Taking Out the Outliers II

This is a follow-up to my previous post in which I described Rousseeuw's FastMCD algorithm for using the minimum covariance determinant approach to calculating a robust covariance matrix. I want to use the example from that post (the relationship between the returns of QIM and Quantica over the last 5 years) to explore the behavior of the FastMCD algorithm. Finally I want to suggest a way of combining the advantages of the robust and conventional approaches to covariance analysis.

Taking Out the Outliers

If you do anything that depends upon correlation, you owe it to yourself to be aware of outliers and how to deal with them. For example, a mean-variance optimized portfolio using Modern Portfolio Theory or the Black Litterman model is critically dependent upon, and very sensitive to the portfolio covariance matrix. In turn, the covariance matrix is extremely sensitive to outliers (leverage points).

This post was inspired by a posting on the Tr8dr Blog. The original source paper in which the details of the algorithm are specified is "A Fast Algorithm for the Minimum Covariance Determinant Estimator" Rousseeuw, Van Driessen, 1998. This paper is an implementation of the ideas detailed in "Least Median of Squares Regression", Rousseeuw, 1984. Both papers are easy to find.

In this post I hope to add a little extra color, detail and exploration to the original sources above.