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A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns

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Abstract

This paper proposes a data envelopment analysis (DEA)-based portfolio efficiency evaluation approach integrated with a rebalancing method to help investors acquire efficient portfolios. Two fuzzy portfolio selection models with value at risk (VaR) and conditional value at risk (CVaR) as objectives are proposed under the credibilistic framework. The models are constrained by realistic constraints of short selling/no short selling, capital budget, bounds on investment in an asset, and minimum return desired by the investor. These models are used to compute the benchmark portfolios, which constitute the portfolio efficient frontier. Furthermore, random sample portfolios are generated individually for each model in compliance with their constraints. These random sample portfolios are evaluated in terms of their relative efficiency with risk (VaR or CVaR) as an input and return as an output using DEA. Bearing in mind the volatile nature of the investment market, negative returns are also considered for portfolio efficiency evaluation using the range directional model. Moreover, an efficiency frontier improvement algorithm is used to rebalance the inefficient random portfolios to make them efficient. The proposed approach provides an alternative to the investors to acquire benchmark portfolios using the traditional portfolio selection models. A detailed numerical illustration and an out of sample analysis with the Nifty 50 index from the National Stock Exchange, India, are presented to substantiate the proposed approach.

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Acknowledgements

We thank the Editor-in-Chief, the Associate Editor, and all the esteemed reviewers for helping us improve the presentation of the paper. “The third author, Arun Kumar, is supported by the Rajiv Gandhi National Fellowship for SC Candidates granted by University Grants Commission (UGC), New Delhi, India vide letter no. F1-17.1/2015-16/RGNF-2015-17-SC-DEL-8966/(SA-III/Website)”. “The fourth author, Sanjay Yadav, is supported by the National Fellowship for Other Backward Classes (OBC) granted by University Grants Commission (UGC), New Delhi, India vide letter no. F./2016-17/NFO-2015-17-OBC-DEL-34358/(SA-III/Website)”.

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Authors and Affiliations

  1. Department of Operational Research, University of Delhi, Delhi, India

    Pankaj Gupta, Mukesh Kumar Mehlawat, Arun Kumar & Sanjay Yadav

  2. University School of Basic and Applied Science, Guru Gobind Singh Indraprastha University, Delhi, India

    Abha Aggarwal

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  1. Pankaj Gupta
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  2. Mukesh Kumar Mehlawat
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  3. Arun Kumar
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  4. Sanjay Yadav
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  5. Abha Aggarwal
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Correspondence to Mukesh Kumar Mehlawat.

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Gupta, P., Mehlawat, M.K., Kumar, A. et al. A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns. Int. J. Fuzzy Syst. 22, 824–843 (2020). https://doi.org/10.1007/s40815-020-00801-4

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  • DOI: https://doi.org/10.1007/s40815-020-00801-4

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