The Application Of Robust Statistics To Stock Portfolio Problem

The estimation of expected return and risk for every security in a portfolio is based on observed market data. In reality, however, a few extreme observations which arose from favorable news and bad news for the market in short term often exist in the return sample, and we called them outliers here. As we known, history can not repeat itself. Therefore, when we use these observed data to estimate the expected return and risk of securities, the value of the portfolio based on the estimations will be influenced by outliers, and departure from its actual investment value in the long run, that is what we don't want to see.In order to solve the problem mentioned above, in this thesis, we introduced robust statistical methods into the solving process of portfolio models, so as to reduce the influence caused by the outliers on our investment decision, and make the portfolio value go back to its right rails. For the solving process of Markowitz's mean-variance model and Sharp's single index model, we focused on the Fast-MCD robust estimate method and robust regression method, and then used them to solve the two portfolio models separately.In empirical analysis part, we selected 10 small company stocks from Shanghai A stock market as our sample stocks, and the dates from Jan 1, 2006 to Dec 31, 2008 as our sample period. We tested the effect of robust statistical method on weakening the strength of outliers in the process of optimizing portfolios, and compared the performance of two robust statistical methods with the classical statistical methods. Subsequently, we selected other 10 stocks from the component stocks of Shanghai 50 stock index as our sample stocks to prove the general applicability of robust statistical methods in portfolio problem. At last, we compared the portfolio efficient frontiers derived from the two sample stocks in robust statistical method, and analyzed the reason of the difference.