AMBIGUITIES IN THE CROSS-SECTION ANALYSIS OF PER SHARE FINANCIAL DATA

Abstract

IN ANALYZING the financial characteristics of a particular corporation, it is standard procedure to adjust the data to reflect the current number of shares outstanding. This is necessary to put the various financial measurements on a basis in which the historical time series observations are comparable. If such corrections were not made, many of the data series (e.g., stock prices) would contain disconcerting jumps, proportional in height to the magnitude of any stock splits. Such jumps would cause obvious technical difficulties; for example, they can easily distort autocorrelations by either masking real correlations ot signalling false ones. To illustrate explicitly, if the corporation under study underwent a two for one (say) stock split, then to make the historical financial data comparable through time, the customary procedure is to adjust the previously reported per share measurements (for example earnings and price per share) to the current basis. When these corporate series are made internally consistent, standard statistical techniques can be used in the financial analysis. This includes multivariate analysis of the various time series available on a single corporation. For statistical purposes, a single corporation can be analyzed on an any year basis, provided the observations are comparable. Arithmetically, it is simply a matter of a common divisor. Most often, analysts work on a current basis, however, because that is the basis which is most meaningful at that time. This is the procedure followed by the popular Standard and Poor's Compustat tapes. However, it is shown in this paper that per share observations are not appropriate for intercompany analysis. Thus, while price per share and earnings per share may be studied in the analysis of a single corporation, they cannot be legitimately used in cross-sectional studies. The results can be highly misleading, for the arbitrary number of shares outstanding can have a dramatic impact. For example, one could study the data available for the oil industry in 1967 on the basis of the number of shares outstanding in either 1967 or 1972. Since both are studies of 1967, one might intuitively expect the same results in either case. Unfortunately this is not so. Not only do the obvious statistical characteristics such as univariate means and variances of the per share variables change, but so also do regression and correlation coefficients between these variables. The mean and variance changes may not