Someone has said that maternity is a matter of fact, while paternity is, at best, a matter of opinion. Concerning the field to which this issue of the Journal is devoted, however, there is little difference of opinion — Harry Markowitz is almost universally considered to be the father of portfolio analysis. The essence of the theory appeared in his 1952 article, although the full exposition was not available until several years later.

The concept that corporate investment-growth decisions are constrained by a profit opportunities schedule is central to much of the literature on finance and the theory of the firm. These writings suggest that, for a single firm: (1) the profit opportunities schedule is a decreasing function of investment growth (the slope reflecting, inter alia, competitive conditions); (2) the schedule shifts to the right with changes in national income (except for a firm producing income-inferior goods), and (3) the schedule's position (intercept) at a moment in time reflects a host of factors that are summarized by the term “management.”

This is an exploratory paper. In particular, it consists of explorations conducted around some of the possibilities that might be offered for capital budgeting via recently developed methods, e.g., chance-constrained programming, linear programming under uncertainty, etc.

“Don't put all your eggs in one basket,” is a familiar adage. Economists, such as Marschak, Markowitz, and Tobin, who work only with mean income and its variance, can give specific content to this rule—namely, putting a fixed total of wealth equally into independently, identically distributed investments will leave the mean gain unchanged and will minimize the variance.

This article will concern itself with the various techniques for selecting portfolios of securities. It should be made clear at the outset that a good portfolio is not just an amalgamation of a number of “good” stocks and bonds. Rather, it is an integrated whole, each security complementing the others. Thus, the investment manager must consider both the characteristics of the individual securities and the relationships between those securities. Until recently there was no comprehensive theoretical framework for the analysis of the latter aspect of the portfolio problem. Intuitive judgment and experience were the guidelines used by investment managers.

This paper examines the determinants of underwriters' spreads on tax exempt bond issues. In particular, it investigates the effect on spreads of differences in issue quality, term to maturity, and size. In addition, changing money market conditions and variations in the degree of competition among underwriters of tax exempts are analyzed for their influence on spread behavior. The relationships are studied for virtually all state bond issues sold between July 1, 1959 and December 31, 1965. The principal method of investigation is multiple regression analysis.

The substantial growth of the mutual fund industry during the last few years has attracted the attention of students of finance, economics, and public policy alike. Net assets managed by such funds have grown from approximately $450 million in 1940 to more than $38 billion by June of 1966. During 1965 the mutual fund industry funneled some $5. billion of new (primarily equity) funds into the capital markets; more than twice the $2. billion in new equity raised by all non-financial United States corporations during the year. Growth of the industry has not been uniform, however, but has been concentrated among a relatively small number of highly successful funds.

Questions have been raised in recent years concerning the interpretation of previous studies purporting to show that distributed earnings have had a consistently greater impact on equity prices than have retained earnings. Miller and Modigliani have convincingly argued that if capital markets are perfect and rational behavior of market participants is assumed, the price-earnings ratio of the shares of a firm with a given investment policy should be invariant to alternative earnings-payout ratios. They also point out, however, that with the present tax subsidy on capital gains and the existence of substantial brokerage fees and flotation costs, dividend policy might be expected to have an effect on share prices, even though the amount and direction of this effect is an empirical matter and not determinable a priori.

The Markowitz analysis of efficient portfolio selection, which can be interpreted as solving the quadratic-programming problem of minimizing the variance of a normal variate subject to each prescribed mean value, easily can be generalized (in the special case of independently distributed investments) to the concave-programming problem of minimizing the “dispersion” of a stable Pareto-Lévy variate subject to each prescribed mean value. Some further generalizations involving interdependent distributions will also be presented here.

The origins of the application of quantitative methods to the determination of optimum solutions to managerial problems can be traced back at least as far as 50 years when calculus techniques were first suggested for solution of economic lot size problems. However, the great increase in applications of optimizing techniques occurred after the Second World War with the popularization of the operations research concept and development of a wide variety of mathematical tools — among them linear programming, queuing theory, dynamic programming, and network flow theory. The development of digital computers in the late 1940's substantially reduced computational problems associated with the use of many mathematical methods and also made possible the use of simulation techniques which, without digital computers, are not ordinarily practical because of the large amount of computation involved.

This paper presents the results of a simulation study of the dynamic characteristics of the model built by Professor Chow whose purpose was to study statistically the relevance of the multiplier, accelerator, and liquidity preference as determinants of the national income of the United States.

A firm which produces a single product, whose production cost is a linear function of the production level and where net price per unit is constant, has a Pre-Tax Earnings function which is a linear function of the production level (see Figure I).

In this paper the results of some new structural estimates of liquidity preference may be found. The justification for presenting them is that they differ from earlier estimates in certain ways. In some cases, the implications of these estimates differ sharply from the implications drawn by other observers on the basis of their estimates.

Since the publication of Markowitz's article on “Portfolio Selection,” which was subsequently expanded into a monograph, there has been a great deal of further articulation, a not inconsiderable amount of mathematical programming and sensitivity analysis, the arrival of several competing portfolio balance models, and a near revolution in the theory of money and asset preference. While few formulas for solving a practical problem can claim to have generated as much theoretical fall-out, the new approach to portfolio management apparently has not been very successful at reaching the practitioners for which it was intended.

In a recent article, Donald R. Hodgman set forth a framework for analyzing commercial bank lending behavior which emphasized the relationship of customers to their banks as both depositors and borrowers. Specifically, Hodgman links the borrower's contract rate of interest to the profitability of his deposit account, i.e., banks compete for profitable deposit customers by offering the customer a rate which is lower than the comparable open market rate (adjusted for risk). Hodgman uses the terms deposit relationship and customer relationship to describe this behavior. He argues that compensating balance requirements, the prime rate convention, and provision of services below cost may be viewed as a systematic, rational attempt by commercial banks to maximize long-run profit under existing institutional arrangements when viewed from the perspective of the customer relationship.

Most businesses sell on credit. To administer credit, such companies set credit granting, term, and collection policies. This article analyzes one aspect of credit granting policy: the determination of the optimal number of credit applicants that should be accepted by a creditor. The emphasis in the relevant literature traditionally has been on techniques for estimating a credit applicant's probability of default and, to a lesser degree, on the decision to accept an applicant given his estimated probability of default. Cumulatively, these two decisions are crucial to any business selling on credit.

Most of the insurance oriented literature contains several levels of abstraction regarding the financial solvency of insurance companies. The first level represents those advances in the actuarial profession which are destined to eventually solve the double problem of capacity and capitalization (hereinafter referred to as the Ruin Problem). Most of these works, however, are concerned with developing the tools necessary to determine the theoretical loss distribution in insurance. The emphasis, then, is upon the mean and variance of the total loss distribution as they can be derived from the distribution of frequency and severity.

In a recent article in this Journal, Jacob B. Michaelson and Robert C. Goshay (hereafter M-G) argue that the rule of maximizing share values does not adequately explain the portfolio selection practices of financial intermediaries. Moreover, M-G suggest that their analysis “has ramifications that reach far beyond financial intermediaries.” In particular, they state that “the asset holdings of conglomerate firms and the rationale for mergers may not be fully explicable in terms of maximizing behavior.”

Broadly speaking there are two models to the problem of asset valuation under uncertainty and aversion to risk. Under one, the certaintyequivalent method, each future return is converted to its certainty equivalent and discounted at the pure rate of interest. Under the other, the risk-adjusted discount rate method, each future return is discounted at an appropriate discount rate. The interrelation and validity of these models of asset valuation have come under discussion in two important works on stock valuation.

Econometric models have often been used to explain and predict demand, production and price patterns of agricultural commodities. With computers generally available, estimation and application of these models is a simple matter. In spite of this, there has been nothing written, at least nothing that we are aware of, which details the use of such models as an aid to speculation in commodities futures. This brief note reports successful use of an econometric model and a time-sharing computer system for this purpose.