A multiple objective stochastic portfolio selection problem with random Beta
When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security&...
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| Vydáno v: | International transactions in operational research Ročník 21; číslo 6; s. 919 - 933 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Oxford
Blackwell Publishing Ltd
01.11.2014
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| ISSN: | 0969-6016, 1475-3995 |
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| Abstract | When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported. |
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| AbstractList | When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported. |
| Author | Masmoudi, Meryem Abdelaziz, Fouad Ben |
| Author_xml | – sequence: 1 givenname: Fouad Ben surname: Abdelaziz fullname: Abdelaziz, Fouad Ben email: fba@rouenbs.fr organization: Rouen Business School, Boulevard André Siegfried-76130, Mont-Saint-Aignan, France – sequence: 2 givenname: Meryem surname: Masmoudi fullname: Masmoudi, Meryem email: meryem.masmoudi@gmail.com organization: LARODEC, Institut Supérieur de Gestion, University of Tunis, 41 rue de la liberté, Le Bardo 2000, Tunisia |
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| Cites_doi | 10.1111/0022-1082.00401 10.1016/j.ejor.2005.10.021 10.1016/j.joep.2007.07.001 10.1023/A:1014594617251 10.1111/j.1475-6803.1993.tb00147.x 10.3905/jpm.1980.408744 10.1016/j.cor.2009.09.009 10.1111/1468-2362.00044 10.1016/j.jbankfin.2007.12.025 10.1016/S0167-7152(98)00041-8 10.1057/palgrave.jors.2602133 10.1080/14697680802595643 10.2307/1924119 10.2307/2330303 10.1111/j.1540-6261.1964.tb02865.x 10.2307/3664999 10.1007/s10479-006-0137-1 10.1111/j.1540-6261.1952.tb01525.x 10.1287/mnsc.31.11.1403 |
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| Copyright | 2013 The Authors. International Transactions in Operational Research © 2013 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. Copyright © 2014 International Federation of Operational Research Societies |
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| References | Steuer, R., Qi, Y., Hirschberger, M., 2007. Suitable-portfolio investors, nondominated frontier sensitivity, the effect of multiple objectives on standard portfolio selection. Annals of Operations Research 152, 297-317. Ben Abdelaziz, F., Aouni, B., El Fayedh, R., 2007. Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research 177, 1811-1823. Dong, S., 2006. Value at Risk Methodologies: Development, Implementation and Evaluation. MA thesis, Simon Fraser University, BC, Canada. Anagnostopoulos, K.P., Mamanis, G., 2010. A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research 37, 1285-1297. Markowitz, H., 1952. Portfolio selection. The Journal of Finance 7, 1, 77-91. Markowitz, H., 1959. Portfolio Selection: Efficient Diversification in Investments. John Wiley & Sons, New York. Zenios, S.A., Ziemba, W.T., 2006. Handbook of Asset and Liability Management. Elsevier, Amsterdam. Quaranta, A.G., Zaffaroni, A., 2008. Robust optimization of conditional value at risk and portfolio selection. Journal of Banking & Finance 32, 10, 2046-2056. McDonald, B., 1985. Estimating market model Betas: a comparison of random coefficient methods and their ability to correctly identify random variation. Management Science 31, 11, 1403-1408. Zhang, Y., Rachev, S., 2006. Risk attribution and portfolio performance measurement-an overview. Journal of Applied Functional Analysis 1, 4, 373-402. Kim, M.K., Zumwalt, J.K., 1979. An analysis of risk in bull and bear markets. The Journal of Financial and Quantitative Analysis 14, 5, 1015-1025. Xidonas, P., Askounis, D., Psarras, J., 2009. Common stock portfolio selection: a multiple criteria decision making methodology and an application to the Athens stock exchange. Operation Research International Journal 9, 55-79. Kagan, A., Shepp, L.A., 1998. Why the variance? Statistics and Probability Letters 38, 4, 329-333. Blavatskyy, P., 2008. Risk Aversion, Institute for Empirical Research in Economics, University of Zurich. Working paper number 370. Available at SSRN: http://ssrn.com/abstract=1128106 or http://dx.doi.org/10.2139/ssrn.1128106. Woodward, G., Anderson, H., 2009. Does Beta react to market conditions? Estimates of bull and bear Betas using a nonlinear market model with endogenous threshold parameter. Quantitative Finance 8, 913-924. Levinson, M., 2006. Guide to Financial Markets. The Economist, London. Bhardwaj, R.K., Brooks, L.D., 1993. Dual Betas from bull and bear markets: reversal of the size effect. The Journal of Financial Research 16, 4, 269-283. Rachev, S., Stoyanov, S.V., Fabozzi, F.J., 2008. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty and Performance Measures. John Wiley & Sons, New York. Mitchell, M., Pulvino, T., 2001. Characteristics of risk and return in risk arbitrage. The Journal of Finance 56, 6, 2135-2176. Lintner, J., 1965. 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| References_xml | – reference: Lintner, J., 1965. The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13-37. – reference: Ben Abdelaziz, F., Aouni, B., El Fayedh, R., 2007. Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research 177, 1811-1823. – reference: Blavatskyy, P., 2008. Risk Aversion, Institute for Empirical Research in Economics, University of Zurich. Working paper number 370. Available at SSRN: http://ssrn.com/abstract=1128106 or http://dx.doi.org/10.2139/ssrn.1128106. – reference: Markowitz, H., 1952. Portfolio selection. The Journal of Finance 7, 1, 77-91. – reference: Zhang, Y., Rachev, S., 2006. Risk attribution and portfolio performance measurement-an overview. Journal of Applied Functional Analysis 1, 4, 373-402. – reference: Greene, W. H., 2003. Econometric Analysis (5th edn). Prentice Hall, Englewood Cliffs, NJ. – reference: Kim, M.K., Zumwalt, J.K., 1979. An analysis of risk in bull and bear markets. The Journal of Financial and Quantitative Analysis 14, 5, 1015-1025. – reference: Chen, C.A., 1982. Time series analysis of Beta stationarity and its determinants: a case of public utilities. Financial Management 11, 3, 64-70. – reference: Levinson, M., 2006. Guide to Financial Markets. The Economist, London. – reference: Dong, S., 2006. Value at Risk Methodologies: Development, Implementation and Evaluation. MA thesis, Simon Fraser University, BC, Canada. – reference: Quaranta, A.G., Zaffaroni, A., 2008. Robust optimization of conditional value at risk and portfolio selection. Journal of Banking & Finance 32, 10, 2046-2056. – reference: Shalit, H., Yitzhaki, S., (2002), Estimating Beta. Review of Quantitative Finance and Accounting 18, 95-118. – reference: Lee, S.M., Chesser, D.L., 1980. Goal programming for portfolio selection. The Journal of Portfolio Management 6, 3, 22-26. – reference: Zenios, S.A., Ziemba, W.T., 2006. Handbook of Asset and Liability Management. Elsevier, Amsterdam. – reference: Rachev, S., Stoyanov, S.V., Fabozzi, F.J., 2008. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty and Performance Measures. John Wiley & Sons, New York. – reference: Woodward, G., Anderson, H., 2009. Does Beta react to market conditions? Estimates of bull and bear Betas using a nonlinear market model with endogenous threshold parameter. Quantitative Finance 8, 913-924. – reference: Sharpe, W., 1964. Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance 19, 425-442. – reference: Veld, C., Veld-Merkoulova, Y.V., 2008. The risk perceptions of individual investors. Journal of Economic Psychology 29, 2, 226-252. – reference: Bhardwaj, R.K., Brooks, L.D., 1993. Dual Betas from bull and bear markets: reversal of the size effect. The Journal of Financial Research 16, 4, 269-283. – reference: Steuer, R., Qi, Y., Hirschberger, M., 2007. Suitable-portfolio investors, nondominated frontier sensitivity, the effect of multiple objectives on standard portfolio selection. Annals of Operations Research 152, 297-317. – reference: McDonald, B., 1985. Estimating market model Betas: a comparison of random coefficient methods and their ability to correctly identify random variation. Management Science 31, 11, 1403-1408. – reference: Mitchell, M., Pulvino, T., 2001. Characteristics of risk and return in risk arbitrage. The Journal of Finance 56, 6, 2135-2176. – reference: Xidonas, P., Askounis, D., Psarras, J., 2009. Common stock portfolio selection: a multiple criteria decision making methodology and an application to the Athens stock exchange. Operation Research International Journal 9, 55-79. – reference: Anagnostopoulos, K.P., Mamanis, G., 2010. A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research 37, 1285-1297. – reference: Kagan, A., Shepp, L.A., 1998. Why the variance? Statistics and Probability Letters 38, 4, 329-333. – reference: Bilbao, A., Arenas, M., Jiménez, M., Perez Gladishl, B., Rodríguez, M.V., 2006. An extension of Sharpe's single-index model: portfolio selection with expert Betas. The Journal of the Operational Research Society 57, 12, 1442-1451. – reference: Markowitz, H., 1959. Portfolio Selection: Efficient Diversification in Investments. John Wiley & Sons, New York. – reference: Kandasamy, H., 2008. Portfolio Selection Under Various Risk Measures, ProQuest, Ann Arbor, MI. – reference: Lin, H.J., Lin, W.T., 2000. A dynamic and stochastic Beta and its implication in global capital markets. 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| SubjectTerms | Beta Capital assets Goal programming multiple objective stochastic programming Operations research Portfolio management portfolio selection Random variables risk measures stochastic goal programming Studies |
| Title | A multiple objective stochastic portfolio selection problem with random Beta |
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