Determining the market values of streams of future returns is a task common to many sorts of economic analysis. The literature on this subject is extensive at all levels of abstraction. However, most work has not taken uncertainty into account in a meaningful way.

Security markets in major industrial countries have frequently been referred to as close to perfect markets. Probably the highest quality market for a class of securities is the United States government bill market; however, it is also frequently inferred that the United States listed equity market is also a near perfect market. In a perfect market, no opportunities for profit based upon past price movements or any other past data should exist; stocks in a perfect market are always at their proper price except for purely random fluctuations.

Investment management is a decision-making process which ranges from an individual managing his own small portfolio of securities to institutional investors who manage portfolios valued in millions of dollars. The importance of investment management is readily observed in the increased activity of the securities markets, the close scrutiny given by regulatory agencies to various institutional investors and professional investment managers, the growing market value of pension funds, trust funds, and investment companies, and finally, the increasing number of related research studies which are reported in the financial literature.

The arithmetic formulas appearing in the mathematics of finance are practically useless unless one has available either excellent tables and infinite patience, or working computer programs, a machine, and a budget. The present article shows how a number of useful topics in this area can be dealt with effectively by the more tractable mathematics of continuous processes. The methods yield approximate answers of high quality, and in some cases exact answers as well, with small effort, and have obvious applications in “truth in lending” investigations.

If all urban renewal projects were perfectly divisible and completely independent of one another, and if the urban renewal authority had perfect foresight as well as unlimited funds, the investment decision would be ideally simplified. There would be no need to choose between competing projects, and the urban renewal authority could evaluate each project on its own merits, without reference to any other project. Its decisions would be merely decisions to accept or reject single projects, uncomplicated by portfolio considerations.

The basic idea behind the random walk hypothesis is that in a free competitive market the price currently quoted for a particular good or service should reflect all of the information available to participants in the market that influence its present price. To the extent that future conditions of the demand or supply are currently known, their effect on the current price should be properly taken into account.

The use of the expected utility hypothesis and the “portfolio approach” has recently become quite popular by both writers in monetary theory and in financial management. Most discussions are given within what might be called the Tobin-Markowitz framework. One very important result recently discussed at some length is the Tobin “separation theorem.” This theorem essentially says that a quadratic preference function, or a normal distribution of returns on risky assets is a sufficient condition for the proportions of the various risky assets in a portfolio to be independent of the proportion of the portfolio held in a safe asset. The proofs of this theorem are given within a framework of the decision maker who minimizes portfolio variance for a given portfolio return, using variance as a measure of risk of the portfolio.

With the increasing emphasis on the performance of managers of institutional portfolios, it becomes important to develop an accurate and complete measure of investment results. Accordingly, this study will be devoted to clarification and possible resolution of the following issues:

1. How may operating results be segregated from contributions and withdrawals of capital?

2. How may the “dollar weighting” inherent in compound rates of return be eliminated?

3. Should investment, in the context of return on investment, be cost-based or value-based?

4. How should risk be quantified?

5. Can both risk and return be considered in one composite measure of investment performance?

In recent years, there has been considerable interest in the random walk theory of stock price behavior. This theory, as applied to the stock market, implies that past stock-price movements cannot be used to predict future market prices in such a way as to “profit” from the predictions. By not “profiting,” we mean that a trader using the past history of stock prices cannot apply mechanical decision rules that result in a consistently better performance than a simple buy and hold strategy. If stock price movements were to become systematic so that a “profit” were possible, proponents of the random walk theory argue that a sufficient number of market participants would quickly recognize the recurring pattern and exploit it. In exploiting it, they would drive out the opportunity for “profit,” causing the price series to approximate a random walk.

This paper investigates how the addition of debt to the capital structure of a corporation affects the risk of the stockholders. In the first instance, we will hold the size of the firm constant and substitute debt for common stock. In the second situation, we will allow firm size to change, and will accomplish the increase in size by issuing debt. For both situations, we will first observe the effect of debt on the earnings per dollar of common stock investment. The analysis could also be made using the number of shares of common stock. Since the number of shares of common stock may be changed quite arbitrarily (as, for example, by stock dividends), we want to make the measure invariant to the number of shares outstanding. We will do this by using value of common stock and value of debt. We are then computing the variance of return on common stock investment when we compute variance of earnings per dollar of common stock investment. After considering how debt affects earnings per dollar of stockholders' investment, we will investigate the effect of debt on the total earnings of the stockholders, and on the probability of a deficit.

Two general methods of computing the rate of return on common stock are being discussed widely. These methods are the internal rate of return and the geometric mean of the annual rates of return. The Gordon-Shapiro formulation, , is the best known model of the former type.

It is well known that different combinations of investments involve different risks. In recent years the analysis of risk has tended to focus on two moments of the probability distribution of returns, the mean and variance. This paper considers the effect on the variance of an investment fund of adding dependent investments.

The application of linear programming techniques to the problem of capital budgeting has repeatedly been proposed in the literature. However, while the potential of linear programming models for this important area of business decisions is generally recognized, practical applications still face some severe limitations. This note focuses on one particular problem peculiar to the application of programming techniques to capital budgeting, namely the mutual dependence between the optimal solution of the linear programming model and the discount rate used to calculate the coefficients of its objective function.

The purpose of this paper is to estimate empirically the effect of the deferred call provisions on corporate bond yields using the conceptual framework of callable and call-free yields developed by Jen and Wert [3]. After reviewing briefly the above-mentioned study in Section I, Section II presents patterns of callable and call-free yields of deferred issues from January 1956 to June 1961 by grades, months of offering, and coupon rates and contrasts them with those of the freely callable issues. Section III further contrasts yields of deferred issues with those of freely-callable ones on a pair comparison basis, while Section IV discusses the implication of the study for both the issuers and the investors.

Many Wall Street financial analysts believe that a positive relationship exists between the level of short interest in equities and subsequent movements in the prices of these equities. This view is apparently grounded in the belief that short traders will push prices up in the future as they attempt to cover their short positions.

The increase in corporate liquidity over the past ten years, together with higher levels of interest rates and growing sophistication among corporate treasurers and bank portfolio managers, have contributed to the increasing importance of various money-market instruments. The relative position of the Treasury bill has declined, and bank time certificates of deposits, short-term issues of municipalities, and commercial paper have assumed greater importance. The fundamental reason for the attractiveness of alternatives to Treasury bills is, of course, the additional yield that the investor can obtain in the substitute instruments. The differential yield spread over Treasury bills can be explained substantially by two factors—the difference in marketability and the existence of some default risk on the alternative securities.

Two measures of investment worth: the discounted-rate-of-return and the payback method will be compared here. Many examples can be found in the literature illustrating the serious limitations of the payback method.

According to these examples, an investment proposal may be judged economically undesirable when in actual fact it is highly profitable. This happens when the annual cash flow is not equal, and the investment project promises a relatively large cash flow after the cut-off period.

Commercial bank portfolio models developed by Hester [6], Porter [11], and Kane and Malkiel [7], among others, relate the structure of an asset portfolio to variation in the level of deposits. Similarly, in a recent application of linear programming to asset management, Cohen and Hammer [3] specify a liquidity constraint based upon deposit fluctuations. However, there have been few empirical studies of the determinants of demand deposit fluctuations. The purpose of this paper is to extend the work of Gramley [4], Rangarajan [12], and Wilkerson [14] on the determinants of deposit variability. In this paper, the analysis will be confined to demand deposit variability.

This paper is another step in an attempt at unification, through generalization, of existing theories in various areas of finance. The subject treated here is the valuation of equity shares.

Perhaps one of the most time-honored of technical market indicators is the Advance-Decline Line. Its predictive powers as a leading indicator of the general market have been written about, and historical data on this index are published in Barron's. However, the validity of this series as a leading indicator has not been subjected to rigorous statistical analysis.