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.

We propose a nonparametric kernel estimation method (KEM) that determines the optimal hedge ratio by minimizing the downside risk of a hedged portfolio, measured by conditional value‐at‐risk (CVaR). We also demonstrate that the KEM minimum‐CVaR hedge model is a convex optimization. The simulation results show that our KEM provides more accurate estimations and the empirical results suggest that, compared to other conventional methods, our KEM yields higher effectiveness in hedging the downside risk in the weather‐sensitive markets.