In Modern Portfolio Theory, the correlation coefficients decide the risk of a set of stocks in the portfolio. So, to understand the correlation coefficients between returns of stocks, is a challenge but is very important for the portfolio management. Usually, the stocks with small correlation coefficients or even negative correlation coefficients are preferred. One can calculate the correlation coefficients of stock returns based on the historical stock data. However, in order to control the risk of portfolio, we need to well predict the correlation coefficients of stock returns in the early future.

In this thesis, different stock return models, such as Historical Model, Constant Correlation Model, Multi-Group Model, Single-Index model, and Multi-Index Model are studied. For Single-Index Model and Multi-Index Model, the beta parameter adjustment techniques, Blume's technique and Vasicek's technique are applied. We randomly select a sample of 100 stocks from S&P 500 index, and study the historical data from 07/01/1992 to 07/01/2012. The data are separated to four periods, five years in each period. We use the data from 07/01/1992 to 07/01/2002 to predict the correlation coefficients and compare with the real correlation coefficients of the period form 07/01/2002 to 07/01/2007; and use the data from 07/01/1997 to 07/01/2007 to compare the prediction of correlation coefficients with the real correlation coefficients of the period from 07/01/2007 to 07/01/2012. The results indicate that the Multi-Index Model gives better prediction compared with other models.