In recent years the application of discriminant analysis to two-category (dichotomous) classification problems in empirical financial research has substantially increased. However, these studies have given relatively little attention to design and interpretation difficulties associated with discriminant analysis. Consequently, the conclusions and generalizations that can be drawn from such studies are frequently tenuous and questionable. This paper's purpose is to discuss the methodology of discriminant analysis. While the paper is oriented toward financial applications of discriminant analysis, our discussion is not peculiar to finance. Furthermore, many of the methodological issues we address are relevant to the general problem of developing and testing dichotomous classification models and arise whether model developing is by discriminant analysis or some other method.

The purpose of this paper is to examine empirically the dividend, investment, and financing decisions of French firms. A basic premise of the study is that increased perspective in business finance can be gained through better understanding of the financial behavior of companies outside one's domestic economy. While the literature of finance and economics includes many significant empirical studies based on dividend, investment, and financing data on American firms, the body of evidence on continental European firms is still relatively small, owing in large part to the difficulties encountered in gathering meaningful financial data on individual firms. In order to examine for the first time the relationship of dividend and investment decisions in France, using well-known models of financial bahavior, we were able to obtain annual data on a sample of French companies over a seven-year period. Our intent is to add to the understanding of the robustness of these models by demonstrating their empirical validity in Europe and to report several differences from previous empirical findings for American firms.

There is broad consensus that three types of risk confront the potential bond purchaser: the risk of default (possible interest and/or principal loss), the risk of interest rate changes (possible principal loss or gain if the bonds are sold before maturity), and price level risk (loss of purchasing power). The analysis in this paper is directed toward the first of these risks, the risk of default. By assuming that investors require interest rate adjustments on debt subject to default sufficient to give them an expected present value equal to the present value associated with the investment of their funds in default-free securities, we examine the process that determines the risk-adjusted equilibrium interest rate and the factors affecting that rate. We also examine the implications of the model for the cost of debt and a firm's debt capacity.

Strides have been made recently in the discovery and refinement of theoretical models which purport to describe the relationship between asset prices and their risk attributes. (See especially Lintner [13,14,15], Sharpe [19], Mosin [17,18] and Fama [7,8.9].) The models have gained widespread acceptance because of their intuitive appeal and because most reported empirical evidence [1,4,5,11,20,21] allegedly supports their predictive value. It is our purpose to analyze critically one aspect of the nature of this evidence, reveal its inherent weakness, and to design an alternative test to examine the risk-return function. After observing the performance of an extremely large number of issues over long periods of time, we find little support for the notion that risk premiums have, in fact, manifested themselves in realized rates of return.

Portfolio analysis has generally been restricted to problems in, at most, two dimensions, expected return and risk, the latter usually measured by standard deviation. In two papers Jean [2, 4] has attempted to extend the analysis to three and many dimensions by deriving risk premiums as functions of higher order moments. This paper corrects several errors in his work and derives a normative, individual pricing model for risky securities analogous to the capital market line within the framework of a perfect market.

In recent years the expected-utility approach to decision making under risk has gained increasing acceptance among portfolio theorists. On the other hand, the mean-variance (MV) approach of Markowitz [13], which has dominated portfolio theory in the past, continues to enjoy great popularity. In MV theory, the investor is assumed to rank his preferences for risky returns solely in terms of their means and variances, with higher means and lower variances, being preferred. Tobin [20] showed that MV theory is consistent with expected utility theory in the special case of joint-normally distributed asset returns. The MV approach enjoys a ready acceptance among practitioners, and requires only modest informational and computational inputs. Perhaps its most attractive feature is its ability to decompose the overall portfolio problem into a sequence of much simpler problems: first, the “efficient” set of portfolios (which minimize variance for any given mean return) is calculated, and then the investor chooses one of the efficient portfolios in a manner consistent with his personal preferences. This efficient set is the same for all investors having the same mean-variance-covariance estimates of risky-asset returns, and can, in principle, be determined once and for all using parametric quadratic programming [12, 22] Despite these real advantages, the MV theory embodies certain problems of principle in the case of nonnormally distributed asset returns, and this fact has led to increasing emphasis on the presumably more rational expected-utility theory.

Preference orderings of uncertain prospects have progressed from the two-moment EV model first developed by Markowitz [1952] to the more general efficiency analysis that is based on the entire probability function. This general efficiency approach, referred to as the Stochastic Dominance (SD) approach, does not depend on specific assumptions about the investor's utility function and has been shown to be theoretically superior to the “moment methods” [1].

The dramatic surge of the commodity option market over the past few years may well be illustrated by the growth (before its collapse) of one leading option writer, Goldstein, Samuelson, Inc., whose sales rose from $1 million in 1971 to over $45 million by the end of 1972. The commodity option market is closely related to the commodity futures market, except that options are available only on the so-called “international” commodities.

The first major study of industry effects in market returns was performed by King [2]. He used principal components analysis and clustering techniques on a sample of 63 companies chosen from six 2-digit industries based on Security and Exchange Commission codes. SEC codes are similar to the Standard Industrial Classification codes defined by the U.S. Bureau of the Budget [4]. SIC codes are 4-digit codes based on the principal end product of the firm. They are chosen so that, as the lowest order digit is removed, the companies are aggregated into broader but still similar groups.

The purpose of this note is to present a simple computational algorithm to approximate the E, S portfolio selection model. The essential feature of the model is the utilization of the familiar linear programming framework by representing risks as a series of linear constraints. Suppose we have m states and n securities, and we assume the investor is able to specify the contingent returns for all securities in each state. Following [7], we define risk as being the downside deviation from the investor's target rate of return.

More than twenty years ago the portfolio selection problem was stated as a parametric quadratic programming problem [3]. Since that time there has been an ongoing search for methods that would allow reductions in both the data and the computational effort required to implement the Markowitz formulation. Markowitz himself developed a special algorithm for the problem [4] Sharpe followed with his famous diagonal model [6], a linear programming approximation for the special case of mutual funds [7], and a linear programming approximation for the general problem [0]. And during this period there were substantial advances in quadratic programming computer codes. A very fast code is now widely available [1], but the size of the code itself (a listing of the annotated program runs to more than 3,000 lines) makes its everyday use for portfolio selection somewhat unattractive.

Although they did not affect the individual rates of return per inflationary period that were the main concern of our study previously published in the Journal, it has recently come to our attention that there were computational errors in the summary weighted average real returns. Thus, we are taking this opportunity to correct the original errors and also to update the study results for the period from December 31, 1968, through December 31, 1973. In the analysis and discussion which follows it is assumed that the reader is familiar with the previous study and the methodology employed. Therefore, Table 1 is simply a correction of Table 4 in the 1971 article. This is followed by a discussion of the revised results and changes in conclusions prompted by the adjusted results. Table 2 contains nominal and real rates of return for the period from December 31, 1968, to December 31, 1973, nominal and real rates of returns for the full period from December 31, 1965, to December 31, 1973, and finally, a new set of weighted average returns using the figures updated through 1973.

Listing of common stock on an exchange is believed by many to have a positive value for the firm. One implication of purported advantages has been improvement in the price of the stock when it is listed. Another advantage to an investor could be a reduction in the risk level of a security through trading location changes. The purpose of this research is to investigate the effect upon a security's risk level when its trading location is transferred to the New York Stock Exchange.

In a recent issue of this journal, Linke and Kim [1], hereafter denoted as L-K, have shown that for finite-time horizons in excess of one period and if, over the same period, the firm's ratio of debt to equity is held constant, the firm's overall required rate of return could be expressed as a weighted average cost of capital. In their proofs L-K distinguish between firms engaging in no financing over the relevant horizon (the nonfinancing case), and those in which such financing is permitted to take place. In the latter case, their procedure is to derive proofs for new debt and equity financing cases separately. In all cases their proofs are correct. However, we wish to draw attention to an implied restriction which must hold in order for their proofs in the financing cases to be valid. Our objective is to set forth a proof which allows both new debt and equity financing simultaneously, and most importantly, which is also free of the implied restriction.