Knowledge that Transforms

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.

Although the importance of evaluating the risk of potential investments has long been recognized, only recently have formulations been developed to include risk as an explicit variable in the decision-making process. The considerable progress being made in this area, both in theory and in application, is attested to by the number and variety of contributions to the literature.

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.

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.

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.