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Portfolio Mean-Variance Approach Modifications:Modulus Function, Principles of Compromise, and ‘Min–Max’ Approach


Affiliations
1 Novosibirsk State Technical University, Russian Federation
2 Novosibirsk State University of Economics and Management, Russian Federation
 

We offer a variant for the problem of portfolio selection, based on the modification of quadratic function. It reduces overestimation of expected returns that arise from large deviations of the market condition. Further, we examine the modified ‘min–max’ approach to portfolio structure. We obtain analytical expressions to solve the portfolio selection model for a few cases. Finally, we offer certain compromise principles between criterial values of the expected return/risk.

Keywords

Mean-Variance, ‘Min–Max’ Approach, Modern Portfolio Theory, Portfolio Selection.
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  • Markowitz, H. M., Portfolio selection. J. Finan., 1952, 7, 77–91.

  • Sharpe, W. F., Capital asset prices: a theory of market equilibrium under conditions of risk. J. Finan., 1964, 19(3), 425–442.

  • Lintner, J., The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econ. Stat., 1965, 47(1), 13–37.

  • Mossin, J., Equilibrium in capital assets markets. Econometrica, 1966, 34(4), 768–783.

  • Black, F. and Scholes, M., The pricing of options and corporate liabilities. J. Polit. Econ., 1973, 81(3), 637–654.

  • Merton, R. C., An intertemporal capital asset pricing model. Econometrica, 1973, 41(5), 867–887.

  • Buckley, I. R. C. and Korn, R., Optimal index tracking under transaction costs and impulse control. Int. J. Theoret. Appl. Finan., 1998, 1(3), 315–330.

  • Guerard Jr, J. B., Takano, M. and Yamane, Y., The development of efficient portfolios in Japan with particular emphasis on sales and earnings forecasting. Ann. Oper. Res., 1993, 45(1), 91–108.

  • Harlow, W. and Rao, R., Asset pricing in a generalized mean-lower partial moment framework: theory and evidence. J. Fin. Quant. Anal., 1989, 24(3), 285–311.

  • King, A. J., Asymmetric risk measures and tracking models for portfolio optimization under uncertainty. Ann. Oper. Res., 1993, 45(1), 165–177.

  • Konno, H. and Watanabe, H., Bond portfolio optimization problems and their applications to index tracking: a partial optimization approach. J. Oper. Res. Soc. Jpn, 1996, 39(3), 295–306.

  • Markowitz, H. M., Portfolio Selection: Efficient Diversification of Investments, John Wiley, 2nd edn, 1991 (1959).

  • Markowitz, H., Todd, P., Xu, G. and Yamane, Y., Computation of mean-semivariance efficient sets by the critical line algorithm. Ann. Oper. Res., 1993, 45(1), 307–317.

  • Rockafellar, R. T. and Uryasev, S., Optimization of conditional value-at-risk. J. Risk, 2000, 2, 21–41.

  • Uryasev, S., Conditional value-at-risk: optimization algorithms and applications. In IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, Proceedings (CIFEr), 2000, pp. 49–57.

  • Cox, J., Ingersoll, J. E. and Ross, S. A., An intertemporal general equilibrium model of asset prices. Econometrica, 1985, 53(2), 363–384.

  • Ho, T. and Lee, S.-B., Term structure movements and the pricing of interest rate contingent claims. J. Finan., 1986, 41(5), 1011–1029.

  • Levy, H. and Samuelson, P. A., The capital asset pricing model with diverse holding periods. Manage. Sci., 1992, 38, 1529–1542.

  • Mei, J., Scheinkman, J. and Xiong, W., Speculative trading and stock prices: evidence from Chinese A–B share premia. Ann. Econ. Financ., 2009, 10(2), 225–255.

  • Cai, X., Teo, K.-L., Yang, X. and Zhou, X. Y., Portfolio optimization under a minimax rule. Manage. Sci., 2000, 46(7), 957–972.

  • Deng, X.-T., Li, Z.-F. and Wang, S.-Y., A minimax portfolio selection strategy with equilibrium. Eur. J. Oper. Res., 2005, 166, 278–292.

  • Polak, G. G., Rogers, D. F. and Sweeney, D. J., Risk management strategies via minimax portfolio optimization. Eur. J. Oper. Res., 2010, 207(1), 409–419.

  • Sharma, A. and Mehra, A., Portfolio selection with a minimax measure in safety constraint. Optimization, 2013, 62(11), 1473–1500.

  • Sun, Y., Aw, G., Teo, K. L. and Zhou, G., Portfolio optimization using a new probabilistic risk measure. J. Ind. Manage. Optim, 2015, 11(4), 1275–1283.

  • Teo, K. L. and Yang, X. Q., Portfolio selection problem with minimax type risk function. Ann. Oper. Res., 2001, 101(1–4), 333– 349.

  • Wu, Z.-W., Song, X.-F., Xu, Y.-Y. and Liu, K., A note on a minimax rule for portfolio selection and equilibrium price system. Appl. Math. Comput., 2009, 208(1), 49–57.

  • Young, M. R., A minimax portfolio selection rule with linear programming solution. Manage. Sci., 1998, 44(5), 673–683.

  • Abdelaziz, F. B., Aouni, B. and Fayedh, R. E., Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res., 2007, 177(3), 1811–1823.

  • Boswarva, I. and Aouni, B., Different probability distributions for portfolio selection in the chance constrained compromise programming model. INFOR, 2012, 50(3), 140–146.

  • Bilbao-Terol, A., Arenas-Parra, M., Canal-Fernandez, V. and AntomilIbias, J., Using TOPSIS for assessing the sustainability of government bond funds. Omega, 2014, 49, 1–17.

  • Gonzalez, E. F., Cervantes, E. L., Castillo, J. N. and Lopez, I. V., Application of multi-objective metaheuristics to public portfolio selection through multidimensional modelling of social return. Gest. Polit. Publ., 2011, 20(2), 381–432.

  • Hasuike, T. and Katagiri, H., Risk-controlled multiobjective portfolio selection problem using a principle of compromise. Math. Probl. Eng., 2014, Article ID: 232375.

  • Li, J. and Xu, J., Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm. Inform. Sci., 2013, 220, 507–521.


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  • Portfolio Mean-Variance Approach Modifications:Modulus Function, Principles of Compromise, and ‘Min–Max’ Approach

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Authors

Alexey Karpovich
Novosibirsk State Technical University, Russian Federation
Alexander Rymanov
Novosibirsk State University of Economics and Management, Russian Federation

Abstract


We offer a variant for the problem of portfolio selection, based on the modification of quadratic function. It reduces overestimation of expected returns that arise from large deviations of the market condition. Further, we examine the modified ‘min–max’ approach to portfolio structure. We obtain analytical expressions to solve the portfolio selection model for a few cases. Finally, we offer certain compromise principles between criterial values of the expected return/risk.

Keywords


Mean-Variance, ‘Min–Max’ Approach, Modern Portfolio Theory, Portfolio Selection.

References





DOI: https://doi.org/10.18520/cs%2Fv115%2Fi3%2F493-498