In this article, we shall discuss several of the alternative definitions of risk that have been proposed from time to time. We shall show that one definition — risk is the probability of loss — leads to a formulation of the investment decision problem as a chance constrained problem. Three different strategies are then proposed by which an investor can reduce risk. It is our belief that professional investors utilize all three strategies and that risk, in many such cases, is not a substantial constraint on investor behavior.

This study is another attempt to analyze the behavior of common stock prices. In the last decade, and even before that, literature has spewed forth an abundant supply of studies in this area, from random walkers, to optimum portfolioers, to performance measurers. Terms such as risk and return, variance and covariance, and variability and volatility proliferate journal pages and our daily conversations.

The classic 1955 paper of Lorie and Savage has stimulated the development of mathematical programming approaches to the analysis of capital budgeting problems. A problem that they considered has been succinctly stated as:

given the net present value of a set of independent investment alternatives, and given the required outlays for the projects in each of two time periods, find the subset of projects which maximizes the total net present value of the accepted ones while simultaneously satisfying a constraint on the outlays in each of the two periods.

The concept of profit sharing—whereby a company provides employees with a contribution above and beyond their regular wages based upon business profits—is very old indeed. Implementation of this concept is witnessed by the many profit sharing plans of all kinds in existence today. However, even though the concept is old and the use widespread, there is a complete void in published literature on the nature of optimal profit sharing plans. It is the purpose of this paper to investigate this subject.

The purpose of this paper is to construct a model for the computation of an optimal cash balance for a bank, although it could be adapted to any organization. By a bank we mean to include both commercial banks and savings banks (mutual savings banks and savings and loan associations). One might also be able to adapt the model to an “international bank” such as the United States holdings of gold and foreign exchange.

This article has two goals. The first is to contrast two widely used definitions of risk aversion. The second is to establish the feasibility of plunging behavior, in the sense that a possibly large number of risk averse investors will not be diversifiers.

With the rapid growth in various types of corporate combinations, many opportunities arise in which increased internal efficiency in the allocation of capital budgeting resources may be obtained. Although the resource-transfer methodology proposed in this paper is discussed within the context of a merger/acquisition environment, the operational analysis conveivably could be applied to multiproduct, multifirm, or multinational situations. This study examines an application in which a linear programming model can be used operationally as an analytical planning device (1) to obtain efficient capital budgets for the merged companies, and (2) to quantify the monetary value of potential gains in efficiency produced by a merger. Conceptually, the model assists management in searching for excess capacity in each company, efficiently combines scarce resources, selects an optimal project list for the merged company, and indicates what the composition of the new capital budget should be. In addition, a variable step function provides for multiplicative adjustments in common resource constraints. These adjustments might be positive (negative) if the combination results in a more than proportionate increase (decrease) in the availability of a scarce resource.

Consider an economy consisting of individuals and firms with the following characteristics: all individuals are rational in the von Neumann- Morgenstern sense and non-neutral toward risk; the dividend streams of some firms are certain, while the dividend streams of the other firms are uncertain; and the economy is equipped with perfect financial markets. In this economy, as we show in the present paper, the value of each firm with a certain dividend stream depends only on the dividend stream itself and the set of future interest rates—i.e., the market value of such firms is independent of the attitudes toward risk and the level of wealth of any individual. However, the value of each firm with an uncertain dividend is, with one exception, not independent of anything: it depends not only on the firm's own dividend stream, the set of future interest rates, and (all) individuals' risk attitudes, but also on the wealth levels of these individuals and on the dividend streams of all other firms with uncertain dividends even when these streams are stochastically independent. The exception occurs when the individuals have exponential utility functions of money. In this case, the market value of each firm with uncertain dividends is independent of other dividend streams and of individual wealth levels if these variables are statistically independent of the firm's dividends. Exponential utility functions of money, of course, are not considered empirically plausible.

A question that bedevils the academic economist, the trustbuster, and the community at large is whether conglomerate merger activity is a force for good or evil. In common with horizontal and vertical merger activity, the critical consideration is whether conglomerate mergers produce better uses of resources, increases in monopoly power, or some mixture of these two results. Economists have been examining these mergers in an effort to determine whether efficiency in the use of resources is, in fact, promoted. However, when investigating this question, the subject of inquiry is usually confined to the optimizing decision of the firm. It has been argued that conglomerate activity involves the best use of resources from the standpoint of the firm.

In retrospect, writing about “risk and valuation” is somewhat akin to killing Hydra, the mythical, many-headed creature which would grow two heads whenever one was cut off. It is only fair to admit at the outset that I cannot lay claim to have slain the beast. As a matter of fact, by the time the reader finishes the article, he may have concluded that the beast has more heads than ever!

J. M. Keynes' theory of portfolio management (modified and refined by Tobin)occupied an important role in his analysis of the demand for money. According to this theory, financial investors were thought to vary the composition of their portfolios between money and securities on the basis of expected yields on securities. When yields were expected to rise, investors would shift out of securities and into money. Conversely, when yields were expected to fall, investors would shift out of money and into securities. Hence, the asset, or portfolio, demand for money was argued to be negatively related to the expected yields on securities.

Markowitz's [2] portfolio selection model was originally concerned with financial investments, but the model's implications for capital budgeting are now well recognized. Markowitz's basic idea is that the optimal portfolio for an investor is not simply any collection of good securities, but a balanced whole, providing the investor with the best combination of “return” and “risk.” Return and risk are to be measured by the expected value and variance of the probability distribution of portfolio return. Although financial writers have generally accepted Markowitz's measure of return, they have not been completely satisfied with his suggested measure of risk [1]. In fact, Markowitz himself had reservations about choosing variance as a measure of risk.1 Besides variance, he considered five other alternative measures of risk:

(1) The expected value of loss;

(2) The probability of loss;

(3) The expected absolute deviation;

(4) The maximum expected loss; and

(5) The semivariance.