基于var的证券投资组合优化模型.doc

基于VAR的证券投资组合优化模型

摘    要
VAR (Value at Risk)是一个在当前的金融市场条件下，各种不同的风险测量一个确定投资的获利的重要方法。
本文在简要介绍了证券投资有关的概念、投资组合风险、VAR概念及计算方法后，在经典的Markowitz均值-方差模型的基础上，加入了VAR约束，研究了基于VAR约束的证券投资组合决策优化模型及它的几何算法，并从VAR模型的数学特性上进行分析，得出了假定给定一个可接受的VAR，如何确定一组给定的证券的投资组合的最大收益，并且同时满足相关的约束条件。假设市场条件是变化的，如何在保证给定投资组合的条件下，在给定VAR范围内，重新获得一个投资组合。
本文的最后部分是对我国股票市场不允许卖空的前提下，从沪深股市上选择了6只股票进行实证分析，运用树形算法得出确定最大预期损失的证券投资组合，并在此基础上提出了对我国股市发展的建议。

【关键词】投资组合  VAR  几何算法  树形算法 
 

 
Portfolio Optimization Model with VaR Constraints
               
Abstract
At the present of finance market, VAR is an important method of ensuring investment profits among varies of risk measurements.
This paper, first of all, introduces some concepts about investment of negotiable securities, the risk of investment combination, the concept of VAR and the measures of calculation. On the basis of the classical Markowitz mean-variance model, this paper adds the VAR restrict, researches the optimizing model of combination of negotiable securities investment under the restriction of VAR and analyzes VAR model on the mathematics characteristic on the basis of the model of Markowitz mean-variance. Under a acceptable VAR, by analyzing the mathematics characteristic of VAR model, this paper comes to a conclusion how to confirm the max income of a combination of negotiable securities investment   and satisfies the relative conditions of restriction at the same time .Supposed the market condition can be changed, how to acquire a new combination investment under the given condition and the given scope of VAR is discussed.
At the end of this thesis, on the condition of our country’s stock market, premising it doesn’t allow to oversell, six stocks with good outstanding achievement are chosen to do an empirical analyzing. Making use of the tree arithmetic, the study achieves a combination of negotiable securities investment of a fixing anticipate max losing, and on the basis of this, some suggestiones on the development of our country’s stock market are proposed.

Keywords：
Investment combination, VAR, Geometry arithmetic, Tree arithmetic
 

 
目    录
1  引言 1
2  证券投资组合的相关概念 2
2.1  证券投资及其属性 2
2.2  组合投资 2
2.3  证券投资组合 2
3  证券投资组合的风险 2
3.1  风险的本质及定义 2
3.2  风险的来源及种类 4
4  证券投资组合优化的必要性及一般思考 6
4.1  现代证券投资组合理论的局限 6
4.2  证券投资组合优化的必要性 8
5  VAR理论的基础及其度量方法 8
5.1  VAR产生的背景 8
5.2  VAR的定义 9
5.3  VAR的三个要素 11
5.4  VAR的计算方法 12
5.4.1  投资组合的VAR度量 12
5.4.2  VAR的三种计算方法 14
6  基于VAR约束的投资组合模型 15
6.1  Markowitz投资组合模型 15
6.2  在VAR约束下的投资组合优化模型 16
6.3  基于VAR约束的投资组合模型的改进 20
6.4  基于沪深两市股票的实证分析 21
6.4.1  样本的选取 21
6.4.2  平均收益率的计算 21
6.4.3  平均收益率的正态分布检验 22
6.4.4  模型的求解算法 23
6.4.5  不允许卖空时的证券组合分析 26
结论 28
参考文献 29
附录 30
致谢 32