Showing papers on "Efficient frontier published in 1980"
TL;DR: In this article, the authors developed a model to measure regional industrial diversification in a Markowitz portfolio context, using the notion of a regional efficiency frontier, arguing that a region can be considered to be optimally diversified when it is on this efficiency frontier.
Abstract: This paper develops a model to measure regional industrial diversification in a Markowitz portfolio context, using the notion of a regional efficiency frontier. It argues that a region can be considered to be optimally diversified when it is on this efficiency frontier. The extent to which a region's portfolio deviates from the efficiency frontier suggests a useful measure of diversification with normative aspects that are conspicuously absent from the more commonly used indices. In this context, regional diversification is then compared to various other measures using Canadian provincial employment data.
37 citations
TL;DR: Roll argues that the security market line (SML) criterion gives ambiguous performance signals for portfolio evaluation as discussed by the authors, and proposes an alternative criterion to measure portfolio performance against the efficient frontier in mean-variance space Since an index does not have to be chosen for this measurement, a degree of ambiguity is removed
Abstract: IN A RECENT ARTICLE in the Journal of Finance [4], Richard Roll argues that the Security Market Line (SML) criterion gives ambiguous performance signals for portfolio evaluation This note reports results of an empirical test of robustness of the SML criterion applied to different indices over two time periods The evidence suggests the ambiguity issue may be moot Roll argues that ambiguity results from the inability to decide upon a unique index to be used in the estimation of portfolio betas When a mean-variance inefficient index is used, portfolios can be ranked on the basis of vertical deviations from an empirically fit SML However, different inefficient indices will yield different SML's, and thus different rankings When a mean-variance efficient index is used, all observations will plot on the SML and it will be impossible to assign rankings to the portfolios As Roll demonstrates, it is possible that rankings can be reversed from one mean-variance inefficient index to another Mayers and Rice [3] take issue with the findings of Roll They do not question Roll's proof of the ambiguity of the SML criterion, but instead argue that the SML criterion can be used to identify superior performance By setting up a model with an informed investor and uninformed investors, they show that the SML criterion will designate inferior portfolio managers correctly, but may incorrectly designate superior portfolio managers Mayers and Rice claim that their conclusions do not warrant rejection of the SML criterion as a ranking device As Roll [5] points out in his reply, Mayers and Rice are missing the point because they assume that everyone agrees upon which market index is to be used An inefficient index is required to obtain rankings of portfolios, but there is no guarantee that the ranking reflects actual preference orderings of investors Roll goes on to argue that the SML criterion should be abandoned because of the ambiguity issue As an alternative criterion, he suggests measuring portfolio performance against the efficient frontier in mean-variance space Since an index does not have to be chosen for this measurement, a degree of ambiguity is removed Roll suggests that if the SML criterion is to be saved, it needs to be empirically demonstrated that commonly used indices do not rank portfolios very differently In the section that follows we examine the ambiguity issue empirically For
22 citations
TL;DR: In this paper, the effect of sampling error on the portfolio ranking was studied and it was shown that in order to keep the error at a reasonable level 5 percent, one needs 50-100 observations, a number that is rarely used in the MV comparison of portfolios.
Abstract: It is common to use historical data in calculating the rates of return of risky options, and these data are used to calculate the mean and the variance, which are employed in the MV preference ranking.
In this paper we study the effect of possible sampling error on the portfolio ranking. It is shown that in order to keep the error at a reasonable level 5 percent, one needs 50-100 observations, a number that is rarely used in the MV comparison of portfolios. The results are almost independent of the correlation between the portfolios.
11 citations
TL;DR: The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.
Abstract: This paper applies mathematical programming to cost-volume-profit (CVP) analysis under contribution margin uncertainty. Three CVP probabilistic chance-constraint models based on various safety-first criteria for decisions under uncertainty are presented and compared. It is shown that a break-even segment of the mean-standard deviation frontier is a set of optimal solutions for the proposed models. An operational parametric quadratic programming (QP) model is constructed, and the efficiency frontier is generated. The procedures for locating an optimal solution on the efficiency frontier are then presented. The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.
6 citations