Optimization of the Enhanced Index Model

With the development of the domestic economy and the increase in household income, the demand for investment has been growing, and funds are widely favored for their safety and flexibility. Enhanced index funds combine the advantages of both passive and active management, with the potential to outperform the market and reduce tracking errors, attracting the attention of many investors. To address the risk that tracking portfolios may incur significant losses due to market index declines, this paper proposes the introduction of a non-parametric Mean Absolute Deviation (MAD) as a downside risk constraint in the enhanced index model, aiming to effectively control the downside risk of the tracking portfolio. Firstly, the study uses a non-parametric method to estimate the MAD and proves that this estimator is a convex function of the portfolio position. Secondly, an enhanced index model is constructed under the MAD constraint, where the objective function consists of a weighted sum of tracking error and excess return. Specifically, we use downside risk to measure tracking error. Finally, it is proven that the model is a convex optimization problem. Empirical research shows that the enhanced index model proposed in this paper, which considers the non-parametric MAD constraint, effectively controls downside risk.