Follow the Leader : Index Tracking with Factor Models

We propose a new methodology to select a subset of assets for (partial) index replication, based on the latest research on factor models of large dimensions. Our method selects the set of leader stocks that can fully capture the systematic risk of the index to be replicated. Our selection methodology is consistent as the sample size and the number of assets jointly approach infinity. Monte Carlo experiments show that our estimated index replica tracks the underlying index with relatively small tracking errors in finite samples. We show the applicability of the method by tracking the S&P 500 equally weighed index with promising out-of-sample performance. Our method can be easily adapted for synthetic index replication and to incorporate measures of liquidity or transaction cost