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*Monthly
Discussion*

* *

* *

**Where Are You
on the Curve?**

Using
S-curves to make forecasts can be effective if you are facing an already
started well-defined competitive growth process. The timeframe of such a
process can vary. For example, if you are looking at a life's career, the
timeframe may consist of many years. If you are looking at a version of Windows
operating system, the appropriate timeframe may consist of many months. If you
are looking at the maturing of your garden's tomatoes, the timeframe may
consist of several weeks. And if you are looking at the reaction of a stock
price to a major acquisition, or the reaction of a stock market to the coming
and going of an interest-rate change, the appropriate timeframe may be only
several days. In each case it is essential to determine the actual position on
the growth cycle before attempting to make any forecasts.

I have half a dozen different ways for doing this
depending on the availability of hard data. They range from the simplest to the
most sophisticated one. One way effective and accessible to the average
non-scientist (i.e., requires no math or other computations) is based on the
fact that the *prospects for growth* affect our emotional
disposition—subconsciously—and thus become intuitively accessible.

The method utilizes the
concepts of calculus. The S-shaped pattern is very sensitive to the rate of
change of the rate of growth. Mathematically, this corresponds to the second
derivative—in other words, the prospects for growth. To better understand the
concept of the second derivative think of traveling with your car. Let us say
that the *distance* you cover as a function of time looks like an S-shaped
curve. (This does not mean that you swerve around but that you change speed as
you drive.) The first derivative—the rate at which the distance changes—is the
car *speed*. When the speed is high, a lot of distance is covered in a
short time. The speed curve is typically bell-shape—that is, low in the
beginning and at the end, but high in the middle of the trip. The second
derivative is the *acceleration*, the rate at which the speed changes. The
acceleration is directly proportional to the force exerted by the car. The more
powerful the car, the higher a speed it can attain in a short time. This curve
goes up and down and up again, since you start at zero, you accelerate, and
then decelerate in order to stop. Exhibit 3 shows the three curves
mathematically calculated. Without loss of generality, the second derivative
has been approximated with straight-line segments to conform to the distinct
phases of growth (business seasons.)

A more relevant example can be found
in a product’s sales. The cumulative number of products sold—the filling of the
market niche—is described by an S-shaped curve. The sales *per quarter*
represent the first derivative. They comprise the product’s life cycle and
follow a bell-shaped curve. In this case the second derivative is the company’s
*investment* in this product. Investment is positive during the product’s
early days and negative—returns instead of investments—during the product’s
later life.

Similarly in the stock market, the
share price during a growth cycle is described by an S-shaped curve. The
returns on investments per unit of time are given by the bell-shaped curve. The
second derivative reflects the prospects for growth, something like the
analysts’ rating, A+, A, A-, or three stars, two stars, and so on.

For *any* growth process, we need
to identify the quantity that corresponds to its second derivative—that is, *the
rate of the rate* of growth, or the prospects for growth. Here are some
examples:

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S-shaped curve (First derivative) (Second derivative)

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Distance Speed Acceleration (force)

Cumulative
sales of product Sales
by trimester Investments in product

Size
of organism Rate
of growth Growth prospects

Stock
price R.O.I. Stock rating

Knowledge Learning Rate of progress

State
of the economy Rate
of economic Value of money

(GNP, $ per capita,
etc.) development (opposite of inflation)

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You can pinpoint your position in the
growth cycle by answering a questionnaire that addresses your emotional world.
The questionnaire determines your position in the cycle with an accuracy of
half a season. As you respond, think of the prospects for the future and the
direction in which they are moving. Or simply whether you feel good or bad,
optimistic or pessimistic toward the future—all this with regard to a product,
an activity, a company, a career, or whatever else may be on your mind. You can
also look at it as follows: if you were to issue stock on it, what would the
analysts give it as a rating? But remember, the activity you choose must
represent something that grows under conditions of natural competition—that is,
the law of survival of the fittest.

Are
the prospects for the future POSITIVE or NEGATIVE?

(Check
one box)

POSITIVE NEGATIVE

1-ٱ Little and stable Little and
stable 6-ٱ

2-ٱ Little and improving Much but
improving 7-ٱ

3-ٱ Much and improving Little but improving
8-ٱ

4-ٱ Much and stable Little and stable
9-ٱ

5-ٱ Deteriorating Deteriorating
10-ٱ

Exhibit
3. Three curves describing a
natural-growth process: the S-curve and its two derivatives (the second
derivative has been approximated with straight-line segments.) The circled
numbers correspond to the numbers of the questionnaire; they point out a
position in a season.

When the employees or stockholders of a company
complete such a questionnaire on their company as a whole, they reveal more
than their perception and mood. They give a better determination of the
company’s position in the business cycle than the opinions of its management
team. Let us try this questionnaire together in a couple of cases. Let us first
consider computers. How do you feel about computer sales? I believe most of you
would agree with me that whether you are an optimist or a pessimist about
future computer sales, the prospects about the future at present are rather
deteriorating. This answer (number 5 or 10 in the questionnaire) positions
computers at around 50% penetration of their market.

Let us do the same thing about the Internet as a whole. Here I think we can agree that Internet’s prospects for the future are high independently if we feel they are stable or increasing. This answer (numbers 3 or 4 in the questionnaire) positions Internet in a “spring” season at the early part of its S-curve.

There is
independent corroboration for the above conclusions. *The Economist*
published the graph of Exhibit 4 last September. It gives qualitative agreement
with our questionnaire results.

Exhibit
4. A graph adapted from *The
Economist*, September 23, 2000.

If Internet and computers, as we treated them above, had stocks of their own, the recommendations at this time would be “buy” the Internet stock and “prepare to sell” the computer stock. The signal for NASDAQ as a whole is mixed. But no matter how you look at it the technology market cannot be nearing saturation. A safe way to put it is to position technology stocks in general somewhere between computers and the Internet.