Showing papers on "Efficient frontier published in 1973"

Optimizing the portfolio selection for mutual funds

Abstract: and performance of investment portfolios [3, 5]. However, most of these studies are primarily concerned with the first two items suggested by Markowitz. For example, the full covariance model of Markowitz and the linear programming model of Sharpe [ 15 ] are capable of determining efficient portfolios, but it is left to the investor to select the one portfolio that best fits his preference. The investor's preference, as a set of goals for a portfolio, with particular characteristics concerning the near-term market, industry company conditions, etc., cannot be easily incorporated into the models suggested by the above cited studies. Yet, these latter factors may have a significant bearing on the risk character of the portfolio, particularly in the case of common stock funds. It is thus desirable to be able to determine various portfolios that are efficient in the long-term sense while meeting fund requirements imposed by managerial judgments concerning near-term conditions. The purpose of this study is to formulate a goal programming (GP) model which, once the investor's objectives are quantified, determines the optimal portfolio from a set of efficient portfolios. The GP model thus designed possesses the effectiveness of the full covariance model by Markowitz as well as many of the simplified features of Sharpe's linear programming approach. Furthermore, the model allows the inclusion of covariance effects without requiring complicated quadratic programming codes.

Risk, Return, and Portfolio Analysis: Reply

Abstract: Professor Tsiang essentially makes two comments on my paper, "Risk, Return, and Equilibrium" (henceforth RRE).1 First, to buttress the assumption that distributions of returns on all portfolios are of the same two-parameter type, RRE references various previous empirical studies. In some of these, for example, Blume (1968) ,2 results are reported in terms of one-period percentage returns-the relevant formulation for the model of RRE while in others, for example, Fama (1965), results are reported in terms of continuously compounded return -that is, the natural log of one plus the one-period percentage return.3 Professor Tsiang chooses to ignore the empirical results for one-period percentage returns. He discusses at length the problems that would arise if, for some reason, I wanted to apply my model of portfolio decisions and capital market equilibrium to continuously compounded returns rather than to percentage returns. Since his criticisms apply to his own inventions, they require no comment from me. Professor Tsiang does raise one issue that is within the framework of my model. He contends that the basic assumption of two-parameter return distributions for all portfolios is not a literal description of reality. He points out that all such two-parameter distributions imply that returns

Risk, Return, and Portfolio Analysis: Comment

Abstract: The mean-variance analysis of portfolio selection has come under heavy attacks in recent years. Borch (1969) has demonstrated that any mean standard deviation indifference curves that are drawn upward sloping can be shown to be inconsistent with the basic axiom of choice under uncertainty. Feldstein (1969) has shown that mean standard deviation indifference curves need not be convex downward, as is usually assumed to be the case, but might change from convex to concave, thus making the usual tangency solution for optimum portfolio of rather dubious value. These criticisms shake the very theoretical foundation of the prevalent portfolio theories, which are built upon the assumption of a system of upward-sloping and convex return-risk indifference curves for every investor. Tobin (1969), one of the pioneers in this field, was forced to concede that the mean-variance approach is justified only when the utility functions of investors are quadratic, or when the outcomes of all investments can be assumed to be normally distributed. Such a defensive position, however, is still vulnerable to attacks. On the one hand, it is now generally recognized that quadratic utility function has an unrealistic implication of increasing absolute risk aversion with respect to wealth, apart from its limited range of applicability. On the other hand, in view of the fact that prices of most stocks and commodities cannot become negative, it is not always appropriate to assume a normal distribution for every investment outcome, which would imply a finite probability of a negative rate of return smaller than -100 percent. Furthermore, progressive taxation with imperfect loss offset, and possibility of hedging by stop-loss sale arrangements would certainly change a symmetric distribution of gross returns into an asymmetric distribution of net returns. It becomes obviously questionable whether we are still justified in applying the mean-variance analysis to net investment returns that are obviously asymmetric in density. Various attempts have been made to salvage the mean-variance analysis. For instance, Samuelson (1970) and Tsiang (1972) have shown that mean standard deviation analysis yields a good approximation regardless of the distribu-