As the eye follows each fluctuation of the DJIA, long or short, it is also found that the same identical fluctuation appears in the more comprehensive average. This is true down to the finest detail resolved by weekly data, and can be shown to be true also for oscillations resolvable only by daily data.

From this really incredible chart, the following conclusions are mescapably drawn:

• The time series of the two averages are so nearly identical that only minor spectral signature differences are possible between them.

• AH results, conclusions, and implications derived from the spectral studies of the DJIA are now s«n to apply (with but minor variations possible) to at least one-fourth of all the issues on both the New York and the American Stock Exchan.

• At any given moment of time, the earnings and earninp potentials for the various issues of the S&P "500" are in all possible states. Some of the issues comprising this broad average have extremely good fundamental situations, some have extremely bad ones, and others exhibit all possible variations in between. If these considerations truly were the basis of price change, we would expect an average of some 500 resulting prices to show no coherency and order at all. In fact, we would expect the resulting price average to be (uite smooth, with price variations due to aU different fundamental situations averaged out. On the contrary, we now see that the average has a spectral signature with all the precise order shown for the DJIA!

• The above reasoning does not negate completely the potential of fundamentals to influence prices. Remember the scale factor difference that has been removed from the data in Figure A II-l before conclusions were drawn. However, the evidence is clear that such factors do not have more than a negligible relationship to price fluctuations. The impact, if any, has to be in the area of volatility or the long-term, smooth price motion upon which the fluctuations of the spectral model ride. Given a lower frequency limit of the fluctuation model corresponding to periods of 18 years (or even of 9, or 4.5 years) it is seen that the remaining effect of fundamental factors must be quite smooth and slow changing indeed!

• Further, the same lines of reasoning apply to the DJIA. Again the earnings, earnings potential, and all other fundamental factors vary widely between the 30 issues involved at any given time, and certainly are not the same as for the constituents of the S&P "500." Again, not only do price changes supposedly due to these factors fail to average out, but the spectral signature displays coherency-tr/Juf goes beyond to show the same coherency exhibited in the larger average! The conclusion is unavoidable that those fundamental considerations that are widely held to be so very effective in causing price change-and in fact are used as the basis for stock purchases and sales by individuals and institutions alike-simply are not the principal reason for the price motion that occurs!

• Finally, inspection of the timing of the turns of the fluctuations of the two averages demonstrates vividly the incredible degree of time synchronizalion of the spectral components involved in the fluctuations. Once again, if significant differences in spectral component phasing existed between individual issues, the fluctuations in the DJIA should at least be "smeared." This thinking would be even more valid for the average of 5{ stocks, and the near-perfect identicatity of fluctuations between the two averages would be simply impossible. This attribute of the principle of commonality was demonstrated with a single issue (Standard Packaging) in Chapter Two, and is dramatically extended by the implications of Figure A IM.

appendix three

The Source and Nature of Transaction Interval Effects

• Theoretical Yietd-Rate Maximums vs. Trarwaction interval

• The impact of Compounding

• The Effect of Sinusoidal Rate Summation

In Chapter One, it was demonstrated on a single issue that, given perfect transaction timing, yield rate is inversely proportional to transaction interval.

The effect demonstrated using a single stock can be quantified further. The same procedure was apphed to 300 stocks, selected at random from both the New York and American Exchanges in equal numbers. Yield rate versus transaction interval was determined for each and the results averaged. The results appear on the left in Figure A .

THEORETICAL YIELD-RATE MAXIMUMS VS. TRANSACTION INTERVAL

The curve is inversely exponential with a significant "knee" between ten and 20 weeks. For transaction intervals of less than ten weeks the potential yield rate increases very steeply.

The significance of this, of course, is that it is worth almost any resource expenditure required to achieve significant shortening of average transaction intervals.

THE IMPACT OF COMPOUNDING

In the same figure, on the right, are plotted two samples of the yield rate versus transaction interval directiy from the compound interest law. It is obvious that the curve on the left derives its principal shape from the compounding effect. The lower of the two compound interest curves applies for average transaction profits often %each, while the upper one is derived for average transaction profits of 20% each. The

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