The major theories of finance leading into the main body of this research are discussed and our experiments on studying the risk and co-movements among stocks are presented. This study leads to the application of Random Matrix Theory (RMT) The idea of this theory refers to the importance of the empirically measured correlation (or covariance) matrix, C, in finance and particularly in the theory of optimal portfolios However, this matrix has recently come into question, as a large part of it does not contain useful information but rather noise. Therefore, recent work has indicated that the theory of optimal portfolios, which depends on C, is not adequate. We use RMT in order to measure the noise component of C, and then we examine the methods of differentiating noise from information. We go on to develop a novel technique of stability analysis for the eigenvectors of C after noise removal. Further, changes in the portfolio associated with the riskiest position, (as given by the largest eigenvalue and associated eigenvector), are investigated using the results of the previous chapters. From the results, we observe periods of comovements of stocks, which change regularly because of some key events m the market. These periods are characterised by a linear relationship between price and eigenvalue change. However, the residuals in this model are strongly dependent on granularity (1e sampling rate) with fit breaking down at rates smaller than five days. Possible reasons for this breakdown are presented in detail.