Portfolio Construction And Performance Analysis Based On Two Covariance Matrices Adjustment Methods

With the completion of financial market of China, investors, especially institutional investors pay more and more attention to risk management of portfolio. Markowitz, the pioneer of modern portfolio theory, proposed mean-variance mode, while a series of problems such as error accumulation and model instability arised when solving optimal portfolio. An important approach to solving these problems is to adjust the covariance matrix, this paper introduces two adjustment methods.The traditional sample covariance matrix calculated by historical data tends to underestimate the risk of optimal portfolio. This article defines bias statistics to describe such underestimation effect. Assuming such estimation deviation may be related to the eigen factors of the covariance matrix, method of numerical simulation is applied to give accurate and stable estimator of the bias statistics. We use estimated bias statistics to adjust the covariance matrix and get eigen-adjusted covariance matrix. The results of our research show that eigen-adjusted covariance matrix not only overcomes the underestimation problem from the traditional method when solving for optimal portfolio but also effectively reduces the out-of-sample risk of the optimal portfolio.The optimal portfolio obtained from the objective function with L1constraint of weight vector on portfolio, when solving the traditional mean-variance model, has the properties of sparse and stable. This paper introduces the theoretical basis of L1constraint and the algorithm of solving constrained the mean-variance model, and the real financial data verify the sparsity and stability of the portfolio.Finally, this article constructs five portfolios from29CITIC industry index by our two adjustment methods of covariance matrix. We analysis the annualized return, annualized risk and annualized Sharpe ratio of this five portfolios from June2005to June2013.After comparing with the performance of same period of the Shanghai Composite Index and Shenzhen Component Index, we find that the portfolio constructed by two adjustment method have achieved desirable performance.