## Crosssectional Regression Analysis

While DCF models are enjoying a rapidly increased popularity in the investment community, they have been adopted by only a small fraction of the practicing security analysts.18 The majority of security analysts still values common stocks by applying some sort of earnings multiple (price earnings ratio) to either present earnings, normalized earnings, or forecasted earnings. Approaches to the establishment of the P/E ratio cover a vast range. Some firms use the historical P/E ratios for companies or the historical P/E ratio for a company relative to the market P/E ratio. Another approach, and one popular in many of the standard texts of security analysis, is to list and discuss large numbers of factors that should affect P/E ratios but leave the weighting and often the explicit definition of these factors up to the security analyst.19 Still another approach is to take the broad determinants of common stock prices, earnings, growth, risk, time value of money, and dividend policy and to measure these and weight them together in some manner to form an estimate of the P/E ratio. This section reviews one way to do this. We discuss the use of cross-sectional regression analysis to define the weights the market places on a set of hypothesized determinants of common stock prices. Attempts to use this technique to measure the influence of potential determinants of common stock prices were very popular in the 1960s, and there is an indication that interest in them has recently revived.

The relationship that exists in the market at any point in time between price or price earnings ratios and a set of specified variables can be estimated using regression analysis. This is the same tool that was used to determine Betas in Chapter 5. Figure 18.2 presents the relationship between P/E ratios and forecasted growth for a sample of stocks as of the end o F1971. Each point in the diagram represents the P/E ratio and forecasted growth rate for a company as of the end of 1971. The straight line is fitted via regression analysis and its equation is given by20

Price/Earnings = 4 + 2.3 (growth rate in earnings)

The usual technique of relating price or price earnings ratios to more than one variable is directly analogous to this. Called multiple regression analysis, it finds that linear combination of a set of variables that best explains price earnings ratios.

"This comes from an assumption of a constant payout ratio. The solution is

"This comes from an assumption of a constant payout ratio. The solution is

'"For one survey in this area, see Bing [12]. Graham, Dodd, and Cottle [46], perhaps the best-known book on security analysis, takes this approach. "This example comes from Cohen, Zinbarg, and Zeikel [25], p. 244.

'"For one survey in this area, see Bing [12]. Graham, Dodd, and Cottle [46], perhaps the best-known book on security analysis, takes this approach. "This example comes from Cohen, Zinbarg, and Zeikel [25], p. 244.

Figure 18.2 P/E ratios versus growth rates.

One of the earliest attempts to use multiple regression to explain price earnings ratios, which received wide attention, was the Whitbeck-Kisor model [79]. We indicated earlier that the price of a share of stock was related to earnings, dividend policy, growth, and risk. We could have said, equally well, that the price earnings ratio of a stock was related to dividend policy, growth, and risk. It was exactly this relationship that Whitbeck and Kisor set out to measure. In particular, they obtained estimates of earnings growth rates, dividend payouts, and the variation (standard deviation) of growth rates from a group of security analysts. Then, using multiple regression analysis to define the average relationship between each of these variables and price earnings ratios, they found (as of June 8, 1962) that

Price earnings ratio = 8.2

+ 1.50 (earnings growth rate) + 0.067 (dividend payout rate)

— 0.200 (standard deviation in growth rate)

This equation represents the estimate at a point in time of the simultaneous impact of the three variables on the price earnings ratio. The numbers represent the weight that the market placed on each variable at that point in time. The signs represent the direction of the impact of each variable on the price earnings ratio. We might take some comfort from the fact that the signs are consistent with what theory and common sense would lead us to expect: the higher growth, the higher the dividends (growth held constant), and the lower risk, the higher the price earnings ratio. The equations tell us that on average a 1 % increase in earnings growth is associated with a 1.5-unit increase in the price earnings ratio, a 1%

increase in the dividend payout ratio is associated with af0.067-unit increase in the price earnings ratio, and a 1% increase in the standard deviation of growth is associated with a

0 2-unit decrease in the P/E ratio.

An equation such as this can be used to arrive at the theoretical P/E ratio for any stock. S'mply by substituting the forecasted earnings growth rate, dividend payout ratio, and risk lor the stock on the right-hand side of the equation, one arrives at a theoretical P/E ratio. We can illustrate this with the IBM example used previously.21 When IBM's price was i()5, IBM's growth was forecast at 12%, its dividend payout ratio was 50%, and its standard deviation in growth rate was about 5. Substituting these numbers in the expression for pi ice earnings ratios presented earlier, we get a theoretical P/E ratio of 28.55. Many researchers have taken what seems like a small step from here and advocated buying stocks with theoretical price earnings ratios above their actual price earnings ratios, and selling short stocks with theoretical prices below their market price earnings ratio.

Literally hundreds of models like the Whitbeck-Kisor model have appeared in print -.nice the 1960s.

Every conceivable variable and combination of variables has been tried.22 The common element of almost all of these models is that they are highly successful in explaining stock pi ices at a point in time, but they are much less successful in selecting the appropriate blocks to buy or sell short. It is not uncommon for these models to explain more than 80%

01 the difference in stock prices at a point in time. This gives us confidence that the models can be helpful in finding the variables and set of weights that determine price at a point in time. Why, then, haven't they been more successful in picking winners? The theory behind their use in finding under- and overvalued securities is that the market price will mnverge to the theoretical price before the theoretical price itself changes. There are at least three reasons why this might, in fact, not happen23:

I. Market tastes change. With changes in market tastes, the weight on each variable changes over time.

?.. The values of the inputs, such as dividends and growth in earnings, change over time. 1. There are firm effects not captured by the model. We discuss each of these in turn.

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