An Empirical Study Of Fama-French Factor Based Approach For High Dimensional Covariance Matrix Estimation In The Chinese Stock Market

Portfolio selection is playing a more and more important role in the stock market. The fundamental issue for many stock investors and scholars is to obtain the optimal portfolio among a huge number of stocks. Markowitz (1987) introduced the well-recognized mean-variance optimal portfolio allocation model, but it may not perform well in practice, due to the difficulty in depicting the covariance structure among different assets. In particular, as the number of underlying assets grows, traditional sample covariance estimate may no longer be consistent with the true covariance, thus leading to poor performance in portfolio construction.Some may think of circumventing the above problem by increasing the sample size for sample covariance estimate, but that may not always work in practice. Alternatively, one could consider replace the sample covariance estimate by a more robust covariance estimate with nice asymptotic property. Recently, there are several papers discussing how to construct covariance for high dimensional data. Among all, Fan, Fan and Lv(2008) propose to estimate the covariance based on the Fama-French three factor model and they demonstrate its superiority over traditional sample covariance via theoretical derivation and simulation studies. Motivated by Fan et al.’s study, we consider an empirical study on Chinese stock market. Based on the Fama-French three factor model, we obtain the high dimensional covariance estimate and construct the corresponding optimal portfolio, which turns out to have better performance than the optimal portfolio constructed from sample covariance.