STATISTICS
by Gordon W. Neal
Here's a statistical view of the stock market using the Standard & Poor's 500 as the basis for analysis, and a collection of fundamental influences.
Assessing whether the overall market is priced right is a goal of most investors. To do so, we can look at ways that the market has valued itself in the past, and there is plenty of data available. The Standard & Poor's 500 stock index is a good base, since it is a gauge of general market performance going back several decades. There are, besides earnings and dividends, other recognized market influences. Some are:
- Interest rates: These affect stock prices in at least two ways: First, by altering the return from financial instruments that compete with common stocks, and second, by changing the cost of funds needed to conduct business. Rising rates depress stock prices.
- Cost inflation: This can increase the dollar value of earnings over the long term, but also raises borrowing and other costs. Usually negative, particularly in the short term.
- Book value of stock: Book value may have some influence on prices.
Each factor is at least partly independent of the others, so stock prices are likely to be influenced by more than one variable. Several mechanisms are available for processing market data. One of these, linear regression analysis, is particularly suitable for weighing factors that can plausibly influence stock prices.
REGRESSION ANALYSIS
Linear regression analysis is a mathematical procedure for determining whether and to what extent variables relate to one another ? that is, how a change in one is reflected as a change in another. It assesses mathematical relationships among variable factors that are not open to exact solutions. It can be used to estimate the value of some element (the dependent variable) that depend upon the levels of one or more other elements (the independent variables). The relationship is expressed as an equation:
y = a + b1x1 + b2x2 + . . . bnxn
y = Dependent variable
a = Constant
b1, 2,...n = Regression coefficients; these measure the effect of an independent variable when the other independent variables are held constant
x1, 2,...n = Independent variables
Figure 1: 1985-96 S&P 500 PERCENT DEVIATIONS. Here's the percent deviation for the actual S&P 500 versus the estimate based on the 1948-96 database regression analysis.
Gordon W. Neal, a retired mechanical engineer, is a graduate of the University of Nebraska who has spent a major part of his career doing economic analyses of engineering projects. He can be reached at 714 963-6387 or via E-mail at 102010.306@compuserve.com.
