Two new mean–variance enhanced index tracking models based on uncertainty theory

Abstract

The enhanced index tracking (EIT) problem is concerned with selecting a tracking portfolio that achieves an excess return over a given benchmark with a minimum tracking error. This paper explores the EIT problem by providing two new mean–variance EIT models based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables and stock return distributions are estimated by experts instead of from historical data. First, this paper formulates an uncertain enhanced index tracking (UEIT) model and analyzes the characteristic of the UEIT frontier. Then to reduce the tracking portfolio’s risk, this paper adds a risk index (RI) constraint to the UEIT model and proposes a UEIT-RI model. Next, by comparing the UEIT and UEIT-RI models this paper gives the advantages of the two models. Investors can choose the model according to their preferences. Finally, this paper conducts numerical examples to illustrate the application of the two models and the analysis results.