一种多目标规划的投资组合优化方法的实证分析

          一种多目标规划的投资组合优化方法的实证分析   报告要点： 1. 本文选择A股市场4个不同规模的股票作为研究对象，分别定 义为小盘股、中盘股票、大盘股票、超大盘股票 2. 本文选择小盘价值、上证中盘、中证100、超大盘作为对应基 准标准进行研究。 3. 本文研究投资组合中发现不同规模股票的投资组合效率更高。 这表明不同规模股票的运行对大盘的影响较大。 4. 在投资组合数量8-33之间的投资组合相对收益小于绝对收益。 5. 不同规模的投资组合的风险与收益成正比。 作者：徐清振 电话：0755-******** e-mail: xqz1997@163.com 报告编号：2011065 完成时间：2010-9-07     独立声明：本报告所采用的信息及数据均来源于公开可得到的资料。   目  录 Abstract    I 1.    Introduction    1 2.    The single objective problem    3 3.    The multi objective problem    4 4.    The empirical analysis of the portfolio in China’s stock market    7 5. Conclusion    13 References    13 Abstract This paper describes a necessary condition for Pareto optimality. It is derived by reducing the multi objective programming under inclusion constraints to systems of single objective problem and then using known results of them. We use the portfolio model for China's securities market. In order to exceed Shanghai Composite Index, we select some stocks of china market for portfolio. All the data are publicly from stock exchange of Shenzhen or Shanghai. A comprehensive analysis of the results is provided. The result is reasonable and efficient. It is clarified that the nonlinear program model can analyze the entire possible portfolio case. Keywords: multi objective (single objective) programming; inclusion constraints; optimality condition; Portfolio optimization 1. Introduction Many researchers devote to study more efficient and practical portfolio strategy, especially for stock market invests. In this section, we survey some of this work. Generally speaking, these approaches can be divided into two parts: new method and traditional method with development. Qingzhen Xu（Qingzhen Xu, et al, 2007）focuses on a M/G/1 queue system with multiple vacations and server close-down time. He solve the probability generating function (P.G.F.) of stationary queue length and LST of waiting time. Qingzhen Xu（Qingzhen Xu, et al, 2011） develop a Genetic Algorithms to forecast American Shares Price Index. They can forecast DJI trend that can improve portfolio achievement. Gordon J. Alexander,etc（Gordon J. Alexander,2010） think sensible choices of ex-ante alpha can lessen the risk. Most practitioners use ex-post alpha to assess the risk-adjusted performance of managers. Joop Huij, etc. (Joop Huij, 2011) take the R-squared value from regressing fund returns, the estimated equation as follows, In the conclusion, the portfolio should take into account multiple market segments at the same time. Yan Chen (Yanchen, et al, 2010) use time adapting genetic network programming to optimize portfolio. They think TA-GNP method is more effective on the portfolio optimization problem. F. Castro, etc(F. Castro,J.2011) provide an algebraic approach to integer portfolio problems. Tanja Magoc,etc(Tanja Magoc,et al,2011) show that fuzzy methods outperformed other techniques, especially in the Shanghai Market. Chen Chen,etc provide a robust portfolio model for index tracking. The basic model is as follows, , Subject to , and , . Above the basic model, they improved the standard robust formulation, as, , And transformed to be as, Optimality conditions for multi objective programming problems have been studied extensively in the literature. Many efforts have been made to the problem: where (B.Aghezzaf,1999;P.Kanniappan,1983 ) In this paper, we consider the following multi objective programming under inclusion constraint: (MOP)                        Where ,each is Frechet differentiable and is a set-valued map. In fact, the constraint “ ” is general and inclusive of “ ”, since we can set to be “ ” and is the nonnegative orphans of . Our aim in this paper is to get the optimality condition of problem (MOP) by a lemma which helps reducing multi objective optimality problem to systems of single objective ones. In this paper, section 1 is the introduction of portfolio optimizations. Section 2 presents the single objective problem. Section 3 presents the multi objective problem. Section 4 presents the empirical analysis of the portfolio in China’s stock market. Section 5 presents the summary and conclusions. 2. The single objective problem Let and be two Banach space, and and are the continuous duals of and , respectively.  We write for the canonical bilinear forms respect to the dualities . Now, we are concerned with the single objective optimization problem (P)                      where is a Frechet differentiable function on a Banach space and is a set valued map defined in with nonempty closed convex values in another Banach space . Let be the feasible set, that is, Suppose that the barrier cone of Is closed and does not depend on , this is case, for example, when is locally Lipchitz (T.Amahroq,et al,2003). For every , the support functions of is defined as follows: And it is assumed to be Frechet differentiable in this paper. Definition 1:  is said to be regular of Problem (P) if the system