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Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model

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Abstract

Investment decision making, or portfolio selection, can be a complicated process affected by many factors. However, there is no doubt that two aspects are usually understood by investors most intensively—return and risk. What is the most suitable combination of return and risk for a particular investment strategy? Well-known mean–variance model can answer this question. However, this concept is burdened by some drawbacks. The main one is a type of implemented risk measure. To eliminate this shortage, a concept of semivariance was developed. However, this improvement cannot resist an instability of the typical uncertainty, i. e. unstable development of return and risk over time. This significant aspect of an investment decision making can be considered by a fuzzified mean-semivariance model. Then the vague return and risk are designed as triangular fuzzy numbers. The proposed fuzzy mean-semivariance model is solved by fuzzy programming techniques. Contribution of a designed methodological process for a portfolio selection under unstable uncertainty is demonstrated on making a portfolio from the stocks traded on the RM-SYSTÉM Czech Stock Exchange. The results are analyzed and confronted with output of more commonly used mean-semivariance model from the algorithmic-application perspective.

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Notes

  1. Asset also represents the market portfolio necessary for fuzzy semivariance concept.

  2. The market portfolio from fourteen stocks is composed under naive strategy.

  3. The matrices of semicovariances are large to be included in this paper.

References

  • Ang JS, Chua JH (1979) Composite measures for the evaluation of investment performance. J Financ Quant Anal 14:361–384

    Article  Google Scholar 

  • Ballestero E (2005) Mean-semivariance efficient frontier: a downside risk model for portfolio selection. Appl Math Financ 12:1–15

    Article  Google Scholar 

  • Balzer LA (1994) Measuring investment risk: a review. J Invest 3:47–58

    Article  Google Scholar 

  • Barro D, Canestrelli E (2014) Downside risk in multiperiod tracking error models. Cent Eur J Oper Res 22:263–283

    Article  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manage Sci 17:141–164

    Article  Google Scholar 

  • Borovička A (2020) Stock portfolio selection via mean-semivariance model. Quantitative methods in economics—multiple criteria decision making XX. Púchov, 27.05.2020–29.05.2020. University of Economics, Bratislava, pp 13–20

    Google Scholar 

  • Butler KC, Joaquin DC (2002) Are the gains from international portfolio diversification exaggerated? The influence of downside risk in bear markets. J Int Money Financ 21:981–1011

    Article  Google Scholar 

  • Cheklov A, Uryasev S, Zabarankin M (2003) Portfolio optimization with drawdown constraint. In: Scherer B (ed) Asset and liability management tools. Risk Books, London, pp 263–278

    Google Scholar 

  • Chen W, Wang Y, Zhang J, Lu S (2017) Uncertain portfolio selection with high-order moments. J Intell Fuzzy Syst 33:1397–1411

    Article  Google Scholar 

  • Chen W, Li S-S, Zhang J, Mehlawat M (2020) A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model. Soft Comput 24:2515–2526

    Article  Google Scholar 

  • Chu TC, Tsao CT (2002) Ranking fuzzy numbers with an area between the centroid point and the original point. Comput Math Appl 43:111–117

    Article  Google Scholar 

  • Dorohonceanu B, Marin B (2002) A simple method for comparing fuzzy numbers. CiteSeerX Scientific Literature Digital Library and Search Engine

  • Estrada J (2007) Mean-semivariance behavior: downside risk and capital asset pricing. Int Rev Econ Financ 16:169–185

    Article  Google Scholar 

  • Glawischnig M, Seidl I (2013) Portfolio optimization with serially correlated, skewed and fat tailed index returns. Cent Eur J Oper Res 21:153–176

    Article  Google Scholar 

  • Grossman SJ, Zhou Z (1993) Optimal investment strategies for controlling drawdowns. Math Financ 3:241–276

    Article  Google Scholar 

  • Gupta M, Bhattacharjee D (2010) Multi objective problem in fuzzy environment where resources are triangular fuzzy number. Eur J Sci Res 46:99–106

    Google Scholar 

  • Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Set Syst 47:81–86

    Article  Google Scholar 

  • Hogar W, Warren J (1974) Toward the development of an equilibrium capital market model based on semi-variance. J Financ Quant Anal 9:1–11

    Article  Google Scholar 

  • Huang X (2007) Portfolio selection with fuzzy returns. J Intell Fuzzy Syst 18:383–390

    Google Scholar 

  • Huang X (2008) Mean-semivariance models for fuzzy portfolio selection. J Comput Appl Math 217:1–8

    Article  Google Scholar 

  • Huang D, Zhu S, Fabozzi FJ, Fukushima M (2010) Portfolio selection under distributional uncertainty: a relative robust CVaR approach. Eur J Oper Res 203:185–194

    Article  Google Scholar 

  • Janková Z (2019) Comparison of portfolios using Markowitz and downside risk theories on the Czech stock market. Innovation management, entrepreneurship and sustainability 2019. Prague, 29.05.2020–31.05.2020. Prague University of Economics and Business, Prague, pp 291–303

    Google Scholar 

  • Jansen DW, Vries CG (1991) On the frequency of large stock returns: putting booms and busts into perspective. Rev Econ Stat 73:18–24

    Article  Google Scholar 

  • Kara G, Özmen A, Weber G-H (2019) Stability advances in robust portfolio optimization under parallelepiped uncertainty. Cent Eur J Oper Res 27:241–261

    Article  Google Scholar 

  • Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to the Tokyo stock market. Manage Sci 37:519–531

    Article  Google Scholar 

  • Lai YJ, Hwang CL (1992) Fuzzy mathematical programming. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Levy H (1999) Introduction to investments. International Thomson Publishing, Cincinnati

    Google Scholar 

  • Liu Y-J, Zhang W-G (2013) Fuzzy portfolio optimization model under real constraints. Insur Math Econ 53:704–711

    Article  Google Scholar 

  • Mabuchi S (1988) An approach to the comparison of fuzzy subsets with α-cut dependent index. IEEE T Syst Man Cyb 18:264–272

    Article  Google Scholar 

  • Mao JCT (1970) Models of capital budgeting, E-V vs. E–S. J Financ Quant Anal 4:557–675

    Article  Google Scholar 

  • Markowitz HM (1952) Portfolio selection. J Sci 7:77–91

    Google Scholar 

  • Markowitz HM (1959) Portfolio selection: efficient diversification of investments. Wiley, New York

    Google Scholar 

  • Markowitz HM (1991) Portfolio selection: efficient diversification of investments. Blackwell, Cambridge, Mass

    Google Scholar 

  • Markowitz HM, Todd P, Xu G, Yamane Y (1993) Computation of mean-semivariance efficient sets by the critical line algorithm. Ann Oper Res 45:307–317

    Article  Google Scholar 

  • McCahone C (1987) Fuzzy set theory applied to production and inventory control. Dissertation, Kansas State University

  • Mohamed RH (1997) The relationship between goal programming and fuzzy programming. Fuzzy Set Syst 89:215–222

    Article  Google Scholar 

  • Parra MA, Terol AB, Uŕia MVR (2001) A fuzzy goal programming approach to portfolio selection. Eur J Oper Res 133:287–297

    Article  Google Scholar 

  • Pekár J, Čičková Z, Brezina I (2016) Portfolio performance measurement using differential evolution. Cent Eur J Oper Res 24:421–433

    Article  Google Scholar 

  • Pla-Santamaria D, Bravo M (2013) Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips. Ann Oper Res 205:189–201

    Article  Google Scholar 

  • Prakash A, Chang C, Pactwa T (2003) Selecting a portfolio with skewness: recent evidence from US, European, and Latin American equity markets. J Bank Financ 27:1375–1390

    Article  Google Scholar 

  • Ramík J, Římánek J (1985) Inequality between fuzzy numbers and its use in fuzzy optimization. Fuzzy Set Syst 16:123–138

    Article  Google Scholar 

  • RM-SYSTÉM (2021a) Basic information. RM-SYSTEM web. https://www.rmsystem.cz/ spolecnost/zakladni-informace. Accessed 31 Jan 2021

  • RM-SYSTÉM (2021b) Stock prices. RM-SYSTEM web. https://www.rmsystem.cz/kurzy-online/akcie/easyclick. Accessed 15 Jan 2021

  • Simkowitz M, Beedles W (1978) Diversification in a three-moment world. J Financ Quant Anal 13:927–941

    Article  Google Scholar 

  • Sortino FA, Price LN (1994) Performance measurement in a downside risk framework. J Invest 3:59–64

    Article  Google Scholar 

  • Stevenson S (2001) Emerging markets, downside risk and the asset allocation decision. Emerg Mark Rev 2:50–66

    Article  Google Scholar 

  • Swisher P, Kasten GW (2005) Post-modern portfolio theory. J Financ Plan 18:11–74

    Google Scholar 

  • Tobin J (1958) Estimation of relationships for limited dependent variables. Econometrica 26:24–36

    Article  Google Scholar 

  • Tran L, Duckstein L (2002) Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Set Syst 130:331–341

    Article  Google Scholar 

  • Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (I) and (II). Fuzzy Set Syst 188:387–405

    Article  Google Scholar 

  • Zhang B, Peng J, Li S (2015) Uncertain programming models for portfolio selection with uncertain returns. Int J Syst Sci 46:2510–2519

    Article  Google Scholar 

  • Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Set Syst 1:45–55

    Article  Google Scholar 

Download references

Acknowledgements

The research project was supported by Grant No. IGA F4/42/2021 of the Internal Grant Agency, Faculty of Informatics and Statistics, Prague University of Economics and Business, and also was processed with contribution of long-term institutional support of research activities by Faculty of Informatics and Statistics, Prague University of Economics and Business.

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  1. Department of Econometrics, Faculty of Informatics and Statistics, Prague University of Economics and Business, W. Churchill Sq. 4, Prague, Czech Republic

    Adam Borovička

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Borovička, A. Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model. Cent Eur J Oper Res 30, 595–616 (2022). https://doi.org/10.1007/s10100-021-00791-0

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