Cluster Risk Parity– A Visual Representation
The following graphic is borrowed from a static risk parity approach via Salient Capital Advisors: http://www.theriskparityindex.com/static/pdfs/Salient-Risk-Parity-Index-White-Paper.pdf. The visual is useful for readers to understand the nuances and relative merits of a Cluster Risk Parity (CRP) approach. In their approach the individual assets and clusters are defined in advance, and thus there is no dynamic clustering method used. However, the concept that they use is similar: balance risk contributions both within and across “clusters” of assets. In this case it is important to clarify that the size/area of each slice of the pie chart is a function of risk contributions NOT percentage capital allocations.
As you can clearly see from this specific chart, it is very similar in spirit to the “All-Weather” Portfolio or even the simpler Permanent Portfolio . The main difference is that the latter portfolio schemes represent “strategic asset allocation” alternatives, while Cluster Risk Parity (and also the Salient Index) is a dynamic asset allocation framework. GestaltU does a good job describing why it is important to prefer dynamic approaches in a recent post: http://gestaltu.blogspot.com/2013/01/the-full-montier-absolute-vs-relative.html. In reference to CRP the advantage is creating a framework that does not require having to pre-specify the assets and weights in advance on a static basis. Instead, it permits the ability for the portfolio to adapt to changes in the variance/covariance matrix of asset returns — which have proven especially useful in a dynamic framework to normalize risk exposure. This framework is so generic that it can be adapted to any type of risk factor or regime framework with relative ease.
CSSA 
Hi David, CRP sounds very appealing. I have a couple of questions:
1) Is there anyway one can optimally choose the number of clusters?
2) How sensitive are the clusters with respect to changes in the entries correlation matrix (or similarity matrix)? In other words, will an asset jump from one cluster to other over time erratically?
3) What type of similarity measures are there beyond correlation and pca?
Many thanks,
John
hi John, the questions you are asking are all good–but they require in depth discussion. I will try to answer some of these issues. Here is one good link to explore: http://radio.feld.cvut.cz/matlab/toolbox/fuzzy/fuzzyt42.html . Another is: http://www.pami.uwaterloo.ca/pub/hammouda/sde625-paper.pdf It is possible to attempt to find an optimal number but that depends on what you are trying to do. If you use correlation (again this depends a lot on the clustering algorithm) for example, the thresholds will determine the number of clusters. What I have found is that the performance of a cluster algorithm (at least those that I have developed or tested) are not that sensitive to the threshold, and you can always trade multiple portfolios with tiered thresholds (or numbers of clusters) to ensure stability. In terms of the sensitivity–it is important to note that having assets jump from one cluster to the other over time can be beneficial if the distance estimates are correct out of sample. this will produce a much better portfolio that adapts to change in the correlations for example—-however assuming that the estimate is poor then obviously changing cluster membership is a significant drag on performance and risk. If you are simply trying to reduce transactions and keep a stable set of clusters then it is necessary to use long lookbacks for the distance metric and/or less granular data (ie like monthly or weekly data) to reduce sensitivity to change.
best
david