CVaR-LASSO Enhanced Index Replication (CLEIR): outperforming by minimizing downside risk

ABSTRACT

Index-funds are one of the most popular investment vehicles among investors, with total assets indexed to the S&P500 exceeding $8.7 trillion at-the-end of 2016. Recently, enhanced-index-funds, which seek to outperform an index while maintaining a similar risk-profile, have grown in popularity. We propose an enhanced-index-tracking method that uses the linear absolute shrinkage selection operator (LASSO) method to minimize the Conditional Value-at-Risk (CVaR) of the tracking error. This minimizes the large downside tracking-error while keeping the upside. Using historical and simulated data, our CLEIR method outperformed the benchmark with a tracking error of $\sim 1\mathrm{\%}$. The effect is more pronounced when the number of the constituents is large. Using 50–80 large stocks in the S&P 500 index, our method closely tracked the benchmark with an alpha $2.55\mathrm{\%}$.

KEYWORDS:

• Stochastic programming
• conditional value-at-risk
• LASSO
• enhanced indexation

JEL CLASSIFICATION:

• G11
• D81
• C63

Acknowledgments

We thank Mark Taylor (Editor), the anonymous reviewer, for helpful discussions and useful suggestions. Yong Jin also acknowledges generous financial support of the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 25508217) and the Learning and Teaching Enhancement Grant (Project No.: 1.21.xx.8ADP). All errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Chen, Desai, and Krishnamurthy (2013) find that the magnitude of short sales is around $15.65\mathrm{\%}$ of net assets on average; thus, we choose a penalty level $s=1.5$, which limits the short sales up to $25\mathrm{\%}$.

² Following Goto and Xu (2015), we randomly select 300 stocks with careful imputation of the missing data using the value-weighted index returns, then calculate the mean vector and variance-covariance matrix as the true parameters to generate 30 years return vectors under the multivariate normal distribution assumptions. Next, we still use the ‘rolling horizon approach’ as the portfolio universes (1)-(4), and use the equal weighted portfolio returns as the benchmark.

Additional information

Funding

This work was supported by the Hong Kong Polytechnic University [The Learning and Teaching Enhancement Grant (Project No.: 1.21.xx.8ADP)];Research Grants Council, University Grants Committee [Project No. PolyU 25508217].