Monthly Discussion



Forecasting the DOW via the Divisor


The average price of the 30 DOW industrials is the main ingredient in the calculation of the DJIA. Amazingly this number does not change significantly over time! An endless stream of stock splits has kept this number more or less constant over the years. It is the corresponding decrease of the divisor預lso involved in the calculation of the DJIA葉hat is responsible for the impressive growth of the market. Exhibit 3 shows how DOW痴 average price has been narrowly confined in the range $40 to $80 for the better part of the twentieth century, averaging around $60. All along the divisor has been decreasing. But the price has recently dropped to $43 and the divisor has stalled for an unusually long time (see Exhibit 4).



Exhibit 3. The purple line is a linear fit to the data. The average price of the DOW痴 30 industrials shows practically no long-term trend and has been generally confined inside the range $40 to $80. (The data sampling is every six months except for the last 4 years when the sampling is daily).


Exhibit 4 shows the evolution of the multiplier, i.e., the inverse of the divisor. Its growth during the late 1990s mirrors the growth of the DJIA. The recent stagnation of the market can be seen as a consequence of the fact that the average DOW price has been dropping and more importantly because the multiplier has not been growing. Both the average price and the multiplier should normally increase. I say normally because the former behaves like an invariant (see Predictions), and the later has been following an S-curve; both phenomena are manifestations of natural laws. And since an increase of the multiplier is intrinsically linked to a further decrease of the average price (stock splits cause both), some real growth is in store for us.


Exhibit 4. The divisor has been constantly decreasing; its inverse葉he multiplier揺as been increasing. The purple line is an S-curve fit. The good agreement argues as evidence for a natural growth process.


One may argue that the average DOW price could remain at $43 for a long time; after all it happened between 1970 and 1982. It may happen again, but the DJIA should nevertheless increase at the rate of 15% per year because of the multiplier (projection of purple line in Exhibit 4). The only way to accommodate zero growth is for the multiplier to remain flat at today痴 level. But looking at Exhibit 4 it becomes obvious that such a thing cannot happen under 渡ormal circumstances, because it involves a serious deviation from the S-curve. As for what normal circumstances are, my standard definition is that normal are the things we have all ready witnessed. In other words even a war, like the one in the Gulf, could be considered normal circumstances. After all, when it took place the stock market did not go to pot!

We can now forecast the DJIA by assuming a constant average price for the 30 industrials and a growing multiplier as per Exhibit 4. The result is shown in Exhibit 5. The traditional level of the average price, namely US$60, gives the yellow line, but assuming the average price will remain at today痴 level (US$43) gives the purple line. And this conservative estimate promises a DJIA of 10,000 for the end of 2002!



Exhibit 5. The yellow line is obtained when we use the fitted curves (purple lines) from above Exhibits 3 and 4. The purple line results if we assume the DOW痴 average price will remain constant at today痴 level, namely $43. The forecasted rate of growth is of the order of 15% per year.


The discontinuity of the purple line comes from the fact that today the multiplier forecast is above the actual multiplier. If we want to adjust for a smooth transition between forecasts and actuals in Exhibit 5 we should subtract around 640 points from the forecast. We end up with a DJIA of 9,360 by year痴 end.