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.

“Capital Growth and the Mean-Variance Approach to Portfolio Selection” Nils H. Hakansson Volume VI, No. 1

Three main approaches to the problem of portfolio selection may be discerned in the literature. The first of these is the mean-variance approach, pioneered by Markowitz [21], [22], and Tobin [30]. The second approach is that of chance-constrained programming, apparently initiated by Naslund and Whinston [26]. The third approach, Latané [19] and Breiman [6], [7], has its origin in capital growth considerations. The purpose of this paper is to contrast the mean-variance model, by far the most well-known and most developed model of portfolio selection, with the capital growth model, undoubtedly the least known. In so doing, we shall find the mean-variance model to be severely compromised by the capital growth model in several significant respects.

The approach of selecting a portfolio of stocks on the basis of expected return and variance was introduced by Markowitz [18] in 1952 and subsequently was more fully developed by him [19] in 1959. Since this time, there has been considerable research either directly concerned with, or related to, the Markowitz model. The utility implications of his assumption that an investor chooses a portfolio solely on the basis of expected return and variance (where variance is identified with risk) have been studied, [1], [A], [22], and [31]. A simplified method of solving for the efficient set of portfolios under the assumption of a regression structure has been developed by Sharpe [26], and approximation methods have been suggested [25] and [29]. Empirical tests (with partially contradictory conclusions) of portfolio selection theory are described in [5], [7], [8], [20], and [27]. Studies of economic questions (such as liquidity preference, equilibrium stock prices, substitutability of risky assets, etc.), as formulated within the portfolio model, can be found in [10], [11], [13], [14], [16], [23], and [28]. A related portfolio selection approach, based on the assumption of a Pareto underlying distribution, has been suggested by Fama [6]. A modification by Baumol [2] introduced a confidence limit criterion. Also, some initial attempts have been made at deriving related adaptive models of portfolio selection, [21], [30].

Considerable attention has been focused in the past two decades on the substitutability of the liabilities of private nonmonetary financial intermediaries for money, narrowly defined as the sum of currency and demand deposits adjusted. Discussion concerning this topic related to the United States, and most of the empirical work has been confined to that country. The essential folklore of that discussion crossed the border into Canada and is now even reflected in its textbooks on Canadian money and banking. However, very little empirical work has been done in Canada to examine this lore.

A substantial amount of scholarly effort in recent years has been devoted to the determination of the relationship between banking structure and performance. In general, the results of these studies indicate that banking structure affects both the price and quantity of banking services, but, for practical policy purposes, the impact of banking structure is quite small. Yet, the results of these studies have been inconclusive and contradictory to a substantial degree.

This paper presents the results of a study which sought to determine whether the status of large member banks as owner-controlled or management-controlled has borne a significant relation to bank profit rates during recent years. The impetus for the study was provided by the view, encountered frequently in the literature, that management-controlled firms may place less emphasis on profit rate than owner-controlled firms, sacrificing it for performance goals regarded as more consistent with management interest. W. Baumo.1 [1, p. 4 and pp. 101–104], for example, has argued that management-controlled firms may sacrifice profit rate in order to achieve higher growth rate and reduced risk acceptance. R. Monsen and A. Downs [11] suggest that such firms may sacrifice both profit rate and growth rate for reduced risk acceptance. K. Cohen and S. Reid, in their study of bank merger activity during 1952–1961 [5], argue that bank managers, as compared to bank owners, place more emphasis on growth rate and less emphasis on profit-associated variables. Other possibilities present themselves. Management-controlled firms may sacrifice profit rate directly for management salaries, bonuses, and fringe benefits, including benefits associated with management prestige. The management-controlled firms may simply pursue efficiency less vigorously.

The Sharpe or diagonal portfolio model has been accepted by a large segment of both academic and practical researchers in portfolio theory. The model is tractable, requires a relatively small set of inputs, and is viewed by many to present “reasonable” assumptions regarding the workings of the security market.

Efficiency analysis is concerned with isolating the efficient subset of investments (portfolios) for all investors belonging to a specified group. In order to construct a meaningful efficiency criterion, i.e., one which holds for more than one investor, care must be exercised to ensure that the investors' efficient set is independent of their wealth.

The purpose of this note is to demonstrate that the explicit introduction of consumption patterns alters the traditional relationship between expected return and variance presented by Markowitz, Tobin, Sharpe, Lintner, and others.

In a recent paper by Lusztig and Schwab, a sensitivity analysis was performed on a linear programming capital budgeting problem where selection of projects is based on the criterion of present values. Their model is typical of current practice in the literature, and it is the point of this paper to indicate that a better model exists which allows more flexibility of assumptions and will yield the same results as a present value criterion. The model to be presented here uses a terminal value (horizon value) criterion for selection of the optimum set of investment projects.

In the allocation of capital to investment projects, it is unlikely that optimal decisions will be reached unless anticipated inflation is embodied in the cash-flow estimates. Often, there is a tendency to assume that price levels remain unchanged throughout the life of the project. Frequently this assumption is imposed unknowingly; future cash flows are estimated simply on the basis of existing prices. However, a bias arises in that the cost-of-capital rate used as the acceptance criterion embodies an element attributable to anticipated inflation, while the cash-flow estimates do not. Although this bias may not be serious when there is modest inflation, it may become quite important in periods of high anticipated inflation. The purpose of this note is to investigate the nature of the bias and how it arises.

The problem of cash management, in its simplest form, is to formulate decision rules which control the level of a firm's cash balance to meet its demands for cash at minimum total discounted cost. Control is achieved by transacting securities for cash. The cost of control is the commission expense [13]. Optimality depends on balancing excess opportunity costs of holding balances which are too large and having excess buying and selling costs (to meet cash obligations) of balances which are too small.

During the “credit crunch” of 1966, starts of single-family residences fell 19.2 per cent, from 964,000 to 779,000. At that time, 10 states had usury laws limiting the maximum nominal interest rate that could be charged to individuals on residential mortgages to 6 per cent. When interest rates rose to high levels in 1966, there were widespread complaints that this artificial restriction caused residential construction to decline by even larger amounts in those states having 6 per cent usury laws as lenders shifted funds to other states not having this restriction. However, when nominal interest rates rise to the legal maximum, mortgages trade at a discount and the effective yield rises above the legal rate. Presumably, it is the effective yield, not the nominal rate, that is relevant for directing the flow of funds into alternative investments. Thus, there is good reason to doubt that the usury laws did restrict residential construction in spite of the contention by those in the mortgage and construction industries. The purpose of this study is to determine if—and if so, to what extent—state usury laws caused a decline in residential construction in 1966.