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PRINT VS. THEORETICAL

Within each trading day in the DJIA, each of the industrialВ  stocks reach their price highs and price lows at different times during the day. The print low or high is the actual level the DJIA reaches at some specific time during the trading day. The theoretical level in the DJIA is the cumulative print lows and highs of all the DJIA stocks during the trading day. The average almost never reaches its theoretical high or low for the trading day because it would require all stocks in the average to top or bottom at the exact same time. For most data from the 1930s through the 1960s, the intraday print highs or lows are either unknown or unavailable and will have to be approximated or interpolated with theoretical or closing levels. In cases after the 1960s, hourly data can also be used

to approximate price.

A LOOK BACK

At the bottom of the market on July 8, 1932, the theoretical low on the DJIA was 40.56, with a closing low of 41.22. From this point, the DJIA advanced to a theoretical high of 195.59 and a closing high of 194.40 on March 10, 1937. Somewhere between 40.56 and 41.22 on July 8, 1932, was the actual print low in the market, and somewhere between 194.40 and 195.59 on March 10, 1937, was the actual print high.

Calculating the percentage increase, or the growth in the price of the average from July 1932 to March 1937, an increase of 382% can be seen on a theoretical basis and 372% can be seen on a closing basis. For this analysis, I am going to average these two figures into a 377% increase to approximate its percentage advance on a print basis. This percentage increase matches the 14th number in the Fibonacci sequence, 377. (You can try different methods ofВ  interpolating to achieve the print figures or averaging combinations of theoretical and closing, but the result will be the same: 377% +/-2%.) This percentage increase is graphically represented in Figure 1.

After the 1937 high, the DJIA corrected more than 50% in value during the next fiveВ  years to a low in April 1942.

From there, another advance began that lasted almost 24 years, finally ending in 1966. In the same graph, you can

also see the percentage increase from April 28, 1942, to February 9, 1966.

Using the same techniques as before, this period saw an increase of approximately 987% in the price of DJIA stocks. The theoretical and closing lows at the bottom of April 1942 were 92.69 and 92.92, respectively, and the theoretical and closing highs at the February 1966 high were 1001.11 and 995.15, respectively.

Thus, the maximum and minimum increases possible on a print basis were 971% toВ  980%. Figure 1 shows an increase of 987% between 1942 and 1966. Although we know the increase in the price of the Dow industrials was somewhere between 971% and 980% on a print basis, in the case of the 1932 to 1937 advance, we can onlyВ  approximate the exact print level.

I labeled the 1942 to 1966 advance in Figure 1 as 987%, which represents the 16th num ber in the FibonacciВ  sequence and is 1% above the 971-980% level advance on a print basis that we just calculated. The significance of this is not that it matches the exact Fibonacci number but that it is representative of the growth rate found in the additive process of the sequence.

The number 987 is an alternate to that of 377 in the Fibonacci sequence and represents two stages of growth, or 2.618 times the growth seen from 1932 to 1937. Remember that each number in the Fibonacci sequence is 1.618 greater than the previous number, and alternate numbers are 2.618 greater: (1.618)(1.618) = 2.618.

Although the 1942 to 1996 advance is about a percent shorter than it should be, based on the Fibonacci numbers, another approach would be to take the actual closing low of 1932, calculate the percentage advance to 1937, and

then apply it to the 1942 low. Using the closing low of 41.22 in 1932 and the closing high of 194.4 in 1937, a percentage increase of 371.6% can be calculated. Multiplying a 371.6% increase by 2.618 projects an increase of 972.8%.

This percentage increase calculated off theВ  1942 closing low of 92.92 projects a closing high of 996.8. As mentioned before, the closing high in February 1966 was 995.15, just 1.65 points away from the 2.618 closing

projection. It is impossible to know the exact numbers without exact print data, but for the purpose of further analysis, it is clear that there is a very strong and significant Fibonacci relationship between the advances of 1932-37 and 1942-66.

FIGURE 1: DJIA, 1942-66. Here’s an increase of 987% between 1942 and 1966. Although we know the increase in the price of the Dow industrials was somewhere between 971% and 980% on a print basis, as in the case of the 1932 to 1937 advance, we can only approximate the exact print level.