Solving the index tracking problem based on a convex reformulation for cointegration

Abstract

This paper derives a mixed-integer non-linear optimization (MINLP) problem from the cointegration methodology and checks its convexity. We apply this approach to solve the index tracking (IT) problem using datasets from two distinct stock markets. The MINLP reformulation encompasses stock selection procedure and is optimized through branch-and-cut algorithm. The quality of the generated portfolios demonstrated lower turnover, which implies lower transaction costs over time and better performance in most instances regarding their tracking error in-sample and out-of-sample when compared with the traditional cointegration based IT portfolios.