Dynamic asset trees and portfolio analysis

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns and provides a meaningful economic taxonomy of the stock market. In order to study the dynamics of this asset tree we characterize it by its normalized length and by the mean occupation layer, as measured from an appropriately chosen center. We show how the tree evolves over time, and how it shrinks particularly strongly during a stock market crisis. We then demonstrate that the assets of the optimal Markowitz portfolio lie practically at all times on the outskirts of the tree. We also show that the normalized tree length and the investment diversification potential are very strongly correlated.