Equity Importance Modeling With Financial Network and Betweenness Centrality

Financial market has been investigated from many perspectives. The recent emerging financial network methods model the market as a network. The edge between two vertices, or two equities are modeled as the correlation coefficient of the return on the prices of two equities in a period. A common question one can pose is that how can we determine the importance of an equity in the market. From a financial perspective, market-cap is an indicator of importance. But what is its correspondence from a financial network point-of-view? Degree distribution is an intuitive answer. However, after investigating on the betweenness centrality, which is another importance measurement of the graph, we found a high correlation between the betweenness centrality and market-cap. Degree of a vertex, in our case, denotes the number of equities that are highly correlated to it, which shows its local importance and lacks the capability to reflect its importance from a market-wide view. However, betweenness centrality of a vertex encodes global information. It measures the level to which a vertex is need by others along shortest path. In the experiment, we build a financial network using 473 stocks out of the SP-500 pool, during a one year period from June, 2008 to June, 2009. Betweenness centrality is calculated based on the known fasted Brandes algorithm. It is found that the average market-cap of the 20 stocks with largest degree is 29.0 billion dollars, slightly larger than that of the SP-500 stocks, which is 23.5 billion dollars. However, the average market-cap of the stocks with 20 largest betweenness is 50.5 billion dollars, more than twice of the SP500’s average market-cap. The market-cap-betweenness plots also shows an upward tendency, meaning that betweenness values are positive correlated with the market-caps, while the market-cap-degree plots doesn’t show such phenomenon.