On Using Statistical Factor Models in Optimizing Long-Only Portfolios
by Patrick Burns.
Abstract: Realized tracking errors are examined for a series of optimized portfolios using various estimates for the variance matrix. It is clear that the benchmark should be added mathematically to the variance matrix using the constituent weights — this dramatically outperforms the case where the benchmark is a separate asset in the return matrix or where relative returns are used. The common belief that factor models are to be preferred to sample variance estimates is confirmed, but only on condition that the benchmark is added mathematically to the variance matrix.
See also the blog post “How to add a benchmark to a variance matrix”.