An Efficient Optimization Approach for a Cardinality-Constrained Index Tracking Problem

摘要

In the practical business environment, portfolio managers often facebusiness-driven requirements that limit the number of constituents in theirtracking portfolio. A natural index tracking model is thus to minimize atracking error measure while enforcing an upper bound on the number of assetsin the portfolio. In this paper we consider such a cardinality-constrainedindex tracking model. In particular, we propose an efficient nonmonotoneprojected gradient (NPG) method for solving this problem. At each iteration,this method usually solves several projected gradient subproblems. We show thateach subproblem has a closed-form solution, which can be computed in lineartime. Under some suitable assumptions, we establish that any accumulation pointof the sequence generated by the NPG method is a local minimizer of thecardinality-constrained index tracking problem. We also conduct empirical teststo compare our method with the hybrid evolutionary algorithm and the hybridhalf thresholding algorithm \cite{L1/2} for index tracking. The computationalresults demonstrate that our approach generally produces sparse portfolios withsmaller out-of-sample tracking error and higher consistency between in-sampleand out-of-sample tracking errors. Moreover, our method outperforms the othertwo approaches in terms of speed.