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:



                                    Bell-shape curve                          Up and down and up

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


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)



          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.