Active Risk Constraints for Regression Based Index Tracking

Regression based index tracking selects tracking portfolios based on the linear regression characteristics of the available assets. The approach is suited to Mixed Integer Linear Programs where the number of assets in the tracking portfolio is limited compared to the number of constituents in the benchmark portfolio. Current approaches do not account for the active risk of the tracking portfolio, resulting in concentrated portfolios with high tracking error. This paper considers two extensions, both a linear and quadratic formulation, to the current approaches. The resulting portfolios are more diversified, have lower tracking error and tracking difference, and have appropriate levels of beta.