This blog post is available as a PDF here.


  • 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.

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients.

Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn.

Corey is a frequent speaker on industry panels and contributes to, ETF Trends, and’s Great Speculations blog. He was named a 2014 ETF All Star by

Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University.

You can connect with Corey on LinkedIn or Twitter.