IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v76y2018icp28-37.html
   My bibliography  Save this article

Estimation of cardinality constrained portfolio efficiency via segmented DEA

Author

Listed:
  • Zhou, Zhongbao
  • Jin, Qianying
  • Xiao, Helu
  • Wu, Qian
  • Liu, Wenbin

Abstract

The cardinality constrained portfolio selection problem arises due to the empirical findings that investors tend to hold a limited number of assets. Yet the lack of fast computational methods for frontier of cardinality constrained portfolio investments makes the performance evaluation of this problem a long-standing challenge. Classic Data Envelopment Analysis (DEA) models have been justified valid in evaluating and ranking portfolio performance. Unfortunately, when it comes to the cardinality constrained portfolio selection problem, the DEA models fail to approximate the portfolio efficiency (PE) since the real frontier is discontinuous and not concave. To solve this problem, we propose a segmented DEA approach based on data segment points. A searching algorithm is introduced to approach the real segment points and proved to be valid. In each segment, the frontier is continuous and concave; hence, classic DEA models can be applied to evaluate the PE. The simulation results further indicate that the segmented DEA approach proposed in this paper is effective and practical in evaluating the cardinality constrained portfolio performance.

Suggested Citation

  • Zhou, Zhongbao & Jin, Qianying & Xiao, Helu & Wu, Qian & Liu, Wenbin, 2018. "Estimation of cardinality constrained portfolio efficiency via segmented DEA," Omega, Elsevier, vol. 76(C), pages 28-37.
    • Handle: RePEc:eee:jomega:v:76:y:2018:i:c:p:28-37
    DOI: 10.1016/j.omega.2017.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316306788
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2017.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    2. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.
    3. repec:bla:scandj:v:87:y:1985:i:4:p:594-604 is not listed on IDEAS
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Liu, Wenbin & Zhou, Zhongbao & Liu, Debin & Xiao, Helu, 2015. "Estimation of portfolio efficiency via DEA," Omega, Elsevier, vol. 52(C), pages 107-118.
    6. W. Briec & K. Kerstens & J. B. Lesourd, 2004. "Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 1-27, January.
    7. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    8. William N. Goetzmann & Alok Kumar, 2008. "Equity Portfolio Diversification," Review of Finance, European Finance Association, vol. 12(3), pages 433-463.
    9. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    10. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2011. "Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function," European Journal of Operational Research, Elsevier, vol. 210(1), pages 81-94, April.
    11. Murthi, B. P. S. & Choi, Yoon K. & Desai, Preyas, 1997. "Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 98(2), pages 408-418, April.
    12. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    13. Brandouy, Olivier & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2015. "Frontier-based vs. traditional mutual fund ratings: A first backtesting analysis," European Journal of Operational Research, Elsevier, vol. 242(1), pages 332-342.
    14. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    15. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    16. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    17. Duan Li & Xiaoling Sun & Jun Wang, 2006. "Optimal Lot Solution To Cardinality Constrained Mean–Variance Formulation For Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 83-101, January.
    18. Nalpas, Nicolas & Simar, Leopold & Vanhems, Anne, 2016. "Portfolio Selection in a Multi-Input Multi-Output Setting:a Simple Monte-Carlo-FDH Algorithm," LIDAM Discussion Papers ISBA 2016022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    20. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    21. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    22. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    23. Zulia Gubaydullina & Markus Spiwoks, 2009. "Portfolio diversification: an experimental study," Departmental Discussion Papers 140, University of Goettingen, Department of Economics.
    24. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    25. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    26. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
    27. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    28. Joro, Tarja & Na, Paul, 2006. "Portfolio performance evaluation in a mean-variance-skewness framework," European Journal of Operational Research, Elsevier, vol. 175(1), pages 446-461, November.
    29. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    30. Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April.
    31. Glawischnig, Markus & Sommersguter-Reichmann, Margit, 2010. "Assessing the performance of alternative investments using non-parametric efficiency measurement approaches: Is it convincing?," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 295-303, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiao, Helu & Ren, Tiantian & Zhou, Zhongbao & Liu, Wenbin, 2021. "Parameter uncertainty in estimation of portfolio efficiency: Evidence from an interval diversification-consistent DEA approach," Omega, Elsevier, vol. 103(C).
    2. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    3. Zhou, Zhongbao & Gao, Meng & Xiao, Helu & Wang, Rui & Liu, Wenbin, 2021. "Big data and portfolio optimization: A novel approach integrating DEA with multiple data sources," Omega, Elsevier, vol. 104(C).
    4. Tai Vo-Van & Ha Che-Ngoc & Nghiep Le-Dai & Thao Nguyen-Trang, 2022. "A New Strategy for Short-Term Stock Investment Using Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 887-911, February.
    5. Ioannis E. Tsolas, 2020. "Precious Metal Mutual Fund Performance Evaluation: A Series Two-Stage DEA Modeling Approach," JRFM, MDPI, vol. 13(5), pages 1-13, April.
    6. Zeng, Ximei & Zhou, Zhongbao & Gong, Yeming & Liu, Wenbin, 2022. "A data envelopment analysis model integrated with portfolio theory for energy mix adjustment: Evidence in the power industry," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Wenbin & Zhou, Zhongbao & Liu, Debin & Xiao, Helu, 2015. "Estimation of portfolio efficiency via DEA," Omega, Elsevier, vol. 52(C), pages 107-118.
    2. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    3. Kerstens, Kristiaan & Mazza, Paolo & Ren, Tiantian & Van de Woestyne, Ignace, 2022. "Multi-Time and Multi-Moment Nonparametric Frontier-Based Fund Rating: Proposal and Buy-and-Hold Backtesting Strategy," Omega, Elsevier, vol. 113(C).
    4. Zhou, Zhongbao & Xiao, Helu & Jin, Qianying & Liu, Wenbin, 2018. "DEA frontier improvement and portfolio rebalancing: An application of China mutual funds on considering sustainability information disclosure," European Journal of Operational Research, Elsevier, vol. 269(1), pages 111-131.
    5. Tarnaud, Albane Christine & Leleu, Hervé, 2018. "Portfolio analysis with DEA: Prior to choosing a model," Omega, Elsevier, vol. 75(C), pages 57-76.
    6. Tsolas, Ioannis E., 2014. "Precious metal mutual fund performance appraisal using DEA modeling," Resources Policy, Elsevier, vol. 39(C), pages 54-60.
    7. Martin Branda, 2016. "Mean-value at risk portfolio efficiency: approaches based on data envelopment analysis models with negative data and their empirical behaviour," 4OR, Springer, vol. 14(1), pages 77-99, March.
    8. Ruiyue Lin & Zhiping Chen & Qianhui Hu & Zongxin Li, 2017. "Dynamic network DEA approach with diversification to multi-period performance evaluation of funds," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 821-860, July.
    9. Lin, Ruiyue & Liu, Qian, 2021. "Multiplier dynamic data envelopment analysis based on directional distance function: An application to mutual funds," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1043-1057.
    10. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    11. Sepideh Kaffash & Marianna Marra, 2017. "Data envelopment analysis in financial services: a citations network analysis of banks, insurance companies and money market funds," Annals of Operations Research, Springer, vol. 253(1), pages 307-344, June.
    12. Adam, Lukáš & Branda, Martin, 2021. "Risk-aversion in data envelopment analysis models with diversification," Omega, Elsevier, vol. 102(C).
    13. Lin, Ruiyue & Li, Zongxin, 2020. "Directional distance based diversification super-efficiency DEA models for mutual funds," Omega, Elsevier, vol. 97(C).
    14. Kerstens, Kristiaan & Mounir, Amine & de Woestyne, Ignace Van, 2011. "Non-parametric frontier estimates of mutual fund performance using C- and L-moments: Some specification tests," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1190-1201, May.
    15. Andreu, Laura & Serrano, Miguel & Vicente, Luis, 2019. "Efficiency of mutual fund managers: A slacks-based manager efficiency index," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1180-1193.
    16. J. Francisco Rubio & Neal Maroney & M. Kabir Hassan, 2018. "Can Efficiency of Returns Be Considered as a Pricing Factor?," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 25-54, June.
    17. Solórzano-Taborga, Pablo & Alonso-Conde, Ana Belén & Rojo-Suárez, Javier, 2018. "Efficiency and Persistence of Spanish Absolute Return Funds || Eficiencia y persistencia de los fondos de retorno absolutos españoles," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 25(1), pages 186-214, Junio.
    18. Chang, Tsung-Sheng & Tone, Kaoru & Wu, Chen-Hui, 2021. "Nested dynamic network data envelopment analysis models with infinitely many decision making units for portfolio evaluation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 766-781.
    19. Xiao, Helu & Ren, Tiantian & Zhou, Zhongbao & Liu, Wenbin, 2021. "Parameter uncertainty in estimation of portfolio efficiency: Evidence from an interval diversification-consistent DEA approach," Omega, Elsevier, vol. 103(C).
    20. Ioannis E. Tsolas, 2020. "The Determinants of the Performance of Precious Metal Mutual Funds," JRFM, MDPI, vol. 13(11), pages 1-10, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:76:y:2018:i:c:p:28-37. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.