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RANGY and Square Root Volatility (SRV)

Founder & Chief Editor of Gold Eagle
April 28, 1998

Based upon historical superior market performance of South African gold stocks over North-American and Australian precious metals mining shares, it is reasonable to assume that again the South African gold mines will perform even better this time on account of their large reserves and their small market capitalization in the next gold bull market. Not only past performance makes a very convincing argument, but present day fundamentals support this theory - especially in regards to the market capitalization of gold reserves. North-American and Australian gold stocks appear overpriced in comparison to the market cap of South African gold reserves. In view of the reasons mentioned it appears that the South African stocks offer a significantly better value (not realized yet) to their North-American and Australian counterparts.

Apart from fundamentals, the technical side of gold stock evaluation also strongly favors the South African golds. Much has already been said about numerous technical indicators… all except one that is: SQUARE ROOT VOLATILITY. Let us apply the well-known SRV theory to one of my favorite South African gold stocks. The honors of authorship of the SQUARE ROOT VOLATILITY (SRV) theory belong to Norman G. Fosback. The SRV theory was first mentioned in Mr. Fosback's widely acclaimed book "STOCK MARKET LOGIC," first published in 1976. It is indeed an outstanding book of stock market indicators and theories, worthy of any serious market student's close attention.

The following description of the SRV theory is nearly verbatim from the text, except obviously where I apply it to Randgold & Exploration (RANGY) - which closed last Friday at $1.47. It is indeed noteworthy to remember that RANGY is still down 82% from its 12 month high in April 1997.

Square Root Volatility -

"Low priced stocks are more volatile than high priced stocks. A formal statement of that assertion is the Square Root Rule which hypothesizes that the magnitude of a stock's price move is directly related to the price of the stock: the lower the price of the stock the more volatile it is, and, the higher the price of the stock the less volatile it is.

Specifically, the Square Root Rule states that given a certain market advance, all stocks change in price by adding a constant amount to the square root of their beginning prices. For example, if the average priced stock advances from $25 to $36, the square root of the average price has moved from 5 (the square root of 25) to 6 (the square root of 36), or up 1 point. In accordance with the Square Root Rule, we would then expect all other stocks to add one point to the square root of their prices.

Hence, a $4 stock (whose square root is 2) should advance to 9. (the square root of 9 is 3), and a $100 stock (whose square root is 10) should advance to 121 (the square root of 121 is 11). The following table summarizes the results.

Square Root Volatility Table
Starting Price Ending price % Change

Note that although each stock adds 1 point to the square root of its beginning price, the percentage changes in actual prices are dramatically different. The lower the price of the stock, the greater is its percentage advance. And the higher the price of the stock, the less is its percentage advance.

In a declining market, when all stocks should lose the same number of point from the square root from their beginning prices, we would expect the lower priced stocks to decline more rapidly - and the higher priced issues to decline at a somewhat lesser rate. Unlike the Beta statistic, the SRV factor for a stock is always positive: All stocks are always expected to move in the same direction, albeit in different magnitudes, as the market goes. As a measure of expected performance for a single stock, this is, of course, somewhat unrealistic since all stocks do not always move in the same direction as the market. However, like the Beta statistic, as the portfolio becomes more broadly diversified, SRV becomes a better measure of expected percentage change. For very large portfolios it is extremely accurate. Indeed, the author's research reveals that SRV is usually superior to Beta as an estimator of future expected return, even though Betas are much better known, and more widely used.

Conclusion. Used independently or jointly, the Beta and SRV factors are valuable and highly functional stock selection tools. Most investors would improve their overall performance if they refined their market timing techniques, and simply resorted to holding highly volatile securities during bull markets."

Using Mr. Fosback's SRV factor, I would like to apply it to RANGY, whose price in mid-March was just a buck. For comparison purposes I will expand the sample table used above.

Square Root Volatility Table
Starting Price Ending price % Change
 $   1  (e.g. RANGY)
$   4  (e.g. KRY)    
$ 25  (e.g. ABX)     
$100 (e.g. MSFT)  
$  4
$  9
$ 36

The starting price for RANGY is $1 - and 1 is the square root of 1. According to the SRV concept the ending price should increase the square root by one, making the new square root equal to 2, and therefore the ending price is $4. Consequently, according to Fosback's hypothesis the expected value for RANGY is $4, a quadrupling in price.

To illustrate the point we compared the recent low RANGY price with the approximate prices Crystallex International, Barrick Gold and Microsoft. The expected percent change per the SRV theory ranges from only 21% (Microsoft) to 300% (Randgold).

The price gains indicated above, can be reasonably expected during a bull market. Please bear in mind that Microsoft is now at an all-time high, whereas Randgold is down more than 80% from its 52 week high.

We all are aware that trading theories do not work at all times, but good theories tend to work most of the times. Any prudent investor will also consider other factors before investing in a particular stock. However, in light of all other positive fundamentals and favorable technical factors relating to RANGY, the SRV factor definitely reinforces my belief that the stock will closely follow the SRV theory in the looming gold bull market.

To summarize, the Square Root Volatility theory is based on the premise that lower priced stocks show greater price movements than higher priced stocks. Consequently, in a gold bull market one would expect a low priced gold stock like Randgold to enjoy much greater appreciation than a Crystallex International ($4), or a Barrick Gold ($25), or even a Microsoft ($100).

STOCK MARKET LOGIC: A Sophisticated Approach to Profits On Wall Street by Norman G. Fosback

Founder of Gold-Eagle in January 1997.  Vronsky has over 42 years’ experience in the international investment world, having cut his financial teeth in Wall Street as a financial analyst with White Weld. Vronsky speaks three languages with indifference: English, Spanish and Brazilian Portuguese.  His education includes a degree in Petroleum Engineering from the University of Oklahoma, a Liberal Arts degree from Hartnell College and a MBA in International Business Administration from UCLA – qualifying as Phi Beta Kappa and Tau Beta Pi for high scholastic achievements.  Vronsky believes gold and silver will be recognized as legal tender in all 50 US states and many countries worldwide.  You may reach I. M Vronsky at: [email protected] and/or [email protected]

With gold stolen by Conquistador Francisco Pizarro from the Inca Empire in 1532, Spain financed its conquest of Europe.
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