## The Square Root Theory

We have alluded to the Square of Nine as a **square root calculator**. We have attributed not the discovery of this tool (the actual discovery or date of first use is an unsolved mystery) but its public application to trading stocks and commodities to W.D. Gann. Perhaps it’s worthwhile to know that Gann was not the only financial writer to publicize the seemingly magic power of squares and square roots in forecasting stock prices.

In the early 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 had an absence of exit techniques. 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.

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**. Square roots will always maintain a cozy mainstream relationship with stock prices only because they are an essential component of almost every volatility or option pricing formula.

The theory holds that** stock prices move over the long and short term in a square root relationship**. 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 and 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. The Square of Nine takes these square root relationships to a different level as you will learn in the pages ahead.

“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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