The Relationship between Price Change and Price Level for Common Stocks

Abstract

IA N ILLUSTRATION of Common Stock Price Changes. The kind of price _ changes which will be discussed in this paper are presented in Figure 1. In this figure we have graphs of the annual high and low prices of two common stocks, Inland Steel, a high priced issue, and Interlake Iron, a relatively low priced stock. At the bottom of Figure 1 the actual prices are plotted and from this one can see that Interlake Iron fluctuates less in absolute amount than Inland Steel. In the middle of Figure 1 the price level is taken into account by plotting the logarithms of the annual high and low prices. Thus, the spread between the two lines measures percentage changes and the graph reveals that such changes in price tend to be larger for the low priced stock. At the top of Figure 1 the square roots of the annual high and low prices are plotted and the resulting picture suggests that the fluctuations in the square root of prices are independent of price level. According to the above discussion of Figure 1, price level seems to be a factor in determining price change in common stocks. The question that arises is whether or not there is a consistent relationship between price change and price level. Purpose of this Study. The general purpose of this study is to investigate the likelihood of a relationship between price change and price level of common stocks. The problem, as it is treated in this investigation, consists essentially of three parts: (1) Measuring relationships by means of statistical analysis; (2) Investigating the significance of such relationships; (3) Setting forth some implications of such relationships. Summary of Related Studies. The problem of studying the relationship of price change and price level of common stock prices is related to and was suggested by articles which discuss the tendency of per cent changes in low priced stocks to be higher than the per cent changes in high priced stocks. Along this line some writers have pointed out that changes in the square roots of prices tend to be constant. D. W. Ells-