Index tracking model, downside risk and non-parametric kernel estimation

Abstract

In this paper, we propose an index tracking model with the conditional value-at-risk (CVaR) constraint based on a non-parametric kernel (NPK) estimation framework. In theory, we demonstrate that the index tracking model with the CVaR constraint is a convex optimization problem. We then derive NPK estimators for tracking errors and CVaR, and thereby construct the NPK index tracking model. Monte Carlo simulations show that the NPK method outperforms the linear programming (LP) method in terms of estimation accuracy. In addition, the NPK method can enhance computational efficiency when the sample size is large. Empirical tests show that the NPK method can effectively control downside risk and obtain higher excess returns, in both bearish and bullish market environments.

Some new efficient mean–variance portfolio selection models

“…Various efforts have been made to mitigate the sensitivity of the optimal solution of the Markowitz mean-variance model to parameter fluctuations. (See, e.g., Yao, Li, and Li (2016), Huang, Li, and Yao (2018), Yang, Wen, Liu, Li, and Huang (2019)). Wolf (2003, 2004a) proposed a method utilizing the weighted average of a low-variance target estimator matrix, b Σ target , and the sample covariance matrix rather than the sample covariance matrix.…”

“…Various efforts have been made to mitigate the sensitivity of the optimal solution of the Markowitz mean–variance model to parameter fluctuations. (See, e.g., Yao, Li, and Li (2016), Huang, Li, and Yao (2018), Yang, Wen, Liu, Li, and Huang (2019)).…”