings ratio of 163 compared with GE's 44, there may be less risk investing in Cisco.

Many situations, both biological and economic, exhibit the S-curve pattern. Oil prices have doubled over the last year, but have recently stalled out around $26 a barrel.

1999 Spot Crude-Oil Prices

Source: Reuters

Although it's possible that the price of oil will continue to rise, the S-curve analysis suggests a higher probability of a decline.

Generally speaking, greatest gains can be found in situations where the trend is accelerating, and the greatest losses can be avoided by divesting when the trend starts to flatten.