The paper focuses on investors whose strength of interest in sustainability issues (such as environmental, social, and governance) causes ESG to become a third criterion alongside risk and return in portfolio selection. This causes the efficient frontier to become an efficient surface. This means that an investor’s optimal portfolio is no longer the point of most preferred risk/return tradeoff on the mean-variance (M-V) efficient frontier, but is the point of most preferred risk/return/ESG tradeoff on the investor’s M-V-ESG efficient surface. However, to find such a point requires non-trivial ESG integration which is the name given to the process of integrating ESG into the portfolio construction process after screening. With the third objective transporting the problem into 3D-space, it is difficult to search the efficient surface in any kind of comprehensive fashion using M-V based or other bi-criterion techniques as this is akin to a 2-dimensional being trying to view a 3-dimensional object. To remedy the situation, the paper proposes a tri-criterion approach that computes efficient surfaces and special non-contour curves (called NC-efficient fronts in the paper) that are stretched across the efficient surface so as to dragnet it for the points of best ESG integration within it. Using the methodology and data from the S&P500, the paper conducts computational tests on problems with up to 500 securities and under different constraint conditions so as to know what to expect from the new approach over a range of situations.

本文重点关注投资者，他们对可持续发展问题（如环境、社会和治理）的兴趣使 ESG 成为投资组合选择中与风险和回报并列的第三个标准。这导致有效边界成为有效表面。这意味着投资者的最优投资组合不再是均值方差 (MV) 有效边界上最偏好的风险/回报权衡点，而是投资者 MV-ESG 效率边界上最偏好的风险/回报/ESG 权衡点表面。然而，要找到这样一个点需要非平凡的 ESG 整合，这是在筛选后将 ESG 整合到投资组合构建过程中的过程的名称。第三个目标是将问题转移到 3D 空间中，很难使用基于 MV 或其他双准则技术以任何类型的综合方式搜索有效表面，因为这类似于试图查看 3 维对象的 2 维对象。为了补救这种情况，本文提出了一种三准则方法，该方法计算有效曲面和特殊的非轮廓曲线（在本文中称为 NC-efficient fronts），这些曲线在有效曲面上拉伸，以便将其拉网以获得最佳点其中的 ESG 整合。本文使用标准普尔 500 指数的方法和数据，在不同约束条件下对多达 500 只证券的问题进行了计算测试，以了解在一系列情况下对新方法的期望。