A newly application of the random matrix theory on the exploration of the efficiency of investment portfolios in the Taiwan Stock Market

In the past, the investment portfolio theory regarding stock price deviation was considered to be individual risk that occurred in the market at random. However, the outcome efficiency of portfolios could be influenced by other factors that were found to be interrelated. In this study, we attempted to filter out those random parts of correlation matrix by the walk forward approach (WFA), and applied the Random matrix theory (RMT) that was developed from nuclear physics. We constructed a portfolio and then estimate the accumulation returns and Sharpe ratio. Based on the daily trading records from the Taiwan Stock Exchange (TWSE), the component indexes were grouped into 19 categories from Jan. 2, 2007 to Jan. 29, 2010, and there were a total of 767 data set entries as input information to this study. We employed variance tests, ANOVA, and least squares mean (LSM) to test the results. This study finds that, in general, the random part of stock return increases the portfolio risk, and consequently decreases the efficiency of the portfolio. In addition, this study adapted the concept of principal component analysis to analyze the information eigenvectors, which provided the information sequence for detecting the presence of unusual information that might affect the portfolio. As a result, the new approach could be helpful in forecasting the direction of price fluctuation.   Key words: Stock index, Random matrix theory, investment portfolio theory, principal component analysis, interrelated factor.