Factor-based robust index tracking

We consider a robust optimization approach for the problem of tracking a benchmark portfolio. A strict subset of assets are selected from the benchmark such that the expected return is maximized subject to both risk and tracking error limits. A robust version of the Fama-French 3 factor model is developed whereby uncertatiny sets for the expected return and factor loading matrix are generated. The resulting model is a mixed integer second-order conic problem. Computational results in tracking the S&P 100 out of sample show that the robust model can generate tracking portfolios that have better tracking error and Sharpe ratio than those generated by the nominal model.