Knowledge that Transforms

The mathematical difficulties encountered when attempting to express the internal rate of return (IRR) of a combination of two or more investments as a weighted algebraic sum of the individual investments' IRRs has been recognized in the financial literature for some time. However, in a recent issue of this journal, Professors Reilly and Wecker (hereafter R-W) [3] apply the well-known mathematical impossibility of expressing the root(s) of a polynomial as an algebraic combination of the roots of related polynomials to question the validity of the weighted cost of capital (kw) concept.

The theory of efficient capital markets suggests that if the capital markets are efficient, security prices can be assumed at any time to “fully reflect” all available information. Various forms of the model have been subjected to extensive empirical testing. The results of these tests have been such that in reviewing the literature on the theory Fama [3] states, “ … the evidence in support of the efficient markets model is extensive, and (somewhat uniquely in economics) contradictory evidence is sparse.” Most of the research, however, has been addressed to the question of whether prices “fully reflect” particular subsets of available information. The validity of these results depends on the extent to which the information in the subset used for testing captures the information actually impounded in prices.

Vincent P. Apilado, Don C. Warner, Joel J. Dauten, Evaluative Techniques in Consumer Finance--Experimental Results and Policy Implications for Financial Institutions, The Journal of Financial and Quantitative Analysis, Vol. 9, No. 2 (Mar., 1974), pp. 275-283

Several titles reflecting different approaches to our subject matter were considered for the paper. An historical but somewhat pedantic approach to the teaching of investments might have been titled “Pedagogical Developments in Investments: Past, Present, and Future.” Another possibility was “Sex and the Single Investor, ” a title which probably would have attracted a larger audience. “Beat the Dealer Versus Beat the Market” might well have been an appropriate title in view of our presence here in Las Vegas and also because of recent experience in the securities markets. We finally decided on simply “A Portfolio Analysis of the Teaching of Investments, ” because this seems to better capture the essence of our viewpoint.

The purpose of this paper is to indicate that the opportunity to obtain information regarding the probability distribution of the return on a risky asset, such as a portfolio or a mutual fund, may cause a risk-averse decision maker to accept a single-period actuarially unfair gamble. This behavior is the same as that implied by utility functions that have convex segments, as originally considered by Friedman and Savage [2] and by Markowitz [12], but the utility function derived is not convex on any interval, since it is the envelope of a finite set of strictly increasing, strictly concave functions. Similar utility functions have been obtained, by Fleming [1] because of transactions costs, by Hakansson [4] by imposing a borrowing restriction on an investment-consumption model, and by Masson [14] in the context of an imperfect capital market. In this paper acceptance of single-period actuarially unfair gambles by an individual risk averse with respect to future wealth levels results from the opportunity to acquire information. The acquisition of information creates a set of conditional decisions each of which the individual may treat in an optimal manner, and that set of conditional decisions may induce risk-taking behavior.

The purpose of this article is to produce a conservative estimate of how often traditionally conceived seasonal components are present in prices of individual Dow Jones industrial stocks. A careful estimate is needed to resolve some of the current confusion on the question and to provide basic information along lines suggested by Smidt [27, p. 238]: “… investigations of the random walk hypothesis would be most fruitful if they were conducted in the spirit of attempting to determine the size and extent of systematic tendencies that may exist in price series” (italics added).

The study initially examined the immediate effects that conglomerate acquisitions have on the beta level of conglomerate and nonconglomerate acquiring firms. An analysis was then made of the long-run beta trends of firms that actively engage in conglomerate mergers. The results of the short-term comparative analysis have indicated that systematic risk behavior tends to be responsive in varying degrees to major conglomerate merger activity—with betas changing as a function of the combined premerger values and ρ2 measures showing improvement upon acquisition. At the same time, the regression results clearly revealed that the responsiveness of β to premerger marketrelated variables was considerably greater for the nonconglomerate firms. In contrast, the results of the comparative long-term analysis suggested that the differential effects of conglomerate merger activity on systematic risk are more of a marginal or limited nature. That is, unless the firm conducted extensive merger activity, the long-run performance of β and ρ2 indicated that conglomerate mergers have only contributed to increased absolute and relative systematic risk levels—the same pattern exhibited by the nonconglomerate, nonmerging sample.

This paper examines the validity of two widely used methods for forming conditional predicted portfolio returns. The first method relies on a one-period, mean-variance theory of equilibrium expected return, sometimes referred to as the “capital asset pricing model” (CAPM). The second method is based upon a proposal by Markowitz [14] and is called the [market model] (MM).

The shortcomings of a quadratic utility function are so serious and so widely known that by now one might assume that it would simply have been dropped from consideration. Arrow [1] and Pratt [6] have shown that such a function implies ever increasing absolute risk aversion, that is, reduced risk taking as wealth increases, which contradicts everyday experience. Moreover, the assumption of quadratic utility also implies ultimate satiation with respect to risk taking. This function has a well-defined maximum beyond which the marginal utility of money declines, and as a result the range of admissable returns must be restricted. Wippern [12] has focused attention on the second of the above two shortcomings. Using a rather ingenious device, based on the Sharpe-Lintner market model [8 and 5], Wippern has measured empirically the admissable range of returns implied by the quadratic utility function. Since his empirical findings imply that returns beyond as little as 1.3 standard deviations from the expected return provide negative marginal utility to investors, Wippern concludes that the Sharpe-Lintner market model, and/or the mean-variance portfolio theory upon which it is based, have “inconsistent and implausible properties.”

Stable distributions are suggested as being the underlying distributions for many economic variables. Capital market variables, in particular, are said to follow a member of the symmetric stable class.