Model explainer — theory, significance, and formulas.

An extension of the 3-factor model (market / size / value) that adds two more drivers: "the effect of consistently profitable companies (RMW)" and "the effect of conservatively investing companies (CMA)". It provides the academic explanation for why Warren Buffett-style quality investing tends to work.

In the two decades following the 3-factor model, "alpha not explained by 3 factors" kept showing up. Two patterns stood out in particular:

• Companies that consistently earn profits tended to deliver higher average returns than those that did not.
• Companies that expanded their assets conservatively tended to outperform those that expanded aggressively.

In 2015, Fama and French formally folded these two patterns into the factor model.

As emphasized in the 3-factor explanation, a positive beta does NOT mean "my portfolio is composed of those names" — it means "my portfolio's returns moved together with that factor's returns." RMW and CMA should be read the same way: not "do I directly hold quality companies?", but "did my portfolio's returns rise during periods when quality companies were in favor?"

• RMW (Robust Minus Weak · profitability factor) — the average return of "robust" (high operating-profit) companies minus that of "weak" (low operating-profit) companies. A positive β_R means your portfolio tends to rise during periods of quality-stock strength. This is co-movement of returns, not holdings composition — and it is the academic definition of "the Buffett-style quality effect."
• CMA (Conservative Minus Aggressive · investment factor) — the return of conservatively-investing companies minus that of aggressively-investing companies. A positive β_C means your portfolio tends to rise when conservatively-investing firms lead. A negative β_C means it rises when aggressively-investing firms lead — readable as exposure to a "high-growth-seeking" style.

Practical use — diagnose portfolio style with the 5 betas. β_R > 0 + β_C > 0 means "quality + conservative capital allocation" — consistent with Buffett-style investing. β_R < 0 + β_C < 0 means "high-growth + aggressive investment" — a tech-growth style. The diagnosis is not the portfolio's "label" but a statistical measure of "in which periods did its returns co-move with what?"

The radar above superimposes the 5-factor betas of two hypothetical portfolios. The green polygon (Buffett style) shows positive RMW, CMA and HML — it rises with quality strength, with conservative-investment leadership, and with value leadership. The red polygon (tech growth) has negative RMW, CMA and HML — it co-moves with high-growth, aggressive-investment and growth-stock leadership. The two polygons being mirror images is exactly what "opposite styles" looks like.

• The theoretical foundation for quality / wide-moat ETFs (e.g., QUAL, MOAT)
• Testing whether unexplained alpha under 3 factors was really exposure to RMW · CMA
• A more granular "factor exposure diagnosis" than style boxes

With more factors, the factors themselves can become strongly correlated, raising multicollinearity problems. This tool reports VIF (Variance Inflation Factor) alongside the regression so you can check for it.

• Kenneth R. French — Data Library (Tuck School of Business) · The raw 5-factor data (Fama/French 5 Factors) — this tool's US-stock factor source (Korean stocks use factors we compute in-house)
• Wikipedia — Fama–French five-factor model · Overview of RMW · CMA and the differences vs. the 3-factor model
• Wikipedia — Variance Inflation Factor (VIF) · The multicollinearity diagnostic to read alongside the 5-factor regression