A major difficulty with testing the Modigliani-Miller (M-M) theory of the effect of leverage on the firm's value arises from the existence of interfirm differences in operating risk. Based upon the Sharpe-Lintner capital asset pricing model, the present study develops a test of the M-M theory that takes cognizance of heterogeneity with respect to operating risk. The empirical results support the M-M theory: holding total systematic risk constant, there was no relationship between leverage and required rates of return on equities. That is, investors appear to demand complete compensation for the increase in systematic risk attributable to financial leverage.

The objective of this paper is to carry out tests of the general hypothesis, most recently urged by Scherer [14, pp. 100–102] and Weston and Brigham [17, p. 689], that the cost-of-equity capital of small industrial corporations is greater than that of large industrial corporations. The paper denotes this cost as ke and defines it as the expected rate of return on the stock of a company when the current price of the stock is in equilibrium. A common designation of ke of course is the equity capitalization rate. It will be noted that this definition of the cost-of-equity capital abstracts from the flotation costs that are usually incurred when companies sell new stock. Archer and Faerber [2] have already shown that these costs are inversely related to the size of companies.

Professors Alberts and Archer provide a valuable addition to our understanding of capital markets and how resources are allocated to firms of different asset sizes. Their hypothesis is that the cost of equity capital to smaller firms is higher than it is to larger industrial firms. They test their hypothesis by analyzing the variability of returns of 658 industrial firms and attempt to determine whether variability of return is inversely related to asset size. The authors assume that for all firms Ke must equal the sum of the risk-free rate of interest and a risk premium, when risk is defined by four different measures. Two measures of risk use ex post rates of return on book value and two measures of risk employ ex post rates of return on market value. In the first two cases, risk is defined as variability of the firm alone and, in the second two cases, risk is defined as the firm's variability incorporated with the variability of a market portfolio of securities.

The bear market of the late sixties amidst inflation has led to growing concern over the validity of the proposition that stocks provide a good hedge against inflation. Conflicting arguments have been raised on both sides of the issue but a synthesis has as yet failed to emerge. The gains resulting from a careful assessment of the various propositions are obvious. If stock prices are adversely affected by inflation, the financial analyst must search for other hedges against the erosion of the purchasing power of money, while the economist must note that inflation has a depressing effect on economic growth through the rise of the cost of capital.

In this paper the traditional capital asset pricing model is reformulated as a system of simultaneous equations in which returns on similar securities are treated as endogenous variables and in which pertinent financial data for particular firms and a market factor are treated as exogenous variables. Such a system is estimated, and serious questions are raised concerning the tenability of the simple linear model so often used to explain capital asset prices under uncertainty.

Modern micro-capital theory offers three major alternative choice theoretic approaches from which a set of market equilibrium prices can be derived. These approaches are:

1. Time-state preference theory of Arrow [1] and Debreu [6],

2. The capital asset pricing model (hereafter CAPM) of Sharpe [34], Lintner [23], and Fama [7],

3. The capital growth model of Kelly [16], Breiman [5], and Latané [17]

Professors Simkowitz and Logue (S-L) remind us that capital asset pricing is a simultaneous process. Their approach differs from traditional capital market models [3 and 6 ], where an investment's risk and return characteristics depend solely on a structural relationship between asset and market portfolio returns. Simkowitz and Logue argue that, within groups of homogeneous securities, investment returns are determined simultaneously and that market portfolio return as well as certain firm-related factors are exogeneous determinants of investment returns. This comment will, first, examine their basis for a simultaneous model and, then, look at presented empirical results.

Since this comment should be primarily addressed to Professors Bicksler's and Thorp's own research and results, I will not consider those pages that contain the authors' interpretation of prior studies.

Professors Bicksler and Thorp study the short-run properties of the optimal growth model via Monte Carlo simulation. This is an interesting idea because of the mathematical difficulty of the problem.

In so far as the concept of systematic risk is predicated on the Sharpe-Lintner theory of capital market equilibrium [5, 4], the time-horizon of systematic risk must conform with the time-horizon of market equilibrium. Since it has been suggested that market equilibrium is instantaneous [3, p. 188], it would follow that systematic risk should also be instantaneous. This paper is, therefore, concerned with the evaluation and measurement of instantaneous risk. Although Jensen [3] has made a similar attempt in a much larger study, we have reason to believe it is not satisfactory. We shall then begin in Section I by discussing Jensen's approach to the horizon problem. In Section II, an alternative procedure of evaluating systematic risk is suggested. Section III concludes the paper by comparing estimates of instantaneous risks based upon weekly returns of 30 Dow-Jones stocks. The motivation behind the paper is obvious. A correct formulation of instantaneous systematic risk is not only a logical extension of the capital market equilibrium theory but is also a yardstick for measuring portfolio performance in terms of risk and return.

Ex ante predictions of the riskiness of returns on common stocks — or, in more general terms, predictions of the probability distribution of returns — can be based on fundamental (accounting) data for the firm and also on the previous history of stock prices. In this article, we attempt to combine both sources of information to provide efficient predictions of the probability distribution of returns. We predict two parameters of the distribution of returns for each security in each year: the response to the overall market return (β), and the variance of the part of risk, specific to the security, that is uncorrelated with the market return. A cross section of time series data on returns and accounting variables, taken primarily from the Compustat tape, is used. Several recent developments in statistical methodology are applied.

This study deals with behavioral assumptions that necessarily underlie the theory of asset valuation. Recognized logical and empirical implausibilities associated with the particular set of assumptions that provides the underpinnings of much currently espoused asset theory are reviewed. A valuation model based on a more realistic set of behavioral assumptions is then proposed and tested empirically.

In their present paper. Professors Cheng and Deets (hereafter C-D) attempt to derive a measure of instantaneous systematic risk for securities and portfolios which is consistent with the Sharpe-Lintner-Mossin capital asset pricing model when the true market horizon is infinitesimally short. In so doing, they assert that Jensen's resolution of the horizon problem for such a market horizon is incorrect. In the comments which follow, I shall attempt first to indicate explicitly the causes for the differences in the Jensen and C–D results, and second, to evaluate their relative merits.

Major points covered by Paul H. Cootner in his discussion of “The Prediction of Systematic and Specific Risk in Common Stocks” by Barr Rosenberg and Walter McKibben have been incorporated by the authors in the revised version of their paper.

Professor Huntsman's paper is a welcome addition to the growing literature on portfolio theory. Traditional mean-variance analysis, in spite of its obvious simplicity and its ability to explain portfolio diversification, has come under increasing attack, both for the theoretical weaknesses underlying the technique and for its failure to recognize that investors manifestly prefer returns that are positively skewed to those that are not.