CVaR-Cardinality Enhanced Indexation Optimization with Tunable Short-Selling Constraints

Enhanced-index-funds have attracted considerable attention from investors over the last decade, which aims at outperforming a benchmark index while maintaining a similar risk level. In this paper, we investigate an enhanced indexation methodology using Conditional Value-at-Risk (CVaR). In particular, we adopt CVaR of excess returns as risk measurement subject to cardinality constraint for controlling the tracking portfolio scale precisely, and tunable short-selling constraints for adjusting the margin of each risky asset adaptively within the budget of short-selling. As the resulted model is a mixed 0-1 binary program, we propose an improved hybrid heuristic method, where a customized relax-round-polish is embedded to improve the quality of the iterative population. Computational results on five standard data sets from OR-library show that our proposed method is generally superior to the naive portfolio strategy and the CVaR-LASSO method in terms of the out-of-sample excess return, Sharpe ratio, and maximum drawdown of the portfolio.