DISCOVERING ZERO-COVARIANCE-PORTFOLIO CURVES FOR CAPITAL ASSET PRICING MODELS OF MULTIPLE-OBJECTIVE PORTFOLIO SELECTION

Abstract

Markowitz originates portfolio selection as the birth-place of modern finance. Sharpe originates capital asset pricing models (CAPM) as one quintessence of modern finance. Black and Fama then discovered the existence of a unique zero-covariance portfolio on the minimum-variance frontier. Fama and Roll further proved their CAPM. Recently, researchers have gradually realized additional objectives and extended portfolio selection into multiple-objective portfolio selection. However, there is still limited research to leap from multiple-objective portfolio selection to capital asset pricing models of multiple-objective portfolio selection. In such an area, this paper contributes to the literature as follows: First, we prove the existence of a (whole) curve of the zero-covariance portfolios for a 3-objective model. Second, we extend traditional locating and propose locating a unique portfolio on the curve. Lastly, we extend general k-objective models. This paper acts as a theoretical foothold for accomplishing capital asset pricing models of multiple-objective portfolio selection.