What does the Carhart 4-factor model add beyond Fama-French, and how does momentum factor work?

The Carhart (1997) 4-factor model extends Fama-French by adding a momentum factor (WML — Winners Minus Losers). It was originally developed to evaluate mutual fund performance.

The Model:

E(Ri) - Rf = bi_mkt x (Rm - Rf) + bi_smb x SMB + bi_hml x HML + bi_wml x WML

What Is the Momentum Factor?

Momentum is the empirical observation that stocks that performed well over the past 3-12 months tend to continue performing well, and losers tend to continue losing. This is one of the most robust anomalies in finance.

WML Construction:

• Winners: Top decile (or quartile) of stocks ranked by past 12-month return (skipping the most recent month to avoid microstructure effects)
• Losers: Bottom decile (or quartile)
• WML = Return of Winners portfolio minus Return of Losers portfolio

Historically, WML has averaged about 6-8% per year in US equity markets.

Why Add Momentum?

Carhart showed that many mutual funds with apparent alpha under the 3-factor model were actually just riding momentum. Once you control for WML, much of the 'skill' disappears.

Worked Example:

Harbor Point evaluates two fund managers:

Manager A — Eastgate Growth Fund:

Actual excess return: 9.20%. Alpha = 9.20% - 8.45% = +0.75%

Manager B — Westfield Value Fund:

Actual excess return: 8.60%. Alpha = 8.60% - 7.40% = +1.20%

Manager B shows higher true alpha despite lower raw returns because Manager A's performance was largely explained by momentum exposure (WML loading of 0.55).

Exam tip: CFA Level II often presents a fund's 3-factor alpha and asks whether adding momentum changes the conclusion about manager skill. A fund with high momentum loading and positive 3-factor alpha may have zero or negative 4-factor alpha — meaning the manager was just buying recent winners rather than demonstrating stock-picking ability.

Learn more about performance attribution models in our CFA Level II course on AcadiFi.