Paul A. Samuelson, Limited Liability, Short Selling, Bounded Utility, and Infinite-Variance Stable Distributions, The Journal of Financial and Quantitative Analysis, Vol. 11, No. 3 (Sep., 1976), pp. 485-503

In a recent article in this Journal, Amir Barnea [1] proposes a criterion for assessing the market-making efficiency of New York Stock Exchange specialists. The appealing aspects of Barnea's method are that it uses publicly available data (common stock prices) and operates on a variable of primary concern to investors, the variance of returns on common stock. The difficulty we see in applying his approach, however, is that Barnea's performance criterion can be sensitive to a number of factors in addition to any impact the specialist might have, and that effective specialist intervention might have either a positive or negative impact on the performance measure. Thus, his specialist ranking seems to be quite misleading, and his empirical findings appear to be amenable to a substantially different interpretation than that which he provides.

Traditional models of portfolio selection assume that all assets are traded in competitive markets, so that rates of return to any individual investor are fixed. This paper represents an extension of portfolio theory to the case in which asset markets are not perfectly competitive and rates of return cannot be taken as given. Klein [10] has noted that, when asset markets are imperfect, the separation theorem no longer holds but does not solve explicitly for the relationship between risk and return. Here for simplicity we shall consider the case of the investor who has a monopoly in an asset he creates, so that its risk and return characteristics are determined by the decisions of the portfolio selector and hence are endogenous. It will be shown that even if the market for an asset in the portfolio is imperfectly competitive, as long as the demand curve for the asset is well behaved, the locus of efficient portfolios facing the investor, which is composed of combinations of the riskless asset and the optimal combination of risky assets, will be a concave function, as opposed to a linear function in the competitive case. In other words, the introduction of capital market imperfections does not affect the positive slope of the efficient set of portfolios. Moreover, the expected return on the imperfectly competitive asset will be shown to be easily decomposable into the standard risk premium and a monopoly premium.

In recent years a number of papers have been concerned with the determination of necessary and sufficient conditions for portfolio separation and for myopia. As a result of these earlier investigations, it is known that a necessary and sufficient condition both for portfolio separation and for myopia is that the investor's utility function exhibit risk tolerance, that is a linear function of wealth. What is lacking in the existing literature is a clear demonstration of the economic relevance of linear risk tolerance for portfolio separation and myopia. It is hoped that this paper will help to fill the gap by an analysis of separation and myopia using the standard tools of price theory: indifference curves, budget lines, and Engel curves. Viewed in this perspective, a substantial part of the analysis can be amplified and clarified in terms of the geometry of the situation.

R. N. Anderson, John A. Haslem, John B. Leonard, An Empirical Analysis of the Impact of Branching on Demand Deposit Variability, The Journal of Financial and Quantitative Analysis, Vol. 11, No. 3 (Sep., 1976), pp. 455-464

Multiasset portfolio selection models stated in terms of the expected utility criterion generally require the evaluation of multiple integrals. This reality has severely hindered attempts towards the development of computation methods to determine optimal portfolio allocations when there are a large number of assets. Aside from special cases, expected utility is not convergent into a simple closed form; the complexity from the point of view of computation is then perhaps most easily appreciated if one realizes that every iteration in a nonlinear program demands the estimation of several integrals (see Ziemba [23] for details). Such calculations are extremely costly when the number of assets is large. It is, consequently, of interest to approximate the expected utility function by a function which is easier to optimize over the set of feasible portfolios.

Barr Rosenberg, James A. Ohlson, The Stationary Distribution of Returns and Portfolio Separation in Capital Markets: A Fundamental Contradiction, The Journal of Financial and Quantitative Analysis, Vol. 11, No. 3 (Sep., 1976), pp. 393-402