Abstract
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.
Highlights
Bachelier (1900) first introduced the random concept into the economic system, arguing that the reason for price changes of stocks and bonds was intangible random variation. Samuelson (1965) and Mandelbrot (1966) used mathematical methods to prove that stock price change is one kind of random motion, and they regarded the physical particle of Brownian movement as a rational economic entity, and they produced the Random walk theory (RWT). Fama (1965) assumed that the economic entity is rational and proved the stock price was stated as the model of random walk
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
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
Summary
Bachelier (1900) first introduced the random concept into the economic system, arguing that the reason for price changes of stocks and bonds was intangible random variation. Samuelson (1965) and Mandelbrot (1966) used mathematical methods to prove that stock price change is one kind of random motion, and they regarded the physical particle of Brownian movement as a rational economic entity, and they produced the Random walk theory (RWT). Fama (1965) assumed that the economic entity is rational and proved the stock price was stated as the model of random walk. Fama (1965) assumed that the economic entity is rational and proved the stock price was stated as the model of random walk. He thought that the market would respond to all messages, and he proposed the Efficient Market Hypothesis (Fama, 1970). Hong et al (2000) believe that the different communication speeds of good and bad information cause delayed reaction to short-term information All of these researches have proven that the change of stock price was not like RWT, and they deny the existence of efficient markets
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