Random Matrix Theory and Cross-correlations in Global Financial Indices and Local Stock Market Indices

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [{\lambda}_, {\lambda}+], where {\lambda}_- and {\lambda}_+ are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis

Correlation and Network Topologies in Global and Local Stock Indices

This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indices increased with time, the local indices showed a decreasing trend except for drastic changes during crises. The average correlation of the local indices exceeded the global indices during the crises from 2000-2002, implying a strong correlation structure among the local indices during this period due to the detrimental effect of the dot-com bubble. The threshold networks (TN) were constructed in the observation time window by assigning a threshold value and determining the network topologies. A significant change in the network topologies was observed due to the financial crises in both markets. The Jaccard similarities were also determined using the common links of TNs. The TNs of the financial network were not consistent with the evolution of the time, and the successive TNs of the global indices were more similar than those of the successive local indices. Finally, the Jaccard similarities identified the change in the market state due to a crisis in both markets.Comment: 11 pages,4 figure

Investigation of the Financial Stability of S&P 500 Using Realized Volatility and Stock Returns Distribution

In this work, the financial data of 377 stocks of Standard & Poor’s 500 Index (S&P 500) from the years 1998–2012 with a 250-day time window were investigated by measuring realized stock returns and realized volatility. We examined the normal distribution and frequency distribution for both daily stock returns and volatility. We also determined the beta-coefficient and correlation among the stocks for 15 years and found that, during the crisis period, the beta-coefficient between the market index and stock’s prices and correlation among stock’s prices increased remarkably and decreased during the non-crisis period. We compared the stock volatility and stock returns for specific time periods i.e., non-crisis, before crisis and during crisis year in detail and found that the distribution behaviors of stock return prices has a better long-term effect that allows predictions of near-future market behavior than realized volatility of stock returns. Our detailed statistical analysis provides a valuable guideline for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods

Investigation of the financial stability of S&P 500 using realized volatility and stock returns distribution

In this work, the financial data of 377 stocks of Standard & Poor's 500 Index (S&P 500) from the years 1998-2012 with a 250-day time window were investigated by measuring realized stock returns and realized volatility. We examined the normal distribution and frequency distribution for both daily stock returns and volatility. We also determined the beta-coefficient and correlation among the stocks for 15 years and found that, during the crisis period, the beta-coefficient between the market index and stock's prices and correlation among stock's prices increased remarkably and decreased during the non-crisis period. We compared the stock volatility and stock returns for specific time periods i.e., non-crisis, before crisis and during crisis year in detail and found that the distribution behaviors of stock return prices has a better long-term effect that allows predictions of near-future market behavior than realized volatility of stock returns. Our detailed statistical analysis provides a valuable guideline for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods