本文選題：投資組合 + 均值方差模型�。� 參考：《華東師范大學》2013年碩士論文

【摘要】：隨著我國金融市場的日益完善,投資者尤其是機構投資者們越來越關注投資組合的風險管理,投資組合的理念被越來越多的投資者所熟知,對投資組合的研究也越來越深入�，F代投資組合理論的先驅Markowitz提出了均值方差模型,但該模型在求解最優(yōu)投資組合時卻面臨誤差累計、模型不穩(wěn)定等一系列問題。調整模型輸入的協(xié)方差矩陣是解決這些問題的關鍵。本文介紹了解決這些問題的兩種協(xié)方差矩陣調整方法。 用傳統(tǒng)方法得到的樣本協(xié)方差矩陣往往傾向于低估最優(yōu)投資組合的風險,本文定義了偏差統(tǒng)計量來刻畫這種低估效應,猜測這種估計偏差很可能與協(xié)方差矩陣的特征因子有關,并通過數值模擬的方法準確而穩(wěn)定地估計出這種偏差。在此基礎上,我們用估計偏差對協(xié)方差矩陣作調整,得到特征調整的協(xié)方差矩陣。本文的研究結果表明,特征調整的協(xié)方差矩陣不僅克服了傳統(tǒng)樣本協(xié)方差矩陣在估計最優(yōu)投資組合風險時的低估問題,還能夠有效降低投資組合的樣本外風險。 在求解傳統(tǒng)的均值方差模型時,對組合權重向量施加L1約束之后得到的最優(yōu)投資組合具有稀疏性和穩(wěn)定性。本文闡述了L1約束的理論基礎,介紹了求解帶約束的均值方差模型的算法,并用實際金融數據展示了組合的稀疏性和穩(wěn)定性。 最后,本文基于兩種協(xié)方差矩陣調整方法用29個中信行業(yè)指數構建了5個投資組合。我們分析了5個投資組合自2005年6月至2013年6月的年化收益、風險和夏普比率,并與同一時期上證綜指和深證成指的表現作比較,發(fā)現根據兩種調整方法構建的投資組合在所考察的時間段內均取得了優(yōu)于對照組合的業(yè)績。
[Abstract]:With the improvement of China's financial market, investors, especially institutional investors, have paid more and more attention to the risk management of portfolio. The concept of portfolio is well known by more and more investors, and the research on portfolio is becoming more and more in-depth. The pioneer Markowitz of modern portfolio theory puts forward the mean variance model, but this model is a model. In solving the optimal portfolio, it is faced with a series of problems such as accumulative error and model instability. The key to solve these problems is to adjust the covariance matrix of the model input. In this paper, two covariance matrix adjustment methods for solving these problems are introduced.
The sample covariance matrix obtained by the traditional method tends to underestimate the risk of the optimal portfolio. This paper defines the deviation statistics to describe the undervaluation effect. It is guessed that the estimation deviation is likely to be related to the characteristic factor of the covariance matrix, and the deviation is estimated accurately and steadily by the numerical simulation method. On this basis, we use the estimated deviation to adjust the covariance matrix and get the covariance matrix of the characteristic adjustment. The results of this study show that the covariance matrix of the feature adjustment can not only overcome the underestimation of the traditional sample covariance matrix in the estimation of the optimal portfolio risk, but also can effectively reduce the external wind of the portfolio. Risk.
When the traditional mean variance model is solved, the optimal portfolio is sparsity and stability after applying the L1 constraint to the combined weight vector. This paper expounds the theoretical basis of the L1 constraint, introduces the algorithm for solving the mean variance model with constraints, and shows the sparsity and stability of the combination with the actual financial data.
Finally, based on two covariance matrix adjustment methods, 5 portfolios are constructed with 29 CITIC industry indices. We analyzed the annual income, risk and SHARP ratio of 5 portfolios from June 2005 to June 2013, and compared with the performance of the Shanghai Composite Index and Shenzhen stock index at the same time, and found that the two adjustment methods were constructed. The built portfolios achieved better performance than those in the control group during the period examined.
【學位授予單位】：華東師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F832.51;F224

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本文編號：2020235