There now exists a formidable documentation of the hypothesis that time series of common stock prices follow random walks. Taking these empirical demonstrations as convincing, additional work has largely fallen into two classes: (a) direct theorizing and testing of the exact nature of the random price-generating process; and (b) theorizing and testing of the implications of random walks in common stock price for the values of related securities such as warrants and convertibles.

During the first half of the 1960s the U.S. Treasury conducted eleven advanced refundings. Publicly held Treasury securities aggregating $188,631 million were made eligible for exchange and $62,642 million were exchanged — an aggregate exchange ratio of 33 percent.

In many nonlinear programming applications the objective function has an inherent uncertainty that depends upon a set of random variables that have a known distribution. If one wishes to optimize the expectation of the objective, as suggested by the expected utility theorem, then as is shown here one can often solve such problems by modifying standard nonlinear programming algorithms. To illustrate what is involved, the details and justification for the application of the interior parametric sequential unconstrained maximization technique and the generalized programming method for the solution of such problems are given. Some related problems with stochastic constraints for which the solution method applies are mentioned and an example of a portfolio selection problem is given.

Consider the following linear programming problem, which is denoted by (S): The various vectors and matrices have the following dimensions: a = an m-vector Aj = (j = 1 … n), an m by njmatrix, bj = (j = 1 … n), an mj-vector, Bj = (j = 1 … n), an mj by nj matrix, Cj = (j = 1 … n), an nj-vector, and xj = (j = 1 … n), a variable nj-vector.

Problems with this decomposable structure have been extensively studied in economics and management science literature, because they arise in several economic contexts and situations. Therefore, (S) lends itself to more than one economic interpretation, but the following one is hereby adopted for the purposes of this paper: (S) models a two-level manufacturing organization, consisting of headquarters and n producing divisions. Let this organization be called simply “the company”. The company can produce and sell a number of different products, thereby obtaining fixed unit contributions. These contributions are given by the vectors c1, c2, … cn. The products are produced by the different divisions. The variable vector xj (j = 1 … n) gives the production program for the jth division.

The purpose of this paper is to derive and test a model of the dividend-saving decision for a shareholder wealth-maximizing firm. Starting with the basic proposition that shareholders should prefer capital gains income to dividend income in a world of differential taxes and transactions costs, dividends are viewed as basically a residual in the corporate decision process. The term residual does not imply that there is no dividend decision or that dividend policy does not affect the worth of the firm since, as argued, the selection of an optimal level of dividends in an uncertain environment still involves the forecasting of future investment needs and the selection of a dividend-saving program to finance these needs at minimum cost. The relevant costs in this context relate to the possible accumulation of excess liquidity resulting from insufficient dividends on the one hand and the possible need for external equity financing resulting from excessive dividends on the other.

If a firm is considering replacing part of its productive facility because of obsolescence rather than wear-and-tear (e.g., purchasing a new model machine), it weighs the expected gains against the expected costs. A problem may arise when the rate of technological innovation for the type of machinery is extremely rapid. Such replacement may yield a gain if made today, but because innovations are so rapid, a year's delay in replacement may yield a greater net gain, and it would seem wiser to wait the year. But each year the same reasoning seems to hold; the more rapidly innovations seem likely to occur, the more likely a firm is to delay. If technology is advancing quickly enough, a firm may never consider any time a good time for replacement.

Most insurance companies are involved in reinsurance activities. For the majority, reinsurance means laying-off portions of the risk that they have assumed in the primary insurance market. A few other companies assume these laid-off risks. Our concern is with the former companies; that is, those seeking to cede a portion of their risk.

Elliott's basic proposition is praiseworthy. Nevertheless, I have a number of serious reservations about the implications of his model and the reliability of its predictions. Some of my reservations relate to the theoretical foundation of the model itself, while others are concerned with his methodology and estimation techniques.

The theory of choice under conditions of certainty has been extended by Von Neumann and Morgenstern [8], Friedman and Savage [5], Marschak [13], and others to conditions involving risk by assuming that individuals maximize their expected utility. The application of this theory to portfolio selection, to efficiency criteria, and to the explanation of the well-known phenomenon of diversification of assets has been carried further by Markowitz [11 and 12], Tobin [17], Samuelson [15], Sharpe [16], and Lintner [10], and more recently by Hadar and Russell [5] and Hanoch and Levy [8].

The literature of Index numbers contains much discussion of the relative merits of geometric and arithmetic averages of prices and quantities. The controversy on this subject dates from the middle of the nineteenth century and is fully described by Crowe [2], In recent times both types of averages have been applied to security price relatives to measure the performance of groups of securities over time. The purpose of this paper is to demonstrate the properties of these security indexes and to show the relationships between them and an index based upon a more general type of average called the power mean. The concluding section of this paper contains the proof of an interesting and important limit property which provides the conceptual link between geometric and arithmetic security indexes.

The dividend decision is a residual corporate decision and yet it is not a residual corporate decision. This theme runs through Professor Higgins' paper. It is based on the one hand on Higgins' belief that other decisions are more important and should take precedence over the dividend decision, and on the other, that the dividend decision is a function of these more important decisions. If dividends were truly residual, they would be explained by the corporate budget identity. In the empirical analysis, however, dividends are a function of other balance sheet decisions. In this sense the decision is neither active nor residual but passive. The reader wonders why the author insists on this role for dividends when interdependency in decision making is the more appealing (and inevitable) framework.

Professor Basil Kalymon, in his recent article [1], correctly asserts that the appropriate variance for the portfolio selection model, reflecting portfolio risk, should measure the risks created “not only by the inherent fluctuations of returns, but also by the decision-maker's lack of perfect information about the parameters of his model” [1, p. 560]. He identifies a significant failing of portfolio selection models, that “the question of estimating the required parameters in the models has been largely sidestepped … by assuming that the parameter values are known” [1, p. 559]. By showing that error in estimating security returns is an important component of risk in portfolio selection models, Professor Kalymon has taken portfolio theory an important step forward.

A proposition is proved which shows that each member of an important class of investment and financing projects has a unique nonnegative internal rate of return. Nonuniqueness of the internal rate of return is thus shown to occur less frequently than formerly believed. The correspondence between the proposition and previous results on the uniqueness of the internal rate of return is briefly indicated.

In [2] Hakansson and Liu presented a multiperiod portfolio model in which there is an optimal myopic policy. In particular, at any decision point j and state m the optimal amount to invest in opportunity i, namely , may be found by maximizing

(42a)

subject to

(42b)

(42c) ,

where the expectation is taken with respect to the β's, and the p's and r are positive constants (r > 1). Assumptions are made in [2] which guarantee that (42) has a unique optimal solution and that the set of vijm which satisfies (42b and 42c) is a nonempty, compact, convex set for all j and m.

In this note a distributed lag model is employed to analyze the flow of capital in outstanding issues of Canadian stocks between Canada and the United States. It is proposed that the movement of such capital reflects, to a large extent, changes in the relative earnings yield on stocks in the two markets.

In a recent article in this Journal, Haugen and Pappas (H-P, hereafter) [1] attempted to prove, within the framework of the capital asset pricing model, the already proven proposition that the cost of capital is invariant with respect to leverage even with risky debt. The H-P proof contains a serious error which we would like to point out in this note.

My purpose in this paper is to outline a new approach to the theory of the balance of payments and of balance-of-payments adjustment (including devaluation and revaluation) that has been emerging in recent years from several sources. Concretely, this new approach is found in the change in policy orientation adopted by the British government under pressure from the International Monetary Fund after the devaluation of 1967 failed to produce the expected improvement in the British balance of payments. The theoretical basis for the new orientation can be traced back to the work of the Dutch economist J. J. Koopmans. The new approach is also evident in the theoretical work of my colleagues at the University of Chicago, and R. A. Mundell and his students, although it is only fair to note that economists elsewhere have been working along similar lines. The essence of this new approach is to put at the forefront of analysis the monetary rather than the relative price aspects of international adjustment.

In his famous 1964 article, Paul A. Samuelson [1] presents what he calls “the only sensible definition of depreciation,” namely, the period change in the present value of future cash flows expected to be generated by an asset.