Random Matrix techniques used in Markowitz Portfolio

• Main Authors: Chang-Yuan Ling, 凌張苑
• Other Authors: Chi-Ning Chen
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/75540977220125892397

碩士 === 國立東華大學 === 物理學系 === 100 === We select 121 stocks in Taiwan stock market and calculate their correlation matrices in the period from 2008 to 2010. The time lags used are 10 and 30 minutes, and the time lengths are from two weeks to one year. We calculate spectral quantities, such as eigenvalues, eigenvectors, inverse participation ratios, and compare the results with random matrix theory in order to separate these eigenmodes into two, random and non-random, groups. This ‘noise’ filtering technique, in which correlation matrices are reconstructed by non-random eigenmodes, can be applied to draw minimal spanning trees to reveal the globally correlated structure of Taiwan stock market. Another important application is for portfolio selection. We apply this technique to a simple model of Markowitz portfolio optimization and discuss the indication of our preliminary results.