Topological properties of a minima spanning tree in the Korean and the American stock markets

Abstract

By using individual stock data listed on the S&P500 and the KOSPI, we investigate a factor that can affect the number of links of a specific stock in a network between stocks created by the minimal spanning tree (MST) method. Among the common factors mentioned in the arbitrage pricing model (APM), widely acknowledged in the financial field, the representative market index is established as a possible factor. We found that the correlation distribution, p(ij), of 400 stocks taken from the S&P500 index was very similar to that of the Korean stock market and that those deviated from the correlation distribution of a time series with a nonlinearity removed by using a surrogate method. We also shows that the degree distribution in the network between stocks obtained by using the MST method for both stock markets follows a power-law distribution with an exponent (S&P500,KOSPI similar to 2.1 while the degree distribution of the time series with nonlinearity eliminated follows an exponential distribution with an exponent delta(S& P500(surrogate), KOSPI (surrogate)) similar to 0.77. Furthermore, the correlation, p(iM), between the degree k of individual stocks and the market index for both the stock markets is positively related to the degree k. Thus, regardless of the market, individual stocks closely related to a common factor in the market, the market index, are likely to be located around the center of the network between stocks while those weakly related to the market index are likely to be placed outside.