On Intensively Criticizing and Envisioning the Research on Multiple-Objective Portfolio Selection from the Perspective of Capital Asset Pricing Models

Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have gradually realized additional objectives and have promisingly extended portfolio selection into multiple-objective portfolio selection. However, there hardly exists research to leap from multiple-objective portfolio selection to multiple-objective capital asset pricing models (as initiated by Markowitz and Sharpe in finance). Moreover, the extension is basically confined to the branches of mathematics, operations research, optimization, and computer sciences. Many researchers sufficiently review multiple-objective portfolio selection. However, the reviews are extensive. Instead, we intensively criticize and envision the research on multiple-objective portfolio selection from the perspective of capital asset pricing models by crystallizing the research limitations and heralding future directions. Specifically, we emphasize seven research limitations for multiple-objective portfolio optimization, multiple-objective capital asset pricing models, and multiple-objective zero-covariance capital asset pricing models. We also generalize from common three-objective portfolio selection to k-objective portfolio selection. Visually, we orchestrate figures to delineate the complexity. Theoretically, this paper heralds challenging but encouraging future directions. Pragmatically, this paper proposes a formulation for the multiple-objective nature of practical convolution in finance.