| Popis: |
This paper explores strategies in portfolio optimization, focusing on integrating mean-variance optimization (MVO) frameworks with cardinality constraints to enhance investment decision-making. Using a combination of quadratic programming and mixed-integer linear programming, the Gurobi optimizer handles complex constraints and achieves computational solutions. The study compares two mathematical formulations of the cardinality constraint: the Complementary Model and the Big M Model. As cardinality increased, risk decreased exponentially, converging at higher cardinalities. This behavior aligns with the theory of risk reduction through diversification. Additionally, despite initial expectations, both models performed similarly in terms of root relaxation risk and execution time due to Gurobi's presolve transformation of the Complementary Model into the Big M Model. Root relaxation risks were identical while execution times varied slightly without a consistent trend, underscoring the Big M Model's versatility and highlighting the limitations of the Complementary Model. |
