Dynamic asset trees and portfolio analysis |
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Authors: | J-P Onnela A Chakraborti K Kaski J Kertiész |
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Institution: | (1) Laboratory of Computational Engineering, Helsinki University of Technology, PO Box 9203, 02015 HUT, Finland, FI;(2) Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary, HU |
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Abstract: | 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 characterise
it by its normalised length and by the mean occupation layer, as measured from an appropriately chosen centre called the `central
node'. We show how the tree evolves over time, and how it shrinks strongly, in particular, 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 normalised tree length and the investment diversification potential are very strongly correlated.
Received 7 August 2002 / Received in final form 28 October 2002 Published online 19 December 2002 |
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Keywords: | PACS 89 65 -s Social systems – 89 75 -k Complex systems – 89 90 +n Other topics in areas of applied and interdisciplinary physics |
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