Dynamic asset trees in the US stock market: Structure variation and market phenomena

Abstract

In this work, employing a moving window to scan through every stock price time series over a period from 2 January 1986 to 20 October 2015, we use cross-correlations to measure the interdependence between stock prices, and we construct a corresponding minimal spanning tree for 170 U.S. stocks in every given window. We show how the asset tree evolves over time and describe the dynamics of its normalized length, centrality measures, vertex degree and vertex strength distributions, and single- and multiple-step edge survival ratios. We find that the normalized tree length shows a tendency to decrease over the 30 years. The power-law of vertex degree or vertex strength distribution does not hold for all trees. The survival ratio analysis reveals an increased stability of the dependence structure of the stock market as time elapses. We then examine the relationship between tree structure variation and market phenomena, such as average, volatility and tail risk of stock (market) return. Our main observation is that the normalized tree length has a positive relationship with the level of stock market average return, and it responds negatively to the market return volatility and tail risk. Furthermore, the majority of stocks have their vertex degrees significantly positively correlated to their average return, and significantly negatively correlated to their return volatility and tail risk.