Using Multidimensional Scaling on financial time series



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Imagine we had a table with the distances between some European cities, but we don’t know any Geography. It would be a complicated task to correctly place them on a map:


However, using “Multidimensional Scaling” the task becomes simple:


Similarly, given distances between time series (in this case NAVs of investment funds) we could carry out the same exercise. This would offer a better understanding of which funds are more alike (and by how much) in an objective way, instead of relying on their names, classification or their historical long term behaviour.

As an example, we are going to take the price series of 20 investment funds belonging to 10 categories (2 of each). We create the map with the data from 2007 to 2009:

Fund map 2007-2009

In the central part some groups appear: fixed income funds on the left-hand side and developing country variable income on the right. Other groups, clearly differentiable from the previous ones and amongst themselves, are real estate, emerging variable income and commodity funds.

There are categories with a high similarity between the two representatives (for example, emerging variable income and global fixed income) and others less similar (commodities or real estate).
Obviously the behaviour of the funds and the relationships between them vary over time such that if we analyse another period, the map is different:

Fund map 2011-2013

The Japanese variable income funds now are clearly differentiable from the rest. The other categories are no longer as separate as in the previous period. Also, the representatives from the same category that were close together before are not anymore, and vice versa.

When is this analysis useful?

There are many distances and time horizons in which doing this analysis could be useful. “Multidimensional Scaling” is strongly linked to decomposition into principal components (Principal Component Analysis) and the next natural step would be to apply an algorithmic method to group the elements together such as Clustering.

These techniques are of use in many different areas; for example universe analysis, automatic classifications, detection of repeated/unnecessary information, or in risk management.

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