Knowledge that Transforms

Professor Wu, in his recent article [8], investigated the trading activities of odd-lotters and their market impact. The purpose of this note is to update the data examined by Wu since recent trends are extremely significant and to question the use and interpretation of some of Wu's original data. In addition, some errors in Wu's article will be discussed.

Professor Stevens has attempted to determine whether or not a consistent financial basis for merger exists as measured by premerger financial characteristics of the acquired firms. He suggests that results of his study are useful in identifying merger motives and in relating such motives to a general framework for analysis of merger movements.

Professors Nielsen and Melicher (N-M) have conducted well an interesting study of merger premiums as related to various measures of synergy connected with those mergers. Their study is another in a growing body of literature concerned with the merger phenomenon which increased substantially during the sixties and has continued into this decade. In order to provide an evaluation of their study, I shall consider their choice of research design and their analysis of research findings.

It has been discovered in the context of various stock valuation models (see [1], [2] and [4]) that the shareholder is indifferent to the proceeds (or subscription) price chosen in a preemptive rights offering of equity capital, provided that the total equity capital raised by the offering is fixed. In this note we generalize this result to any stock valuation model in which arbitrage is present and which values only the total amount of the new investment, that is, places no value on holding more (or fewer) shares with a lower (or higher) market price.

Most large companies develop formal or informal agreements with banks to cover anticipated seasonal or temporary cash needs and/or to provide assurance of the availability of funds against unanticipated cash requirements. We address the problem of determining the optimal limits of available funds a company should maintain under a revolving credit agreement. Typically a company will negotiate a legal commitment with a bank or group of banks for a specified period of time, usually one to three years, in which the bank agrees to extend credit up to a specified maximum amount. During the duration of the commitment, the bank must lend money to the company whenever the company wishes to borrow, provided the amount of money borrowed does not exceed the maximum amount noted in the agreement. The company must not be in default of any of the restrictive covenants of the agreement, such as working capital limits, compensating balances, limits on other indebtedness, etc. Although the agreement itself provides for intermediate-term financing, the agreement often takes the form of short-term (30-60-90 days) renewable notes.

The trading of security options is one of the fastest growing and most dynamic areas of investment concern. When the Chicago Board of Trade's proposal to develop an exchange for trading option contracts is implemented, security option trading will become an even more important aspect of the investment world.

Solving capital budgeting problems with linear and integer programming has been part of the finance literature for some time [21, 22, 23, 7, 14, and 18]. Capital budgeting problems have unique properties that distinguish them from other integer linear problems discussed in the mathematical programming literature. Capital budgeting problems generally have the following characteristics: (1) the matrix tends to be rectangular with more variables than constraints; (2) they are all maximization problems with ≤ constraints and nonnegativity conditions in the general form 0≤xi≤1 in the case of linear programming and xi = 0, 1 in the case of integer problems; and (3) there are often mutually exclusive projects among the variables. The purposes of this note are to illustrate some computational experience using existing integer algorithms to solve a set of capital budgeting problems and to begin to catalog the performance of integer codes on financial problems.

It is likely that warrants will be used increasingly in the future by corporations both as means of sweetening other securities such as preferred stocks and bonds, and as securities in their own right. Many authors have analyzed the characteristics of warrants from the point of view of investors but attempts to develop a procedure for determining the cost to a corporation of issuing warrants have been lacking. We will find it convenient to measure the yield to a corporation of issuing warrants instead of common stock, rather than determining the percentage cost of warrants analogous to the cost of common stock equity, preferred stock, and interest-bearing debt.

A firm periodically makes three major classes of decisions that determine its structure as reflected on its balance sheet. The first relates to the total amount of investment as well as the distribution of this total amount among different types of assets. This decision determines the size of the firm and the structure of the “assets” side of its balance sheet. The second is concerned with the relative proportion of equity versus debt capital to be used in financing the firm. This decision determines the structure of the “sources” side of the balance sheet by establishing relative sizes of liabilities and stockholders' worth. The third is the choice of the proportion of the equity which should be raised through the retention of earnings and the proportion to be raised through the sale of new stock. This decision determines the dividends that will be distributed and the composition of the stockholders' worth portion of the balance sheet.

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.