One-factor model for the cross-correlation matrix in the Vietnamese stock market

• We measure the eigenvalue spectrum of the cross-correlation matrix in the Vietnamese stock market.
• An emerging market has high largest eigenvalue, high correlation, and low sector groups.
• We simulated the largest eigenvalue, and found the effects of the average correlation and number of stocks.
• The repulsion effect is the main cause of the shift of the bulk eigenvalue.
• More useful information could be contained in the RMT bulk eigenvalue.

Random matrix theory (RMT) has been applied to the analysis of the cross-correlation matrix of a financial time series. The most important findings of previous studies using this method are that the eigenvalue spectrum largely follows that of random matrices but the largest eigenvalue is at least one order of magnitude higher than the maximum eigenvalue predicted by RMT. In this work, we investigate the cross-correlation matrix in the Vietnamese stock market using RMT and find similar results to those of studies realized in developed markets (US, Europe, Japan) [9], [10], [11], [12], [13], [14], [15], [16], [17] and [18] as well as in other emerging markets[20], [21], [19] and [22]. Importantly, we found that the largest eigenvalue could be approximated by the product of the average cross-correlation coefficient and the number of stocks studied. We demonstrate this dependence using a simple one-factor model. The model could be extended to describe other characteristics of the realistic data.