A cost-effective approach to portfolio construction with range-based risk measures

Abstract

In this paper, we introduce a new class of risk measures and the corresponding risk minimizing portfolio optimization problem. Instead of measuring the expected deviation of a daily return from a single target value, we propose to measure its deviation from a range of values centered on the single target value. By relaxing the definition of deviation, the proposed risk measure is robust to the variation of data input and thus the resulting risk-minimizing portfolio has a lower turnover rate and is resilient to outliers. To construct a practical portfolio, we propose to impose an ${\ell }_2$-norm constraint on the portfolio weights to stabilize the portfolio's out-of-sample performance. We show that for some cases of our proposed range-based risk measures, the corresponding portfolio optimization can be recast as a support vector regression problem. This allows us to tap into the machine learning literature on support vector regression and effectively solve the portfolio optimization problem even in high dimensions. Moreover, we present theoretical results on the robustness of our range-based risk minimizing portfolios. Simulation and empirical studies are conducted to examine the out-of-sample performance of the proposed portfolios.

Keywords:

• Portfolio optimization
• Transaction costs
• Risk measures
• Statistical learning theory
• ${\ell }_2$-regularized portfolios
• Support vector regression
• Robustness

JEL Classification:

• C31 – Multiple Variables - Quantile Regressions
• C55 – EconometricModeling - Large Data Sets: Modeling and Analysis
• D81 – Information
• Knowledge
• andUncertainty - Criteria for Decision-Making under Risk and Uncertainty
• G11 – GeneralFinancial Markets - Portfolio Choice/Investment Decisions

Open Scholarship

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Acknowledgments

Chi Seng Pun gratefully acknowledges Ministry of Education (Singapore), AcRF Tier 2 grant (Reference No: MOE2017-T2-1-044) and Nanyang Technological University Start-up Grant (Reference No: 04INS000248C230) for the funding of this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The data is openly available at https://data.mendeley.com/datasets/ndxfrshm74/3/files/6b7f4cd6-6996-4031-a002-f99701100f54

Additional information

Funding

Chi Seng Pun gratefully acknowledges Ministry of Education (Singapore), AcRF Tier 2 grant (Reference No: MOE2017-T2-1-044) and Nanyang Technological University, Start-up Grant (Reference No: 04INS000248C230) for the funding of this research.