Knowledge that Transforms

In “Valuation Under Uncertainty, ” which recently appeared in this Journal (September 1967), Houng-Yhi Chen argues [1, pp. 313–314] that “Robichek and Myers' criticism [2, 3] of the use of the risk-adjusted discount rate is unfounded, ” and suggests that our “conclusions must be based in part on a misunderstanding of the risk-adjusted discount rate method.” These charges are without foundation, as we will show here.

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.

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.

We shall investigate the problem of optimal exercising strategy for option holders for the case in which option holders are averse to risk. A model of stock price changes incorporating the Lognormal random walk assumption will be combined with a class of utility functions containing diminishing marginal utility of money. In general, the strategy of waiting until the last possible day to exercise an option, which maximizes expected value, will not maximize expected utility. The strategy which maximizes expected utility is obtained by a dynamic programming formulation of the decision problem. At each day (or decision stage), the option holder may choose to act (exercise) or wait until the next day. Working backwards from the last day, a series of critical prices are obtained, with the optimal strategy being as follows: act if the stock price on any day is greater than the critical price for that day; otherwise, wait. Using the concept of proportional risk aversion developed by Pratt, we will demonstrate that, under certain conditions, a utility function which exhibits increasing proportional risk aversion is sufficient to create a series of finite critical prices. Moreover, once an option is exercised, the option holder continually faces a tactical decision to hold the stock and wait for capital gains or sell and take profits as ordinary income, thereby avoiding further risk. This decision may also be optimized by a dynamic programming scheme similar to the approach used above.

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.

Alan Seelenfreund, George G. C. Parker, James C. Van Horne, Stock Price Behavior and Trading, The Journal of Financial and Quantitative Analysis, Vol. 3, No. 3, Special Issue: Random Walk Hypothesis (Sep., 1968), pp. 263-281

The recent literature in the field of commercial banking has centered to a considerable extent around the branch banking controversy and bank merger activities, particularly as regards their economic effects on banking structure and performance. Much has been said, moreover, about the effects of branching on the “public interest, ” whether such branching is carried out through merger or de novo branching. Public interest is usually defined as including deposit safety, adequate compensation by banks to depositors for the use of their money, availability of credit for borrowers at competitive rates of interest, and, in more general terms, increased competition in banking without sacrificing safety.

John L. Evans, The Random Walk Hypothesis, Portfolio Analysis and the Buy-and-Hold Criterion, The Journal of Financial and Quantitative Analysis, Vol. 3, No. 3, Special Issue: Random Walk Hypothesis (Sep., 1968), pp. 327-342

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?

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.