# SQUARE ROOT THEORY

References to the Square Root Theory as a predictor of stock prices pops up every now and then in financial writings. Norman Fosback used the theory in a 1976 publication called Stock Market Logic to make the case that the normal trading range of low price stocks provides greater profit opportunities than the normal trading range of high price stocks. In 1983, a book entitled The Templeton Touch, by William Proctor, disclosed that one of Templeton's 22 principles for stock market investing was that stock price fluctuations are proportional to the square root of the price.

In the 1950s William Dunnigan developed two stock trading systems called the Thrust Method and the One Way Formula. Both methods had several advantageous entry techniques but each lacked an effective exit technique. Dunnigan was above all a portfolio manager and not happy with the risk-reward aspects of his own trading methods, Dunnigan supported and publicized the Square Root Theory. He went so far as to call this theory the "golden key" and claimed recognition from some economics and statistical trade journals of the era.

## WHAT IS THE SQUARE ROOT THEORY?

The theory holds that stock and other publicly traded instrument prices move over the long and short term in a square root relationship to prior highs and lows. For example, IBM made a monthly closing low of 4.52 in June, 1962 and monthly closing high of 125.69 in July, 1999. This is within a few percentage points of the square of the sum of the square root of the low price + 9 or (2.12+9)^2. GM made a low of 15 in November, 1974 and a high of 95 in May, 1999. Again, a few percentage points from the square of the sum of the square root of the low + 6 or (3.87+6)^2. There are hundreds of these examples across the stock, financial and commodity markets. Even a few minutes with a pile of stock charts and a calculator will build confidence that major highs and lows are related to each other by additions and subtractions to their square roots.

## SQUARE ROOT THEORY IN ACTION

Let’s go through a recent daily chart of the SP500 and see how it works. The SP500 made a pivot low at 1060.72 on Aug-13-2004. Is there a square root relationship to that low that may be predictive of a future pivot high? Are other high and low pivots related by square roots?

Let's do the math. You can refer to the tutorial on constructing a Roadmap Chart in Excel for more detail.

• Aug-13-2004 low = 1060.72 = Square Root 32.568
32.568 + 2.5 = 35.068
35.068 ^2 = 1229.81 = Mar-7-2005 high!
• Mar-7-2005 high = 1229.11 = Square Root 35.058
35.058 - 1.25 = 33.808
33.808 ^2 = 1143.03 = Apr-20-2005 low!
• Apr-20-2005 low = 1136.15 = Square Root 33.706
33.706 + 1.25 = 35.207
35.207 ^2 = 1239.52 = Jul-29-2005 high!
• Jul-29-2005 high = 1245.04 = Square Root 35.285
35.285 - 1 = 34.285
34.285 ^2 = 1175.46 = Oct-13-2005 low!

How did we know to use 1 or 1.25 or 2.5 to add or subtract from the pivot points? Gann said that 90 degrees is very important for the markets. Gann also said that the number 2 represents a full circle or 360 degrees. 1 therefore equals 180 degrees and .500 and 250 90 degrees and 45 degrees respectively. We only had to add or subtract a few increments of .500 or .250 to each pivot point to obtain these results. Longer swings or high priced indexes  may require 3, 4, 5 or even higher base addends or subtrands.

Before Dunnigan and Templeton, probably starting in the early 1900s, W.D. Gann was using square roots as an integral part of his method to forecast stock and commodities prices and times. His method was more complex than what you see here. It appears to have been based on some ideas Gann picked up during his trips to India or Egypt.  Gann used an ennegram, a diagram of numbers constructed in such a way to show square and square root relationships. This ennegram is what’s come to be known as the Square of Nine from the Greek root “enneas” which is the word for “nine.”

Although Gann never revealed exactly how he used the ennegram we can gather from his words that it was probably very important to him: "We use the square of odd and even numbers to get not only the proof of market movements, but the cause." W. D. Gann, "The Basis of My Forecasting Method" (the Geometrical Angles course), p. 1

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