Optimization for the Portfolio Selection Model Maximizing Utility with the Different Lending and Borrowing Rate

Abstract

Abstract: Considering the expected rate of the return of the portfolio and its risk (variance),the author proposed a maximizing the utility portfolio selection model with risk-free asset,and importantly studied the situation in which the lending and borrowing rates of risk-free asset were different.Under short sales situation,using the Lagrange method and Sherman-morrison’s equation,the paper gets the optimal investing rate of every security and studies the efficient frontiers’ character.Under no short sales situation,the paper solves the model by the pivoting algorithm.The algorithm solves the quadric programming problem without adding slack,surplus and artificial variables.It is very efficient and easy to operate.At last,the paper compares the two models using an example and gets the result that risk preference coefficient with short sales and without short sales could reflect the investor’s expected rate of return and variance within the entire interval,and risk-free assets can create investment chance.

Key words: portfolio selection, utility, pivoting algorithm, risk preference coefficient

ZHANG Peng. Optimization for the Portfolio Selection Model Maximizing Utility with the Different Lending and Borrowing Rate[J]. journal6, 2008, 29(5): 113-120.

References

[1] MARKOWITZ H.Portfolio Selection [J].The Journal of Finance，1952,7(1):77-91.

[2] MARKOWITZ H.Portfolio Selection:Efficient Diversification of Investments [M].New York：Basil Blackwall,1959.

[3] DEXTER A S,YU T N W,ZIEMBA W T.Portfolio Selection in Lognormal Market When the Investor has a Power Utility Function:Computational Results [M]//DEMPSTER M A H.Stochastic Programming.New York and London：Academic Press,1980.

[4] PULLEY L M.A General Mean-Variance Approximation to Expected Utility for Short Holding Periods [J].Journal of Financial and Quantitative Analysis,1981,16:361-373.

[5] PULLEY L M.Mean-Variance Approximation to Logarithmic Utility [J].Operations Research,1983,31(4):685-696.

[6] BARON D P.On the Utility Theoretical Foundations of Mean-Variance Analysis [J].The Journal of Finance,1977,32:1 683-1 697.

[7] STEINBACH M C.Markowitz Revisited:Mean-Variance Models in Financial Portfolio Analysis [J].Siam Review,2001,43：31-85.

[8] JOSE TWAGILIMANA.Mean-Variance Model in Portfolio Analysis [D].University of Louisville,2002.

[9] 杨国梁,黄思明.摩擦市场上最优投资组合的一种数值解法 [J].中国管理科学,2006,9(3):62-67.

[10] 黄思明,陈薇,杨国梁.摩擦市场上允许买空卖空的投资组合问题 [J].中国管理科学,2006,14(5):28-32.

[11] 姚海祥，易建新.共同资金投资组合的有效边界与最优策略 [J].应用数学,2006,19(1):1-6.

[12] 张鹏,张忠桢,岳超源.基于效用最大化的投资组合旋转算法研究 [J].财经研究,2005,31(12)：116－125.

[13] 屠新曙,王春峰.含无风险资产时投资组合的效用最大化 [J].天津大学学报,2003,36(2):243-247.

[14] 屠新曙,王春峰,巴曙松.投资组合效用问题的研究 [J].数量经济技术经济研究,2002(5):37-40.

[15] 王春峰,屠新曙,厉斌.效用函数意义下投资组合有效选择问题的研究 [J].中国管理科学,2002,10(2):15-19.

[16] 席少霖.非线性最优化方法 [M].北京：高等教育出版社，1992.

[17] 张忠桢.凸规划－投资组合与网络优化的旋转算法 [M].第1版.武汉：武汉大学出版社,2004.

[18] 张鹏,张忠桢,岳超源.限制性卖空的均值-半绝对偏差投资组合模型及其旋转算法研究 [J].中国管理科学，2006，14（2）：7-11.

[19] 刘善存,汪寿阳,邱菀华.一个证券组合投资分析的对策论方法 [J].系统工程理论与实践,2001(5)：88－92.

[20] 钱颂迪.运筹学（修订版） [M].北京：清华大学出版社,1990.