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A linear risk-return model for enhanced indexation in portfolio optimization

Enhanced indexation (EI) is the problem of selecting a portfolio that should produce excess return with respect to a given benchmark index. In this work, we propose a linear bi-objective optimization approach to EI that maximizes average excess return and minimizes underperformance over a learning period. Our model can be efficiently solved to optimality by means of standard linear programming techniques. On the theoretical side, we investigate conditions that guarantee or forbid the existence of a portfolio strictly outperforming the index. On the practical side, we support our model with extensive empirical analysis on publicly available real-world financial datasets, including comparison with previous studies, performance and diversification analysis, and verification of some of the proposed theoretical results on real data.