Systematically Formulating Investments for Carbon Offset by Multiple-Objective Portfolio Selection: Classifying, Evolving, and Optimizing

Our society is facing serious challenges from global warming and environmental degradation. Scientists have identified carbon dioxide as one of the causes. Our society is embracing carbon offset as a way to field the challenges. The purpose of carbon offset is trying to cancel out the large amounts of carbon dioxide by investing in projects that reduce or remove emissions elsewhere. Examples of carbon offset projects are planting trees, renewable energy projects, and capturing methane from landfills or farms. Not all carbon offset projects are equally effective. In stock markets, investors eagerly pursue carbon offset. Namely, investors favor carbon offset in addition to risk and return when investing. Therefore, investors supervise risk, return, and carbon offset. Investors’ pursuits raise the question of how to model carbon offset for investments. The traditional answer is to adopt carbon offset screening and engineer portfolios by stocks with good carbon offset ratings. However, Nobel Laureate Markowitz emphasizes portfolio selection rather than stock selection. Moreover, carbon offset is composed of multiple components, ranging from business, social, economic, and environmental aspects. This multifaceted nature requires more advanced models than carbon offset screening and portfolio selection. Within this context, we systematically formulate multiple-objective portfolio selection models that include carbon offset. Firstly, we extend portfolio selection and treat carbon offset as a whole. Secondly, we separate carbon offsets into different components and build models to monitor each component. Thirdly, we innovate a model to monitor each component’s expectation and mitigate each component’s risk. Lastly, we optimize the series of models and prove the models’ properties in theorems. Mathematically, this paper makes theoretical contributions to multiple-objective optimization, particularly by proving the consistency of efficient solutions during objective classification and model evolution, describing the structure of properly efficient sets for multiple quadratic objectives, and elucidating the optimization’s sensitivity analyses. Moreover, by coordinating the abstract objective function, our formulation is generalizable. Overall, this paper’s contribution is to model carbon offset investments through multiple-objective portfolio selection. This paper’s methodology is multiple-objective optimization. This paper’s achievements are to provide investors with greater precision and effectiveness than carbon offset screening and portfolio selection through engineering means and to mathematically prove the properties of the model.