Measuring sustainable development goals: an application of modern portfolio theory on sustainability systems

This work presents an application of the modern portfolio theory (MPT). The United Nations 2030 Agenda of sustainable development goals establishes 17 sustainable development goals (SDGs) and 169 targets each associated with indicators, integrating the economic, social and environmental dimensions of sustainable development. This constitutes a complex system to be used by more than 150 countries having different priorities and levels of development. Concerning the 2030 Agenda Goals, MPT can help to define strategies to handle resource allocation problems. In economics, MPT appraises that when choosing a portfolio of assets looking for returns, some investors prefer fewer risks; others accept higher risks. To optimize the countries’ path to sustainability, the decision makers may distribute their resources, acting similarly to an investor. In this case, an SDG corresponds to a portfolio and the assets to the indicators associated with a given Goal. Constructing an efficient frontier of optimal portfolios of assets, MPT provides a method to obtain the maximum possible expected returns for a given level of risk and, besides, the risks and expected returns involved in a weighting choice. The present work restricts the analyses to the indicators of Goal 7 (affordable and clean energy), related to energy sustainability, for the five BRICS countries. This choice leads to an ensemble of situations that highlights the applicability of MPT to sustainability. Calculations are presented in detail for Brazil, and a general discussion is presented for the BRICS. The present approach considers the main features of a multi-criteria decision-making method, except the ranking of options by the decision makers.