## Studying the Network Structure, Connectedness, and Power of the European Stock Markets

The political integration of Europe under the European Union in 1993 was also an economic and financial integration. Since the creation of the European Union, many global investors and analysts consider the developments in the financial markets of any one member country to have a significant impact on the markets of other member countries as well. Previously, such levels of correlation between stock market exchanges of countries in the European Union were studied by constructing large tables containing cross-correlation coefficients and other relevant calculations. While useful, the application of graph and network theory could visually show investors and regulators precisely to what degree European financial markets are connected and which countries have the biggest impact on other markets. The aim of the paper “Network structures of the European stock markets” (Cupal et. al) was to apply network theory to visually understand the correlation and interconnectedness of European stock markets.

First, the correlation coefficients for each pair of markets and stocks were calculated. Then, using a specific type of an undirected connected graph called a minimum spanning tree, a minimum spanning tree of the markets in question were created. A spanning tree is a subset graph of a larger graph that connects every node in the graph with edges, removing any cycles in the graph. In any graph there can be multiple spanning trees. A minimum spanning tree is a spanning tree that takes weight into account and seeks to find the spanning tree in a graph with the smallest weight. For example, in this study, each node in the graph represented a stock exchange. This study looked at the 17 indices representing each member of the European Monetary Union. The weight in this minimum spanning tree was related to the correlation coefficient for a pair of markets so that a lower weight would be placed on a pair of markets that were more strongly correlated. Once the minimum spanning tree of the markets was calculated, it could be studied to understand the correlation and connectedness of European markets. While this graph was undirected, edges between nodes had a different thickness. Similar to strong and weak links, the thickness of the edge signifies the significance that the four largest European markets had on the pair of markets.

Studying the minimum spanning tree graphs of the European financial markets over the long (1 year), middle (30 minutes), and short terms (5 minutes) shows interesting trends. While Germany usually is regarded as the most influential market on other European countries, the French stock market in the graphs usually played the central role as it was connected and correlated to more countries than Germany’s stock market was. Thus, an event in the French stock market may result in more significant ripples across European financial markets than if an event happened in the German stock market. Additionally, the countries with the smallest market caps such as Luxemburg, Greece, and Cyprus were largely unconnected and uncorrelated to the events of other markets. Although the core four markets of Germany, France, Italy, and Spain held considerable network power throughout the long, middle, and short terms, the structure of each network changed depending on the time horizon. For example, the long-term graph showed multiple “center” nodes. This is evidence of the fact that across the long-term no one exchange had the most powerful position in the network such that all other stock exchanges moved in unison with it. In the short-term, however, it was apparent that one node had a powerful network position such that the other markets were heavily correlated to its movements.

The authors of this paper made several interesting conclusions regarding their results. The European financial markets are deeply connected and as a result, investors and regulators should not consider two different European stock markets to be diversified and safe from the movements of other markets. However, this cannot be said about the smaller countries such as Luxemburg, Greece, and Cyprus that have less correlation. Additionally, these researchers ran experiments to look at cross-country correlations of specific stocks and found similar evidence that the stocks of smaller countries correlated less to the stocks in larger countries. Thus, investors seeking diversification would take an interest in the relative independence of the stock markets of smaller European countries. Although researchers created minimum spanning trees for three different time horizons, they found that the four most connected countries remained the same across all three time horizons. Thus the movements in the stock markets of Germany, France, Italy, and Spain always had a significant impact on the stock markets of the other European countries, regardless of the time scale examined.

This study ties into this Networks class and the larger network theory because it studies how nodes in a network interact with each other in both positive and negative ways. Additionally, it creates a mathematical definition and scale for strong and weak ties and uses it to draw conclusions from a mathematical set of data. Finally, this study looked at the relative power of different nodes depending on their position in the network structure and how their position affected other nodes.

Source: http://mme2012.opf.slu.cz/proceedings/pdf/014_Cupal.pdf

great post!