A Control Chart for Postwar Stock Price Levels

Abstract

A CONTROL CHART is a statistical tool for the identification of significant shifts a series of measurements from a continuing process.' A control chart consists of a central line, or normal average level of measured behavior for the process; and two or more control limits, or action levels, above and below the central line. In application one plots a periodic sequence of actual measurements on the control chart over time. As long as these measurements fall near the central line the process is considered to be in control, or the central tendency of the process is considered to hold. Measurements near or beyond one of the control limits, however, signal a shift the process and provide a decision criterion for action to modify the existing strategy. Control charts were originally developed as a dynamic technique for dimensional and quality control of production processes. The statistical properties of control charts, however, may be applied to time series measurements many areas of business and economics. The control chart technique has the advantages of simplicity interpretation, quantification of risk, and a visual analysis of behavior over time. This paper describes a construction method for a control chart for the postwar general level of stock prices as given by Moody's Composite 200 Stock Average. Moody's Average was chosen for the valuable monthly statistics of dividend levels and yields.2 These statistics were used to develop the analysis of the control chart of Figure 1. The control chart technique used here, however, may be readily adapted to other measures of stock price levels such as Standard and Poor's. The necessary adjustments are outlined the concluding section. A workable control chart for stock prices has several interesting applications. The central line requires historical and predictive hypotheses about long run normal levels of market prices. Beyond this the control limits and record of actual behavior furnish a partial test for the plausibility of a set of normative price levels. Further development of control chart techniques should contribute to the theory of the composite intrinsic worth of stocks. The practical side of a control chart stems from the decision criteria furnished by the control limits. If prices shift toward the upper control limits the intermediate term, then overvaluation is signaled respect to the long term assumptions of the central line. In a similar manner prices near the lower limits suggest a temporary undervaluation. Properly prepared and applied the control chart should become a worthwhile addition to the market analyst's kit of tools. In the recent discussions about the value of knowledge and investment analysis, statisticians have generally tested the hypothesis of a random walk model for stock prices.3 In this model, individual price changes are considered to be independent of the preceding or historical series of price changes, and hence analysis of past price movements has no predictive power for the short term future. Acceptance of the random walk model does not destroy the usefulness of intrinsic worth studies, but the economic theory of efficient markets implies that the widespread pursuit of comparative advantage from superior knowledge is self-defeating.4 The latter point is certainly not news to investment analysts, but a control chart offers an additional tool to study the questions of random price variations and intrinsic worth. Essentially a control chart accepts the hypothesis of random price level movements near the central line, but also assumes a high probability of significant shift for price levels close to the control limits. As Eugene F. Fama has stated, one way to support the value of knowledge for investment analysis is to demonstrate superior profits 1. Footnotes appear at end of article.