Selecting portfolios for composite indexes: application of Modern Portfolio Theory to competitiveness

This work presents an application of the Modern Portfolio Theory (MPT) to weight and select indicators for a composite index. MPT is based on the assumption that most of the choices of different states of a given system involve the trade-off between risk and return. In finance, MPT considers that given a set of possible choices for investments, some decision makers may prefer fewer risks while others are willing to accept a higher risk investment. MPT provides the risks and expected returns involved in a given weighted choice and at the same time the level of benefits achieved by this decision. The use of this theory allows constructing an efficient frontier, an optimal set of indicators (portfolio), such that the weighted composite indicator is optimized for a given level of risk, volatility or uncertainty. A discussion on the choice of the best portfolios, i.e., the best-expected level of returns for a given level of risk is presented. The present work proposes to apply MPT to calculate the composite competitiveness indicators of the group of five countries denominated as BRICS (Brazil, Russia, India, China, and South Africa). The input indicators are obtained from the Global Competitiveness Index (GCI) dataset. As an example of the possible applications of MPT to weight composite indicators, a detailed calculation is presented for the case of Brazil. A discussion on the competitiveness of these five countries is given based on the same approach. The study has implications since it provides the composition of portfolios that allows using the principles of MPT as a strategy to handle resource allocation problems. To the best of our knowledge, this is the first study in which the Modern Portfolio Theory is used to analyze composite indexes and in particular performance of countries. This approach allows decision makers to establish policies and strategies to allocate resources through weighting indicators in a composite index, knowing the risks and returns involved in a given choice.