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 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.

Agricultural and Food Policy, Research Methods/Statistical Methods

Christian T. L. Janssen, Comment: Deposit Insurance in the United States--Evaluation and Reform, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1613-1618

The standard F test for linear restrictions in regression is relevant as a criterion but fails to capture the notion of tradeoff between bias and variance. Average squared distance criteria yield operational tests that are more appropriate, depending upon objectives. In the present paper two alternative criteria are developed. The first allows testing of the hypothesis that the average squared distance of a restricted estimator from the parameter point in k space is less than the average squared distance of the unrestricted, ordinary least squares estimator from the same parameter point. The second sets up a test of betterness of the restricted estimator over the unrestricted estimator of E(Y/X), where betterness is again defined in average squared distance.

THIS paper examines the effect of market on the rate of return of selected firms operating in different market environments. It will be shown that the effect of on profiltability depends on the degree of concentration and rate of growth in the industries in which the firm competes, and on the absolute size of the firm. One of the most important propositions of micro-economic theory is that under competitive conditions, rates of return tend toward equality. A casual look at the data will reveal that rates of return are not equal and that differences in rates of return often persist over time. Many studies have utilized industry concentration as a measure of market power and have analyzed the effect of concentration on industry profitability (a sizeable list may be found in Weiss (1971)). Three recent studies have looked at the effect of concentration on profitability using the firm as the unit of analysis (Federal Trade Commission (FTC), Hall and Weiss (1967), and Shepherd (1972)). Although data is not generally available for most firms, the FTC study does examine the effect of relative market share (market divided by the big four firm concentration ratio) on profitability in food manufacturing firms, while the Shepherd paper examines the effect of market for a sample of large, nondiversified firms. The more recent of the above studies emphasize additive multiple regression models. While these models attempt to control for the effects of some dimensions of market structure when focusing on the effect of a particular structure variable, they do not capture the interaction effects of structure variables on profitability. Two independent variables are said to interact if the effect of one independent variable on the dependent variable depends on the level of the other independent variable. Interaction effects may be analyzed in the following three ways (1) specifying an interaction model, (2) including interaction variables in an additive model, or (3) by estimating the parameters of an additive model for subgroups of the total sample. A version of the third method is employed in this study and will be discussed in section I. To illustrate this subgrouping method, suppose we divide our sample into two subsamples (A) firms in highly concentrated industries and (B) firms in lowly concentrated industries. As will be explained below, we expect that the slope coefficient from a regression of profitability on in the high concentration subgroup will be much higher and more significant than the slope coefficient from the low concentration subsample. The primary goal of this paper is to develop and test a theory of the effect of firm on profitability under various competitive situations. We have tried to integrate, formulate, and extend some elements of oligopoly theory and to test the resulting hypotheses. The hypothesis and finding that affects rate of return is greatly strengthened by the more complex interaction hypotheses and findings.1 In carrying out this major goal we also examine the effects of both firm and industry growth on profits, develop new evidence on leverage as a measure of risk, comment on the controversy over the correct measure of profitability, and introduce the concept of market as a so;urce of product differentiation. The paper contains four major sections. The first section develops the theoretical relationship between and profitability. This discussion focuses on the interaction effects on profitability of and the market environReceived for publication September 30, 1971. Revision accepted for publication June 21, 1972. * I am indebted to Ronald G. Ehrenberg, Kenneth Gordon, Marshall C. Howard, James K. Kindahl, Thomas Muench, and George Treyz and two referees for comments and suggestions on an earlier draft of this paper and to Patricia M. Anderson for programming services and comments. ' The interaction findings, especially the growth interaction, support the case for interpreting the data in this cross-section study as representing the effect of on profitability. An examination of the dynamic process by which firms alter their market positions would require time-series data. (See Gale, 1972.)

The aim of this article is to present the findings of an investigation of 69 firms that changed their depreciation accounting method from a form of accelerated depreciation to a form of straight-line depreciation for financial statement purposes. At the completion of the extensive datagathering required for this study it was believed that the 69 firms represented all the firms that made change in the intervening period and were indexed by the major reporting services cited above. Although a few potential switch-back firms have come to light since, it would not seem that their inclusion would significantly influence the study findings. The investigation of 65 switch-back firms during the period in which they decided to change their depreciation method offers some advantages for seeking out the existence of a market influence. The magnitude of the effect of the change on reported net income is significant. For the 60 profitable firms in the sample, the median increase in net income after taxes resulting from the change is 8.64 percent and the range runs from 1.00 percent to 26.8 percent.

The article presents a study designed to answer whether the attest function has already extended into new areas and whether there is evidence that the attest function will he further extended within the foreseeable future. Specifically, extensions to these areas were considered the internal control system of an entity, the efficacy with which management performs its function, financial data beyond that contained in the financial statements including financial projections, and conformance of operations to pre-determined standards, for example, actual performance to budgeted performance. Articles relevant to extensions of the attest function have tended to focus on the "pros" and "cons" of a specified extension. They have not generally been concerned with the examination of available evidence to determine whether a given extension is actually taking place or can be forecasted. The results of such an examination provide the basis for this paper. There is, with one exception, little evidence to support the contention that the attest function has extended into new areas or will be extended in the near future.