Improved Computational Approach for Markowitz Portfolio Optimisation

This chapter presents and analyzes a technique for optimizing an n-asset portfolio that is both efficient and time-saving. In contrast to conventional methods in the literature, which require the specification of asset weights, the approach developed in this study enables portfolio optimization without the explicit introduction of weights. The chapter derives new formulae and provides theoretical validation to support the method’s soundness. A comparative analysis is conducted between this approach and commonly used optimization techniques—such as the Variance-Covariance method and the Generalized Reduced Gradient (GRG) algorithm implemented via the Microsoft Excel Solver. The results demonstrate that the proposed method is not only more powerful but also easier to apply in practice. Furthermore, the study includes a detailed example illustrating how to calculate an optimal portfolio using the new formulae for all 30 Dow Jones Industrial Average (DJIA) stocks. As such, the chapter also serves as a practical guide for teaching and learning mean-variance optimization, offering a more accessible application of the Markowitz model in real-world portfolio construction.