USING RANDOM MATRIX THEORY TO STUDY THE IMPACT OF PORTFOLIO RETURN WITH NOISE TRADING

• Main Authors: Hsu, Shih-Chang, 許世璋
• Other Authors: Goo, Y. Jia
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/71562230597204511319

博士 === 國立臺北大學 === 企業管理學系 === 98 === Based on the noise trading theory proposed by Black (1986) and DeLong et. al. (1990), this study first defines the meanings of information and noise, and then use mathematical deductive method to integrate noise trading and portfolio theory (Markowitz, 1952),and then use random matrix theory which is developed by nuclear physics to get the empirical evidences that impact of portfolio theory with noise trading. The first research proposition of the study is verified that noises are not individual stock risk and therefore, they could not be diversified through investment portfolios. Due to noises, the portfolios correlation matrix might have spurious correlation phenomenon. The second research proposition is that spurious correlation does not have sustainability and therefore, noises could not exist consistently in the stock market. Based on mathematical development, the third proposition is verified that portfolio risk is higher when noises existed. Furthermore, the fourth proposition is verified that due to noises interference, the efficiency of investment portfolios is reduced. Based on these propositions could be verify, proposition 2, proposition 3, and proposition 4 would be transformed to hypothesis 1, hypothesis 2, and hypothesis 3. “With the increase during the holding period, portfolio performance in information and in interference will gradually produce a significant difference” is hypothesis 1, which could be used to test whether noise is systematic risk or not. “The variance in information portfolio is smaller than in interference portfolio” is hypothesis 2, which is used to test whether risk of the portfolio could be rising by noises. Hypothesis 3 tells that, “the Sharpe ratio of information portfolio is higher than interference one”. Using hypothesis 3 could test possibility the efficiency of portfolio would be reduced by noises. There are 1242 samples of this study which uses 19 sector indices daily rate of returns in Taiwan stock market from the beginning in 2005 to the end in 2009. This Study uses method to filter random matrix which was developed by Bouchaud and Potters (2000), and investigates the empirical evidences of effect in portfolio with noise trading every holding periods which be used method of moving windows with 30 and 60 days’ formation periods. The result supports hypothesis 2, but hypothesis 1 and hypothesis 3 was gat partial support.