Knowledge that Transforms

R. Richardson Pettit, Randolph Westerfield, A Model of Capital Asset Risk, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1649-1668

A proposition is proved which shows that each member of an important class of investment and financing projects has a unique nonnegative internal rate of return. Nonuniqueness of the internal rate of return is thus shown to occur less frequently than formerly believed. The correspondence between the proposition and previous results on the uniqueness of the internal rate of return is briefly indicated.

The theory of choice under conditions of certainty has been extended by Von Neumann and Morgenstern [8], Friedman and Savage [5], Marschak [13], and others to conditions involving risk by assuming that individuals maximize their expected utility. The application of this theory to portfolio selection, to efficiency criteria, and to the explanation of the well-known phenomenon of diversification of assets has been carried further by Markowitz [11 and 12], Tobin [17], Samuelson [15], Sharpe [16], and Lintner [10], and more recently by Hadar and Russell [5] and Hanoch and Levy [8].

A belief frequently expressed by observers of the stock market is that groups of institutions tend to trade in the same way at the same time. Two expressions of this belief follow:Frequently reference is made to the ‘impact’ of institutional investors on the stock market. Apparently it is worrisome to the observers of the markets to find that we tend to buy and sell somewhat in unison.

Portfolio selection models based on expected value-semivariance (E-S) criteria have been suggested as offering certain advantages over the expected value-variance (E-V) approach. Although variance is more tractable mathematically, it has not always been satisfying to financial theorists ([3, pp. 278–284], [5], [6], [7, pp. 193–194], and [10, pp. 72–73]). In the pioneering work in portfolio analysis, Markowitz [7, p. 194] observed that semivariance concentrates on reducing losses as opposed to variance which considers extreme gains, as well as extreme losses, as undesirable. In the presence of nonsymmetrical probability distributions, this equal weighting of gains and losses may not adequately describe the alternative portfolios available to the decision maker.

Seha M. Tinic, Richard R. West, Competition and the Pricing of Dealer Service in the Over-the-Counter Stock Market, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 3 (Jun., 1972), pp. 1707-1727

Robert C. Higgins, The Corporate Dividend-Saving Decision, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1527-1541

Harry G. Johnson, The Monetary Approach to Balance-of-Payments Theory, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1555-1572

Robert O. Edmister, An Empirical Test of Financial Ratio Analysis for Small Business Failure Prediction, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1477-1493

The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.