CVaR-cardinality enhanced indexation optimization with tunable short-selling constraints

ABSTRACT

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 article, 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.

KEYWORDS:

• Enhanced indexation
• CVaR
• cardinality
• out-of-sample analysis
• mixed-integer program

JEL CLASSIFICATION:

• G11
• C44
• C61

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The cardinality constraint is $\parallel x{\parallel }_0\le s$ with prescribed $s\in {\mathbb{Z}}_{+}$ in order to restrict the scale of the constructed portfolio.

² The enhanced indexation model is to add an ${\mathrm{\ell }}_{1/2}$ regularized term (i.e. ${\mathrm{\ell }}_{1/2}$ norm) to a trade-off objective function between TE and ER. See model (2.3) of Zhao et al. (2019) for details.

³ The AQP method is designed to solve a tractable quadratic subproblem and an ${\mathrm{\ell }}_{1/2}$ regularized subproblem with closed-form solution alternately. See the iterative process in Section 3 of Zhao et al. (2019) for details.

⁴ See Algorithm 2 of the subsection 'Improved hybrid heuristic method' for details.

⁵ See https://www.ibm.com/analytics/cplex-optimizer for a detailed introduction.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11571271,11971372,71501155,11601409].