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Quantile Regression Based Enhanced Indexing with Portfolio Rebalancing

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Abstract

In this article, an enhanced indexing (EI) model is put forward for portfolio selection to optimize a specific quantile of the return distribution of the benchmark index + alpha return combined with the conditional value at risk to control the downside risk in the portfolio. Constraints on short-selling and portfolio rebalancing with the transaction and holding costs are built in the models as a means of integrating real-life functionalities. The proposed models are linear or mixed integer linear programs. The out-of-sample performance comparison of the proposed model without short-selling with the benchmark index and an existing quantile based EI model on the data sets of several markets across the globe exhibit higher average returns and mean-risk ratios like Sharpe ratio and STARR, thus fulfilling the objective of EI. We also study the out-of-sample performance of our model with short-selling during financial meltdown periods.

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Notes

  1. We did not include indtrack7.txt and indtrack8.txt from the Beasley OR library (Canakgoz and Beasley 2009) because the data sets in the two tracks are large in size leading to a computational challenge in applying the rolling window analysis for solving the mixed integer model by Mezali and Beasley (2013) used in comparison in the empirical analysis.

  2. The t-statistics used in t-test is \(\frac{\mu _{s_1}-\mu _{s_2}}{\sigma _{s_1-s_2}}\), where \(\mu _{s_1}, \;\mu _{s_2}\) are the average returns from strategy \(s_1\) and \(s_2\) and \(\sigma _{s_1-s_2}\) is the standard deviation of the difference of returns from strategy \(s_1\) and \(s_2\).

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Authors and Affiliations

  1. University School of Automation and Robotics, Guru Gobind Singh Indraprastha University, East Delhi Campus, New Delhi, Delhi, India

    Ruchika Sehgal

  2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, Delhi, India

    Aparna Mehra

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  1. Ruchika Sehgal
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  2. Aparna Mehra
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Correspondence to Ruchika Sehgal.

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Sehgal, R., Mehra, A. Quantile Regression Based Enhanced Indexing with Portfolio Rebalancing. J. Quant. Econ. 21, 721–742 (2023). https://doi.org/10.1007/s40953-023-00355-w

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