A new uncertain enhanced index tracking model with higher-order moment of the downside

Enhanced index tracking (EIT) problem is concerned with selecting a tracking portfolio to beat the benchmark on return while having the minimum tracking error. This paper addresses the EIT problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. Under the framework of uncertainty theory, the paper proposes a new uncertain EIT model where the higher-order moment of the downside is used as the tracking error measure, as higher-order moment makes the model more widely applicable and the downside risk is in line with investors’ perception of risk. Besides, some realistic constraints are considered in the new uncertain EIT model. Then, the properties of the proposed model are discussed. To solve the model, we proposed, which is a nonlinear integer programming problem, a meta-heuristic algorithm presented. The efficiency of the algorithm and the applications of the proposed model are illustrated through numerical experiments.