Multi-Factor Investing: Intersectional vs Combination Models

Which one is superior?

August 2026. Reading Time: 10 Minutes. Author: Nicolas Rabener.

SUMMARY

  • Long-short multi-factor funds are at all-time highs
  • Long-only smart beta funds have performed poorly recently
  • Significant differences between the intersectional and combination models

INTRODUCTION

Most investors should focus on asset allocation rather than stock selection, as beating the market seems exceptionally difficult. For fund managers mandated to pursue stock selection, however, factor investing is the only approach with meaningful support from financial research. Even this is challenging, though, since factor premia only manifest over the medium to long term, which naturally clashes with investors’ short-term expectations.

Implementing factor strategies requires a number of decisions, including defining the universe, selecting factors, and constructing the portfolio. Although plenty of single-factor funds exist, most funds actually provide exposure to multiple factors. A small-cap value fund, for example, provides exposure to both the size and value factors.

Fund managers typically combine factors via three models: combination, intersectional, and sequential. We compared all three in previous research articles and found no clearly superior methodology. However, that analysis focused on long-short portfolios, whereas the vast majority of practitioners pursue factor investing through long-only (smart beta) funds.

In this article, we contrast the combination and intersectional models for long-only multi-factor portfolios.

LONG-SHORT MULTI-FACTOR INVESTING

First, we construct long-short multi-factor portfolios using the value, momentum, and quality factors. Value is defined by P/B and P/E multiples, momentum by trailing 12-month performance excluding the most recent month, and quality by return on equity. We use the universe of U.S. stocks, which totals approximately 2,000 stocks in 2026. For the intersectional model, also known as the integrated model, we select the top and bottom 10% of stocks ranked across all three factors. For the combination model, we combine single-factor portfolios comprised of the top and bottom 3% of stocks. As a result, both portfolios comprise approximately 200 stocks on the long side and the same number on the short side. Stocks are weighted eq