A Three-phase Approach to an Enhanced Index-tracking Problem with Real-life Constraints

Abstract

Enhanced index tracking is an emerging strategy for investing money in the stock market and is aimed at achieving outperformance over a given benchmark index while achieving a low tracking error. We consider the problem of rebalancing a portfolio for an enhanced index tracking strategy subject to various real-life constraints, including a lower bound and an upper bound on the expected tracking error. To solve this problem, we propose a three-phase approach consisting of preprocessing, optimization, and learning. In a computational experiment, we applied this approach to rebalance a given portfolio on a monthly basis over a time horizon of 10 years; the data for the S&P 500 benchmark index were provided by the investment company Principal Global Investors. Our approach generated portfolios that were provably close to optimality for all monthly rebalancing decisions. Over the entire horizon of 10 years, the portfolios devised by our approach yielded cumulative returns higher than the S&P 500 index after transaction costs with a moderate tracking error.

Additional information

Notes on contributors

O. Strub

Oliver Strub is a postdoc at the Chair of Quantitative Methods in Business Administration at the University of Bern, Switzerland. He received a Ph.D. and an M.S. degree in business administration and a B.S. degree in economics from the University of Bern. His primary research interest is in portfolio optimization, applications of mathematical programming in data science, and combinatorial optimization.

S. Brandinu

Stefano Brandinu received an M.S. and a B.S. degree in business administration from the University of Bern, Switzerland. His research interests are combinatorial optimization and portfolio optimization.

D. Lerch

Dennis Lerch is a teaching and research assistant at the Chair of Quantitative Methods in Business Administration at the University of Bern, Switzerland. He holds two degrees in business administration (B.S. and M.S.). His research interests are project scheduling, combinatorial optimization, and optimization in finance.

J. Schaller

Jürgen Schaller received an M.S. and a B.S. degree in business administration from the University of Bern, Switzerland. His research interests are combinatorial optimization and matheuristics.

N. Trautmann

Norbert Trautmann is a full professor of quantitative methods in business administration at the University of Bern, Switzerland. He holds an M.S. in business engineering/management science, a PhD in economics, and a habilitation degree for operations research, production, and logistics from the University of Karlsruhe, Germany. His primary research interest is in combinatorial optimization with applications in project management and project scheduling, production planning and control, and portfolio optimization.