How often have you heard that there are connections between financial series? In particular, it’s common to hear that series representing the economy of a region or country are related.
The whole world is influenced by certain major factors, such as wars, economic crises, and political events. There are other connections, too, between geographic locations and their economic situation. There are bound to be moments where they move in the same (or opposite) directions.
It’s easy to see
By looking at the price evolution of some of the world’s main Equity indexes in the last year, we can see similarities in some trends and movements.
How would you visualize these relationships? What if we wanted to see how the different regions are connected?
Using graph theory graphs is a clever way to plot these connections. These graphs are made up of nodes and lines (alternatively, vertices and edges). Each region or country is represented by a node. If a “relationship” exists between two, a line is drawn between them, therefore creating a connection.
So, how do we define a connection between two regions?
Firstly, we calculate the correlation between the 12 series using the index returns during 2017. We then define that a “relationship” exists when the absolute value of the correlation is above a certain threshold or limit, with critical values between 0 and 1.
Any correlation below this critical value means the two indexes are not related and no line joins them together. Correlations above the limit will be connected by a line, to show that a relationship exists.
In this way, we can be more or less ‘demanding’ with our critical value to define the connections. A higher critical value is less demanding and more connections are made, increasing the activity and robustness in the graph. On the other hand, a lower value is more demanding so there are fewer connections, therefore making the graph emptier and less robust.
The three connection graphs have used three critical values in this order: 0.25, 0.5 and 0.75.
When using a small critical value almost all the indexes are connected. If we are more demanding (increasing the critical value to 0.5) we see how only Europe, USA and Japan remain connected. For very high correction values (>0.75) only the European indexes are connected.
You can use this idea to plot with different periods, series or apply it to very different non-financial data.