This blog post is available as a PDF here.

Summary­­

  • The debate for the best way to build a multi-factor portfolio – mixed or integrated – rages on.
  • Last week we explored whether the argument held that integrated portfolios are more capital efficient than mixed portfolios in realized return data for several multi-factor ETFs.
  • This week we explore whether integrated portfolios are more capital efficient than mixed portfolios in theory.  We find that for some broad assumptions, they definitively are.
  • We find that for specific implementations, mixed portfolios can be more efficient, but it requires a higher degree of concentration in security selection.

This commentary is highly technical, relying on both probability theory and calculus, and requires rendering a significant number of equations.  Therefore, it is only available as a PDF download.

For those less inclined to read through mathematical proofs, the important takeaway is this: for some broad assumptions, integrated multi-factor portfolios are provably more capital efficient (e.g. more factor exposure for your dollar) than mixed approaches.