Market timing part 4: Modern Graham Central Value Model
Over the last few weeks, we've been discussing some technical methods by which to time stock market cycles in the S&P 5…… ( SPY ) and the S&P/TSX. The first indicator discussed was the Triple Crossover Moving Average Model. The second indicator discussed was the well-known Fed Model. The third model discussed was Graham's Classic Central Value Model. This week we are going to discuss a second valuation model developed by Benjamin Graham that was showcased in his revised text on Security Analysis. Similar to his classic model, it is a method of determining buying and selling points in the general market through the determination of a central value. The process by which he determines a central value, however, is quite different.
This modern Benjamin Graham central valuation model involves determining an equilibrium or fair-value estimate for the market, as well as an upper and lower valuation range based purely on historical stock price data.
Graham estimated the central value, or fair value, of the market by inserting a linear price line through a series of historical data. He then established various quadrants above and below the linear price line that signaled moderate to high over/under-valuation.
While Graham never detailed what statistical process he followed to determine the positioning of the linear price line, we use linear regression analysis. Simple linear regression uses an independent variable to explain and/or predict the outcome of a dependent variable, while multiple regression uses two or more independent variables to predict the outcome. In this case we regress the dependent variable (S&P 5…… closing price for the U.S. market and the S&P/TSX for the Canadian market) on one explanatory variable (a time dummy variable), which is called a simple linear trend model. The general form of the regression is:
Central Value = (c + k) + Bx + e
Ordinary least squares regression finds a mathematical relationship between closing prices on the index and then fits a straight line to the data set that best approximates all the individual data points.
After a central line is established, we want to identify a way of determining when prices deviate in an abnormal way from the central line (the conditional mean). A standard deviation to one side of the line would capture '4% of the data, or 68% of the data points if we look at one positive and one negative standard deviation. Two standard deviations include approximately 95% of the data points and, on very rare occurrences, observations might fall three or more standard deviations from the mean. Because stock prices don't normally deviate by two or more standard deviations from the mean, it is often assumed that they will revert back towards the central value line once normality is re-established.
Using the regression line and valuation bands, investors can judge when an index is overbought or oversold. Investors might set narrow channels at one standard deviation or wide channels at two standard deviations.
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