On Preliminarily Exploring Multiple-Objective Capital Asset Pricing Models for the Investments of Carbon Offset: Heuristically Proving Different Tangent Planes

Our environment deteriorates primarily due to the emissions of carbon dioxide. Scientists and entrepreneurs promote carbon offset to reduce the emissions. Scientists and investors explore the investments of carbon offset. Some scientists encouragingly construct portfolio selection models but do not completely optimize them. Some scientists encouragingly construct capital asset pricing models (CAPM) but do not completely justify them. Under such contexts, this paper proposes a model of multiple-objective portfolio selection (MOPS) and preliminarily explores multiple-objective capital asset pricing models (MOCAPM). By the classical transition from portfolio selection to CAPM, we introductorily conjecture the extended transition from MOPS to MOCAPM. Specifically, we prove mathematical properties for the model. For instance, its minimum-variance surface is convex, and its feasible region is bounded by the convex surface. We examine whether a point on the minimum-variance surface is nondominated. By the properties, we heuristically prove different tangent planes for MOCAPM (instead of the unique tangent line for CAPM). We tentatively hint the conditions for a unique tangent plane. This paper acts as a footstep of the introductory conjecture.