因子分析-Shrinkage法在投资组合中的理论分析及应用

Theoretical Analysis and Application on Factor Analysis-Shrinkage Method to Portfolio

摘要: 在不允许卖空的投资组合中，投资者往往希望通过投资组合模型得到最优投资组合以达到收益最大且风险最小的目标。本文对马科维茨模型以及重抽样和马科维茨模型相结合的模型进行了研究，但由于投资对象的总体分布不明确，用重抽样方法来估计总体分布可能会高估。Shrinkage法的应用缩减了估计量的方差。基于Shrinkage法及因子分析的思想，本文提出因子分析- Shrinkage法进一步优化估计量。用R软件对股票数据进行了实例分析与验证。

Abstract: In the portfolio with no short sales, investors usually want to get the optimal portfolio model in order to achieve maximum benefits and minimum risk. In this paper, we research the Markowitz model and the combination model of resampling and Markowitz model. However, due to the dis-tribution of investment targets is not clear, the resampling method may overestimate the distri-bution of population. Then the application of shrinkage method has improved the variance of es-timation. Based on shrinkage method and factor analysis, factor analysis-shrinkage method is proposed to further optimize the estimation. Experimental results using the real data of stocks and R software verify the analysis factor-shrinkage method.