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This paper proposes a portfolio optimization model for the Maximal Predictability Portfolio (MPP) construction problem with a cardinality constraint that can be formulated using discrete variables. The problem becomes a mixed integer quadratic programming problem with the non-convex constraint. Therefore, we propose an algorithm to find good-quality solutions quickly. The proposed algorithm is a simple two-step calculation method based on an existing algorithm that repeats to solve the quadratic programming problem. First, we adopt the solution obtained from the MPP construction problem without cardinality constraints as the initial solution, and then we calculate the MPP construction problem with the cardinality constraint using the initial solution. Furthermore, we propose an improvement approach by reducing the number of discrete variables to solve larger-scale problems, such as 1,500 candidate stocks and 1,000 scenarios. In addition, we appeal that the MPP with the cardinality constraint can suppress transaction costs better than the MPP without the cardinality constraint, thereby resulting in better investment performance.
This paper proposes a portfolio optimization model for the Maximal Predictability Portfolio (MPP) construction problem with a cardinality constraint that can be formulated using discrete variables. The problem becomes a mixed integer quadratic programming problem with the non-convex constraint. Therefore, we propose an algorithm to find good-quality solutions quickly. The proposed algorithm is a simple two-step calculation method based on an existing algorithm that repeats to solve the quadratic programming problem. First, we adopt the solution obtained from the MPP construction problem without cardinality constraints as the initial solution, and then we calculate the MPP construction problem with the cardinality constraint using the initial solution. Furthermore, we propose an improvement approach by reducing the number of discrete variables to solve larger-scale problems, such as 1,500 candidate stocks and 1,000 scenarios. In addition, we appeal that the MPP with the cardinality constraint can suppress transaction costs better than the MPP without the cardinality constraint, thereby resulting in better investment performance.
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