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Stock Efficiency Evaluation Based on Multiple Risk Measures: A DEA-Like Envelopment Approach

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Abstract

This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis (DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.

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References

  1. Markowitz H M, Portfolio selection, The Journal of Finance, 1952, 7(1): 77–91.

    Google Scholar 

  2. Xu Y H, Li Z F, and Tan K S, Optimal investment with noise trading risk, Journal of Systems Science & Complexity, 2008, 21(4): 519–526.

    Article  MathSciNet  MATH  Google Scholar 

  3. Dong Y H, Xu C, and Wu S, Pricing a chained dynamic fund protection under Vasicek interest rate model with stochastic barrier, Journal of Systems Science & Complexity, 2019, 32(6): 1659–1674.

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang H, Wang C, and Fang Z, Portfolio selection with random liability and affine interest rate in the mean-variance framework, Journal of Systems Science and Information, 2017, 5(3): 229–249.

    Article  Google Scholar 

  5. Deng X and Liu Y, A high-moment trapezoidal fuzzy random portfolio model with background risk, Journal of Systems Science & Information, 2018, 6(1): 1–28.

    Article  Google Scholar 

  6. Zhou Z, Maximum principle of optimal stochastic control with terminal state constraint and its application in finance, Journal of Systems Science & Complexity, 2018, 31(4): 907–926.

    Article  MathSciNet  MATH  Google Scholar 

  7. Li C L, Liu Z M, and Wu J B, The stochastic maximum principle for a jump-diffusion mean-field model involving impulse controls and applications in finance, Journal of Systems Science & Complexity, 2020, 33(1): 26–42.

    Article  MathSciNet  MATH  Google Scholar 

  8. Morey M R and Morey R C, Mutual fund performance appraisals: A multi-horizon perspective with endogenous benchmarking, Omega, 1999, 27: 241–258.

    Article  MathSciNet  Google Scholar 

  9. Charnes A, Cooper W W, and Rhodes E L, Measuring the efficiency of decision making units, European Journal of Operational Research, 1978, 2(6): 429–444.

    Article  MathSciNet  MATH  Google Scholar 

  10. Xi W and Cheng X R, The difference of capital input and productivity in service industries: Based on four stages bootstrap-DEA model, Journal of Systems Science & Information, 2018, 6(4): 320–335.

    Article  Google Scholar 

  11. Murthi B P S, Choi Y K, and Desai P, Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach, European Journal of Operational Research, 1997, 98(2): 408–418.

    Article  MATH  Google Scholar 

  12. Basso A and Funari S, The role of fund size in the performance of mutual funds assessed with DEA models, European Journal of Finance, 2017, 23(4/6): 457–473.

    Article  Google Scholar 

  13. Hassan A, Chachi A, and Munshi M R, Performance measurement of Islamic mutual funds using DEA method, Journal of Islamic Accounting and Business Research, 2020, 31(8): 1481–1496.

    Article  Google Scholar 

  14. Joro T and Na P, Portfolio performance evaluation in a mean-variance-skewness framework, European Journal of Operational Research, 2006, 175(1): 446–461.

    Article  MATH  Google Scholar 

  15. Briec W, Kerstens K, and Jokung O, Mean-variance-skewness portfolio performance gauging a general shortage function and dual approach, Management Science, 2007, 53(1): 135–149.

    Article  MATH  Google Scholar 

  16. Briec W and Kerstens K, Multi-horizon Markowitz portfolio performance appraisals a general approach, Omega, 2009, 37(1): 50–62.

    Article  Google Scholar 

  17. Lamb J D and Tee K H, Data envelopment analysis models of investment funds, European Journal of Operational Research, 2012, 216(3): 687–696.

    Article  MathSciNet  MATH  Google Scholar 

  18. Branda M, Reformulations of input-output oriented DEA tests with diversification, Operations Research Letters, 2013, 41(5): 516–520.

    Article  MathSciNet  MATH  Google Scholar 

  19. Basso A and Funari S, A data envelopment analysis approach to measure the mutual fund performance, European Journal of Operational Research, 2001, 135(3): 477–492.

    Article  MATH  Google Scholar 

  20. Basso A and Funari S, Measuring the performance of ethical mutual funds: A DEA approach, Journal of the Operational Research Society, 2003, 54(5): 521–531.

    Article  MATH  Google Scholar 

  21. Gregoriou G N, Sedzro K, and Zhu J, Hedge fund performance appraisal using data envelopment analysis, European Journal of Operational Research, 2005, 164(2): 555–571.

    Article  MATH  Google Scholar 

  22. Branda M and Kopa M, DEA-risk efficiency and stochastic dominance efficiency of stock indices, Journal of Economics and Finance, 2012, 62(2): 106–124.

    Google Scholar 

  23. Chen H H, Stock selection using data envelopment analysis, Industrial Management & Data Systems, 2008, 108(9): 1255–1268.

    Article  Google Scholar 

  24. Zhao X J and Zhang H S, Application of Malmquist index in equity mutual funds evaluation in China, Systems Engineering — Theory & Practice, 2010, 30(4): 646–653.

    Google Scholar 

  25. Ismail M K A, Salamudin N, Rahman N M N A, et al., DEA portfolio selection in Malaysian stock market, 2012 International Conference on Innovation Management and Technology Research (ICIMTR), Malaysia, 2012.

  26. Chi G T, Wu H W, and Yan D W, Optimal model of loan portfolio based on the higher central-moment constraints, Systems Engineering — Theory & Practice, 2012, 32(2): 257–267.

    Google Scholar 

  27. Yan D, Hu Y, and Lai K, A nonlinear interval portfolio selection model and its application in banks, Journal of Systems Science & Complexity, 2018, 31(3): 696–733.

    Article  MathSciNet  MATH  Google Scholar 

  28. Leland H E, Beyond mean-variance: Performance measurement in a nonsymmetrical world, Financial Analysts Journal, 1999, 55(1): 27–36.

    Article  Google Scholar 

  29. Markowitz H M, Portfolio Selection: Efficient Diversification of Investments, Yale University Press, New Haven, 1959.

    Google Scholar 

  30. Bawa V S and Lindenberg E B, Capital market equilibrium in a mean-lower partial moment framework, Journal of Financial Economics, 1977, 5(2): 189–200.

    Article  Google Scholar 

  31. Konno H and Yamazaki H, Mean absolute deviation portfolio model and its application to Tokyo stock market, Management Science, 1991, 37(1): 519–531.

    Article  Google Scholar 

  32. Cheng P and Wolverton M L, MPT and the downside risk framework: A comment on two recent studies, Journal of Real Estate Portfolio Management, 2001, 7(2): 125–131.

    Article  Google Scholar 

  33. Chen Z and Lin R, Mutual fund performance evaluation using data envelopment analysis with new risk measures, OR Spectrum, 2006, 28(3): 375–398.

    Article  MathSciNet  MATH  Google Scholar 

  34. Banker R D, Charnes A, and Cooper W W, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 1984, 30(9): 1078–1092.

    Article  MATH  Google Scholar 

  35. Färe R, Grosskopf S, and Lovell C A K, The Measurements of Efficiency of Production, Springer, Dordrecht, 1985.

    Book  Google Scholar 

  36. Farrell M J, The measurement of productive efficiency, Journal of the Royal Statistical Society, 1957, 120(3): 253–290.

    Article  Google Scholar 

  37. Wu J and Liang L, A DEA model for identifying critical input-output performance measures, Journal of Systems Science & Complexity, 2012, 25(2): 275–286.

    Article  MathSciNet  MATH  Google Scholar 

  38. Dai Q Z, Li L, Lei X Y, et al., Considering monopoly maintenance cost for an automobile purchase in China: A DEA-based approach, Journal of Systems Science & Complexity, 2019, 32(4): 1167–1179.

    Article  Google Scholar 

  39. Markowitz H, Todd P, Xu G L, et al., Computation of mean-semivariance efficient sets by the Critical Line Algorithm, Annals of Operations Research, 1993, 45(1): 307–317.

    Article  MathSciNet  MATH  Google Scholar 

  40. Färe R and Lovell C A K, Measuring the technical efficiency of production, Journal of Economic Theory, 1978, 19(1): 150–162.

    Article  MathSciNet  MATH  Google Scholar 

  41. Färe R, Grosskopf S, and Lovell C A K, Production Frontiers, Cambridge University Press, Cambridge, 1994.

    Google Scholar 

  42. Russell R R, Measures of technical efficiency, Journal of Economic Theory, 1985, 35(1): 109–126.

    Article  MathSciNet  MATH  Google Scholar 

  43. Tone K, A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 2001, 130(3): 498–509.

    Article  MathSciNet  MATH  Google Scholar 

  44. Shi Y, Yang Z F, Yan H, et al., Delivery efficiency and supplier performance evaluation in China’s e-retailing industry, Journal of Systems Science & Complexity, 2017, 30(2): 144–162.

    Google Scholar 

  45. Thompson R G, Lee E, and Thrall R M, DEA/AR-efficiency of US independent oil/gas producers over time, Computers & Operations Research, 1992, 19(5): 377–391.

    Article  Google Scholar 

  46. Thompson R G, Brinkmanne E J, Dharmapala P S, et al., DEA/AR profit ratios and sensitivity of 100 large US banks, European Journal of Operational Research, 1997, 98(2): 213–229.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Management, University of Science and Technology of China, Hefei, 230026, China

    Jun Li, Hengxuan Gao, Yongjun Li, Xi Jin & Liang Liang

  2. School of Management, Hefei University of Technology, Hefei, 230009, China

    Jun Li, Hengxuan Gao, Yongjun Li, Xi Jin & Liang Liang

Authors
  1. Jun Li
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  2. Hengxuan Gao
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  3. Yongjun Li
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  4. Xi Jin
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  5. Liang Liang
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Corresponding authors

Correspondence to Jun Li, Hengxuan Gao, Yongjun Li, Xi Jin or Liang Liang.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 72071192, 71671172, the Anhui Provincial Quality Engineering Teaching and Research Project Under Grant No. 2020jyxm2279, the Anhui University and Enterprise Cooperation Practice Education Base Project under Grant No. 2019sjjd02, Teaching and Research Project of USTC (2019xjyxm019, 2020ycjg08), and the Fundamental Research Funds for the Central Universities (WK2040000027).

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Li, J., Gao, H., Li, Y. et al. Stock Efficiency Evaluation Based on Multiple Risk Measures: A DEA-Like Envelopment Approach. J Syst Sci Complex 35, 1480–1499 (2022). https://doi.org/10.1007/s11424-022-0034-y

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  • DOI: https://doi.org/10.1007/s11424-022-0034-y

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