Most portfolio analysis is based on the use of two parameters, the mean and variance, of the statistical distribution of returns. Exceptions to this practice can be found in an empirical work by Arditti [1] and a theoretical paper by Levy [4], both using the third moment around the mean. It is the purpose of this paper to begin a general extension of the two-parameter analysis to three or more parameters. Accordingly, some problems will be solved, but others will be suggested for further analysis.

In two previous articles [11] and [12] a family of normative models of the individual's economic decision problem under risk was presented. At the same time, certain implications of these models with respect to individual behavior were deduced for a class of utility functions. This paper will show that these models also give rise to an induced theory of the formation and operation of firms under risk for the same class of utility functions.

Consider an economy consisting of individuals and firms with the following characteristics: all individuals are rational in the von Neumann- Morgenstern sense and non-neutral toward risk; the dividend streams of some firms are certain, while the dividend streams of the other firms are uncertain; and the economy is equipped with perfect financial markets. In this economy, as we show in the present paper, the value of each firm with a certain dividend stream depends only on the dividend stream itself and the set of future interest rates—i.e., the market value of such firms is independent of the attitudes toward risk and the level of wealth of any individual. However, the value of each firm with an uncertain dividend is, with one exception, not independent of anything: it depends not only on the firm's own dividend stream, the set of future interest rates, and (all) individuals' risk attitudes, but also on the wealth levels of these individuals and on the dividend streams of all other firms with uncertain dividends even when these streams are stochastically independent. The exception occurs when the individuals have exponential utility functions of money. In this case, the market value of each firm with uncertain dividends is independent of other dividend streams and of individual wealth levels if these variables are statistically independent of the firm's dividends. Exponential utility functions of money, of course, are not considered empirically plausible.

Until very recently, in most work on normative models for capital investment planning, it has been assumed that availability of capital is unconstrained; i.e., that money may be freely borrowed or lent at a single market rate of interest, and that no other constraints affect the proper choice of available productive investment projects to be undertaken. Since practical situations almost universally do involve such constraints, the traditional theories have, for the most part, been an unsatisfactory guide to achievement of optimal capital investment behavior in the real world.

This article examines some aspects of the portfolio selection problem when the “no-easy-money-condition” holds and the investor is constrained to stay solvent. The possible presence of a non-capital income is also taken into consideration.

Thomas H. Mayor, Short Trading Activities and the Price of Equities: Some Simulation and Regression Results, The Journal of Financial and Quantitative Analysis, Vol. 3, No. 3, Special Issue: Random Walk Hypothesis (Sep., 1968), pp. 283-298

John H. Wicks, Affluence and High Household Liquidity: Problems and Opportunities: Discussion, The Journal of Financial and Quantitative Analysis, Vol. 1, No. 1, Proceedings of the First Annual Meeting of the Western Finance Association (Mar., 1966), pp. 53-55

Investment analysis, both for purposes of capital expenditures and for financial investments, is based on an evaluation of cash flows. This evaluation involves the application of interest rates in order to determine whether a given option–a series of cash flows–is profitable or not. For numerous reasons, primarily that of simplicity, it has been traditional to assume that the rates of interest used to measure the worth of an investment are constant. With this assumption it is possible to equate the two familiar investment criteria when investments are independent and outlays are not subject to expenditure constraints, i.e., when capital markets are taken to be perfect in the usual sense. An investment is profitable if its net present value is positive when discounting of cash flows uses the (assumed constant) cost of capital, or if its (assumed unique) internal rate of return is greater than the cost of capital. Equivalence of these two criteria is historically most frequently identified with Irving Fisher [3, 4], and his two-period analysis, portrayed graphically, is generally utilized to establish the correctness of the equivalence of the criteria.

This paper is an attempt to improve on the ability of financial management to arrive at a desirable or close to “optimal” cash balance for a firm at a point in time. There have been several comments on this subject in literature over the years including the contributions of Keynes, Hicks and Samuelson. In recent years Baumol and Beranek have presented us with more specific models. This paper tends to be more operational than the Baumol or Beranek presentations and hence tends perhaps to lose some of the sophistication of the more theoretical models; it attempts to present a reasonably operational method for providing for cash balances for transactions and precautionary purposes. But let us first examine these two models briefly.