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Enhanced indexing using weighted conditional value at risk

Author

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  • Ruchika Sehgal

    (Indian Institute of Technology Delhi)

  • Aparna Mehra

    (Indian Institute of Technology Delhi)

Abstract

We propose an enhanced indexing portfolio optimization model that not only seeks to maximize the excess returns over and above the benchmark index but simultaneously control the risk by introducing a constraint on the weighted conditional value at risk (WCVaR) of the portfolio. The constraint in the proposed model can be seen as hedging the risk described by WCVaR of the portfolio. To carry out a comparative analysis of the proposed model, we also suggest an enhanced indexing CVaR model. We analyze the performance of the proposed model at various risk levels on eight publicly available financial data sets from Beasley OR library, and S&P 500, S&P BSE 500, NASDAQ composite, FTSE 100 index, and their constituents, for average returns, Sharpe ratio, and upside potential ratio. Empirical analysis exhibits superior performance of the portfolios from the proposed WCVaR model over the respective benchmark indices and additionally the optimal portfolios obtained from various other enhanced indexing models that exist in the literature. Furthermore, we present evidence of better performance of WCVaR model over the CVaR model for long-term investment horizons.

Suggested Citation

  • Ruchika Sehgal & Aparna Mehra, 2019. "Enhanced indexing using weighted conditional value at risk," Annals of Operations Research, Springer, vol. 280(1), pages 211-240, September.
    • Handle: RePEc:spr:annopr:v:280:y:2019:i:1:d:10.1007_s10479-019-03132-2
    DOI: 10.1007/s10479-019-03132-2
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    References listed on IDEAS

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    1. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
    2. Roman, Diana & Mitra, Gautam & Zverovich, Victor, 2013. "Enhanced indexation based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 228(1), pages 273-281.
    3. Parvez Ahmed & Sudhir Nanda, 2005. "Performance of Enhanced Index and Quantitative Equity Funds," The Financial Review, Eastern Finance Association, vol. 40(4), pages 459-479, November.
    4. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    5. de Paulo, Wanderlei Lima & de Oliveira, Estela Mara & do Valle Costa, Oswaldo Luiz, 2016. "Enhanced index tracking optimal portfolio selection," Finance Research Letters, Elsevier, vol. 16(C), pages 93-102.
    6. Renata Mansini & Włodzimierz Ogryczak & M. Speranza, 2007. "Conditional value at risk and related linear programming models for portfolio optimization," Annals of Operations Research, Springer, vol. 152(1), pages 227-256, July.
    7. Sant’Anna, Leonardo R. & Filomena, Tiago P. & Caldeira, João F., 2017. "Index tracking and enhanced indexing using cointegration and correlation with endogenous portfolio selection," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 146-157.
    8. N. Meade & J. E. Beasley, 2011. "Detection of momentum effects using an index out-performance strategy," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 313-326.
    9. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    10. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
    11. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    12. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    13. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.
    14. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    15. Meihua Wang & Chengxian Xu & Fengmin Xu & Hongang Xue, 2012. "A mixed 0–1 LP for index tracking problem with CVaR risk constraints," Annals of Operations Research, Springer, vol. 196(1), pages 591-609, July.
    16. Rudolf, Markus & Wolter, Hans-Jurgen & Zimmermann, Heinz, 1999. "A linear model for tracking error minimization," Journal of Banking & Finance, Elsevier, vol. 23(1), pages 85-103, January.
    17. Canakgoz, N.A. & Beasley, J.E., 2009. "Mixed-integer programming approaches for index tracking and enhanced indexation," European Journal of Operational Research, Elsevier, vol. 196(1), pages 384-399, July.
    18. Guastaroba, G. & Speranza, M.G., 2012. "Kernel Search: An application to the index tracking problem," European Journal of Operational Research, Elsevier, vol. 217(1), pages 54-68.
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    Cited by:

    1. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
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    3. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy, 2022. "Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion," Annals of Operations Research, Springer, vol. 313(2), pages 691-712, June.

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