Identifying small mean-reverting portfolios

Abstract

Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability trade-off and the significance of predictability in various markets.

Keywords:

• Derivatives securities
• Derivatives risk management
• Derivatives pricing
• Derivatives hedging

Acknowledgements

The author would like to thank Marco Cuturi, Guillaume Boulanger and conference participants at the third Cambridge–Princeton conference and the INFORMS 2007 conference in Seattle for helpful comments and discussions. The author would also like to acknowledge support from NSF grant DMS-0625352, ONR grant number N00014-07-1-0150, NSF CDI grant SES-0835550, a NSF CAREER award, a Peek junior faculty fellowship and a Howard B. Wentz Jr. junior faculty award.