Monday, October 5, 2020

Thinking through clustering for a different but clearer perspective

There are a couple of visuals that are always used in the money manager's toolbox. One tool for quick comparison is the scatter plot of return and risk across different asset classes. Some analysts will get more sophisticated with this visual by looking at how asset classes have moved through time in risk and return space. Some with better visual dexterity will look at three dimensions and include correlation. 

The visual information of risk and correlation is computed and collected in the covariance matrix which is a core component of any optimization. Unfortunately, the covariance matrix can be difficult to work with as more correlated assets are added to the matrix or if there is instability in covariance through time. The impact of covariance sensitivity is less intuitive on risk measurement and asset weight selection but is a critical part of asset allocation. Any optimization is sensitive to multi-collinearity and the difficulty of inversion. If there are more assets that have similar covariance, small changes in statistical characteristics will lead to significant changes in optimized weights; the optimized asset allocation is unstable. 

A tool that can be useful and that is easily visual for money managers is cluster analysis through the use of principal component factorization. Principal component analysis is a data dimensionality reduction tool. It looks for similarity across data or common feature extraction. By eliminating common features, we can find uniqueness. By grouping common features, we can find clusters which can be graphically displayed. 

When assets cluster around common factors or have similar covariance characteristics, asset allocation becomes more difficult. One, there is less diversification benefit. A cluster of assets around principal components will not offer any benefit to investors. Portfolio risk is not diminished. Two, the covariance matrix becomes less stable and optimization becomes harder. The asset allocation will become sensitive to small changes in the price behavior of any asset in the portfolio.

There are quantitative methods for finding clusters and adjusting the covariance matrix, but a first past is to focus on the intuition of cluster analysis. No different than any good data work, plotting the information is a critical first step for analysis. 

As shown in the graph above, there are some well-defined asset clusters and some assets that are unique. Assets in the clusters are going to add little value to the portfolio. Optimization across those clustered assets will shown unstable weights. Assets outside clusters will have strong diversification benefit. Assets outside clusters are more important to a portfolio and should be a place of focused investment effort. Look for commonality of factors and find uniqueness. This process of combination for commonality and uniqueness will always be rewarded.  

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