Cardinality versusq-norm constraints for index tracking
提出用q-范数约束替代基数约束来构建指数追踪组合，通过混合启发式算法求解优化问题，并用真实金融数据比较两种方法的优劣，帮助投资者确定最优成分股数量及权重。
Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating portfolio. In this paper, we propose an alternative based on imposing a constraint on the q-norm (0 < q < 1) of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimization viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimization problems. The empirical analysis of real-world financial data allows us to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.