Optimization of Tracking Error for Robust Portfolio of Risk Assets with Transaction Cost

Affiliation(s)

Hangzhou Institute of Service Engineering, Hangzhou Normal University, Hangzhou, China.

Hangzhou Institute of Service Engineering, Hangzhou Normal University, Hangzhou, China.

ABSTRACT

Based on the optimization of robust portfolio with tracking error, a robust mean-variance portfolio selection model of tracking error with transaction cost is presented for the case that only risky assets exist and expected returns of assets are uncertain and belong to a convex polyhedron. This paper aims to solve the problem of the portfolio with the selection of the ratio on the condition of maximumimum fluctuation of the tracking error, making the expectation of the return to be the maximumimum. It also makes the portfolio’s practical choice by the function of the linear transaction cost as the same time of construction and application of the model. Empirical analysis with five real stocks is performed by the method of LMI (Linear Matrix Inequality) to show the efficiency of the model.

Based on the optimization of robust portfolio with tracking error, a robust mean-variance portfolio selection model of tracking error with transaction cost is presented for the case that only risky assets exist and expected returns of assets are uncertain and belong to a convex polyhedron. This paper aims to solve the problem of the portfolio with the selection of the ratio on the condition of maximumimum fluctuation of the tracking error, making the expectation of the return to be the maximumimum. It also makes the portfolio’s practical choice by the function of the linear transaction cost as the same time of construction and application of the model. Empirical analysis with five real stocks is performed by the method of LMI (Linear Matrix Inequality) to show the efficiency of the model.

Cite this paper

D. Zheng and X. Liang, "Optimization of Tracking Error for Robust Portfolio of Risk Assets with Transaction Cost,"*iBusiness*, Vol. 5 No. 1, 2013, pp. 23-26. doi: 10.4236/ib.2013.51B005.

D. Zheng and X. Liang, "Optimization of Tracking Error for Robust Portfolio of Risk Assets with Transaction Cost,"

References

[1] Markowitz H.M., “Portfolio selection,” Journal of Finance, Vol. 7, 1952, pp. 77-91.

[2] Ben A.,Nemirovski A., “Robust optimization-methodology and applications,” Mathematics Program, Vol. 92, 2002, pp. 889-909.

[3] Ben-Tal A. and Nemirovski A., “Ro-bust convex optimization,” Mathematics of Operations Research, Vol. 23, 1998, pp. 769-805.

[4] Chen W. and Tan,S.H., “Robust portfolio selection based on asymme-tric measures of variability of stock returns,” Journal of Computational and Applied Mathematics, Vol. 232, 2009, pp. 295-304.

[5] Goldfarb D.and Iyengar G., “Robust portfolio selection problems,” Mathematics of Operations Research, Vol. 97, 2003, pp. 1-38.

[6] Lobo Vandenberghe L, Boyd S. and Lebert H., “Second-order cone programming: Interior-point methods and engineering applications,” Linear Algebra Application, Vol. 284, 1998, pp. 193-228.

[7] Pinara M. C.,Tutuncu R H., “Robust Profit Opportunities in Risky Financial Porfolios,” Operations Research Letters, Vol. 33, 2005, pp. 331-340.

[8] Lu Zhaosong, “Robust portfolio selection based on a joint ellipsoidal uncertainty set,” Optimization Methods and Software, Vol. 26, 2011, pp. 89-104.

[9] Fabozzi F.J., Petr N.K., Dessislava A.P. and Sergio M.F., “Robust portfolio optimization,” The journal of Portfolio Management, 2007, pp. 40-48.

[10] Roll R., “A mean - variance analysis of tracking error,” Journal of Portfolio Management, Vol. 18, 1992, pp. 13- 22.

[11] Soyster A.L., “Convex programming with set inclusive constraints and applications to inexact linear program-ming,” Operations Research, Vol. 21, 1973, pp. 1154-1157.

[12] Costa O.L.V. and Paiva A.C., “Robust portfolio selection using linear-matrix inequalities,” Journal of Economic Dynamics and Control, Vol. 26, 2002, pp. 889-909.

[13] Bertsimas D. and Pachamanova D., “Robust multiperiod portfolio management in the presence of transaction costs,” Computers and Operations Research, Vol. 35, 2008, pp. 3-17.

[14] Hong-Gang Xue. Cheng-Xian Xu. and Zong-Xian Feng, “Mean–variance portfolio optimal problem under concave transaction cost,” Applied Mathematics and Computation, Vol. 174, 2006, pp. 1-12.

[15] Erdogany E., Goldfarb D. and Iyengar G., “Robust active portfolio Management,” Department of Industrial Engineering and Operations Research, Columbia University, USA, CORC Technical Report TR-2004-11, Nov.2006. http://www.corc.ieor.colimbia.edu/reports/techreports/tr-2004-11.pdf.

[1] Markowitz H.M., “Portfolio selection,” Journal of Finance, Vol. 7, 1952, pp. 77-91.

[2] Ben A.,Nemirovski A., “Robust optimization-methodology and applications,” Mathematics Program, Vol. 92, 2002, pp. 889-909.

[3] Ben-Tal A. and Nemirovski A., “Ro-bust convex optimization,” Mathematics of Operations Research, Vol. 23, 1998, pp. 769-805.

[4] Chen W. and Tan,S.H., “Robust portfolio selection based on asymme-tric measures of variability of stock returns,” Journal of Computational and Applied Mathematics, Vol. 232, 2009, pp. 295-304.

[5] Goldfarb D.and Iyengar G., “Robust portfolio selection problems,” Mathematics of Operations Research, Vol. 97, 2003, pp. 1-38.

[6] Lobo Vandenberghe L, Boyd S. and Lebert H., “Second-order cone programming: Interior-point methods and engineering applications,” Linear Algebra Application, Vol. 284, 1998, pp. 193-228.

[7] Pinara M. C.,Tutuncu R H., “Robust Profit Opportunities in Risky Financial Porfolios,” Operations Research Letters, Vol. 33, 2005, pp. 331-340.

[8] Lu Zhaosong, “Robust portfolio selection based on a joint ellipsoidal uncertainty set,” Optimization Methods and Software, Vol. 26, 2011, pp. 89-104.

[9] Fabozzi F.J., Petr N.K., Dessislava A.P. and Sergio M.F., “Robust portfolio optimization,” The journal of Portfolio Management, 2007, pp. 40-48.

[10] Roll R., “A mean - variance analysis of tracking error,” Journal of Portfolio Management, Vol. 18, 1992, pp. 13- 22.

[11] Soyster A.L., “Convex programming with set inclusive constraints and applications to inexact linear program-ming,” Operations Research, Vol. 21, 1973, pp. 1154-1157.

[12] Costa O.L.V. and Paiva A.C., “Robust portfolio selection using linear-matrix inequalities,” Journal of Economic Dynamics and Control, Vol. 26, 2002, pp. 889-909.

[13] Bertsimas D. and Pachamanova D., “Robust multiperiod portfolio management in the presence of transaction costs,” Computers and Operations Research, Vol. 35, 2008, pp. 3-17.

[14] Hong-Gang Xue. Cheng-Xian Xu. and Zong-Xian Feng, “Mean–variance portfolio optimal problem under concave transaction cost,” Applied Mathematics and Computation, Vol. 174, 2006, pp. 1-12.

[15] Erdogany E., Goldfarb D. and Iyengar G., “Robust active portfolio Management,” Department of Industrial Engineering and Operations Research, Columbia University, USA, CORC Technical Report TR-2004-11, Nov.2006. http://www.corc.ieor.colimbia.edu/reports/techreports/tr-2004-11.pdf.