基于VAR的證券投資組合優(yōu)化模型

摘    要
VAR (Value at Risk)是一個(gè)在當(dāng)前的金融市場(chǎng)條件下，各種不同的風(fēng)險(xiǎn)測(cè)量一個(gè)確定投資的獲利的重要方法。
本文在簡(jiǎn)要介紹了證券投資有關(guān)的概念、投資組合風(fēng)險(xiǎn)、VAR概念及計(jì)算方法后，在經(jīng)典的Markowitz均值-方差模型的基礎(chǔ)上，加入了VAR約束，研究了基于VAR約束的證券投資組合決策優(yōu)化模型及它的幾何算法，并從VAR模型的數(shù)學(xué)特性上進(jìn)行分析，得出了假定給定一個(gè)可接受的VAR，如何確定一組給定的證券的投資組合的最大收益，并且同時(shí)滿足相關(guān)的約束條件。假設(shè)市場(chǎng)條件是變化的，如何在保證給定投資組合的條件下，在給定VAR范圍內(nèi)，重新獲得一個(gè)投資組合。
本文的最后部分是對(duì)我國(guó)股票市場(chǎng)不允許賣空的前提下，從滬深股市上選擇了6只股票進(jìn)行實(shí)證分析，運(yùn)用樹(shù)形算法得出確定最大預(yù)期損失的證券投資組合，并在此基礎(chǔ)上提出了對(duì)我國(guó)股市發(fā)展的建議。

【關(guān)鍵詞】投資組合  VAR  幾何算法  樹(shù)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    錄
1  引言 1
2  證券投資組合的相關(guān)概念 2
2.1  證券投資及其屬性 2
2.2  組合投資 2
2.3  證券投資組合 2
3  證券投資組合的風(fēng)險(xiǎn) 2
3.1  風(fēng)險(xiǎn)的本質(zhì)及定義 2
3.2  風(fēng)險(xiǎn)的來(lái)源及種類 4
4  證券投資組合優(yōu)化的必要性及一般思考 6
4.1  現(xiàn)代證券投資組合理論的局限 6
4.2  證券投資組合優(yōu)化的必要性 8
5  VAR理論的基礎(chǔ)及其度量方法 8
5.1  VAR產(chǎn)生的背景 8
5.2  VAR的定義 9
5.3  VAR的三個(gè)要素 11
5.4  VAR的計(jì)算方法 12
5.4.1  投資組合的VAR度量 12
5.4.2  VAR的三種計(jì)算方法 14
6  基于VAR約束的投資組合模型 15
6.1  Markowitz投資組合模型 15
6.2  在VAR約束下的投資組合優(yōu)化模型 16
6.3  基于VAR約束的投資組合模型的改進(jìn) 20
6.4  基于滬深兩市股票的實(shí)證分析 21
6.4.1  樣本的選取 21
6.4.2  平均收益率的計(jì)算 21
6.4.3  平均收益率的正態(tài)分布檢驗(yàn) 22
6.4.4  模型的求解算法 23
6.4.5  不允許賣空時(shí)的證券組合分析 26
結(jié)論 28
參考文獻(xiàn) 29
附錄 30
致謝 32