Portfolio Optimization Using a Block Structure for the Covariance Matrix

TLDR: In this article, a global minimum variance portfolio (GMVP) is constructed using an easy to calculate block structure for the covariance matrix of asset returns, which can be found analytically, and as long as simple and directly computable conditions are met, these weights are positive.

Abstract: Implementing in practice the classical mean-variance theory for portfolio selection often results in obtaining portfolios with large short sale positions. Also, recent papers show that, due to estimation errors, existing and rather advanced mean-variance theory-based portfolio strategies do not consistently outperform the naive 1/N portfolio that invests equally across N risky assets. In this paper, we introduce a portfolio strategy that generates a portfolio, with no short sale positions, that can outperform the 1/N portfolio. The strategy is investing in a global minimum variance portfolio (GMVP) that is constructed using an easy to calculate block structure for the covariance matrix of asset returns. Using this new block structure, the weights of the stocks in the GMVP can be found analytically, and as long as simple and directly computable conditions are met, these weights are positive.