Yang Tingting, Huang Xiaoxia
School of Economics, Changzhou University, Jiangsu, Changzhou China.
School of Economics and Management, University of Science and Technology Beijing, Beijing, China.
J Optim Theory Appl. 2022;195(2):723-747. doi: 10.1007/s10957-022-02116-w. Epub 2022 Oct 11.
Enhanced index tracking problem is the issue of selecting a tracking portfolio to outperform the benchmark return with a minimum tracking error. In this paper, we address the enhanced index tracking problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. First, we propose a nonlinear uncertain optimization model, i.e., uncertain mean-absolute downside deviation enhanced index tracking model. Then, we give the analytical solution of the proposed optimization model when stock returns take linear uncertainty distributions. Based on the solution, we find that tracking portfolio frontier is a continuous curve composed of at most different line segments. Furthermore, we give the condition that tracking portfolio return and risk increase with benchmark return and risk, respectively. Finally, we offer some experiments and show that our proposed model is effective in controlling the tracking error.
增强型指数跟踪问题是选择一个跟踪投资组合以在最小跟踪误差的情况下超越基准回报的问题。在本文中，我们基于不确定性理论解决增强型指数跟踪问题，其中股票回报被视为不确定变量而非随机变量。首先，我们提出一个非线性不确定优化模型，即不确定均值 - 绝对下行偏差增强型指数跟踪模型。然后，当股票回报呈线性不确定性分布时，我们给出所提出优化模型的解析解。基于该解，我们发现跟踪投资组合前沿是由至多不同线段组成的连续曲线。此外，我们给出跟踪投资组合回报和风险分别随基准回报和风险增加的条件。最后，我们进行了一些实验，并表明我们提出的模型在控制跟踪误差方面是有效的。
