Multidimensional extension of the Modern Portfolio Theory

Abstract

This thesis, titled Multidimensional Extension of the Modern Portfolio Theory, investigates the feasibility and value of expanding classical portfolio optimization beyond its traditional focus on return and risk. In response to the growing influence of sustainability concerns and regulatory capital requirements in institutional investing, the study integrates two additional dimensions: Environmental, Social, and Governance (ESG) scores and Market Solvency Capital Requirement (SCR) into the construction of the efficient frontier.

Using a dataset of 14 asset classes, the thesis constructs a four-dimensional optimization framework. Each asset class is characterized by expected return, volatility, ESG score, and SCR (calculated using Solvency II regulatory stress factors). Two complementary optimization models are developed: an a posteriori model that filters non-dominated portfolios from a fully enumerated universe, and an a priori model that simulates investor-specific preferences through scoring and lexicographic sorting. Portfolios are generated using tranche-based weight combinations with 3.75% granularity, ensuring transparency and completeness.

The results show that the inclusion of ESG and SCR does not significantly reshapes the efficient frontier. High-ESG portfolios tend to cluster in regions with moderate return and higher volatility, while SCR-efficient portfolios occupy the lower-return, lower-volatility quadrant. Compared to classical 2D portfolios, the 4D optimized allocations differ significantly, favoring assets like Euro Government Bonds and Core Infrastructure when sustainability or capital efficiency is prioritized. These findings confirm that ESG and SCR are not redundant with financial risk-return metrics and can be meaningfully integrated into optimization without distorting outcomes.

Moreover, the thesis demonstrates that such multidimensional optimization is computationally feasible and practically interpretable. Investor-specific portfolios generated under the a priori model (e.g., ESG-focused, return-maximizing, or SCR-conservative) illustrate the range of trade-offs that institutions may face. Importantly, the multidimensional model preserves financial performance while enhancing alignment with real-world regulatory and sustainability goals.

This research makes a novel theoretical contribution by treating ESG and SCR as formal optimization objectives rather than external constraints. It offers a replicable modeling approach for institutional investors seeking to construct portfolios that reflect the complexity of modern investment mandates. The findings reinforce that the efficient frontier is no longer two-dimensional: it is a multidimensional construct that must evolve to meet the intersecting demands of performance, risk management, and responsible capital allocation.