Fama-French 5-Factor & Momentum Regression Workbench

PORTFOLIO FACTOR SENSITIVITIES (β)

Risk-Free Rate (R_f)4.25%

Market Excess Return (R_m - R_f)5.50%

Market Beta (β_mkt)1.05

Size Tilt: SMB (β_smb)0.25 (Small-Cap)

Value Tilt: HML (β_hml)-0.20 (Growth)

Profitability: RMW (β_rmw)0.35 (Robust)

Investment: CMA (β_cma)-0.15 (Aggressive)

Momentum: MOM (β_mom)0.30 (Trend Follower)

Realized Excess Return (R_p - R_f)8.20%

Expected Return (E[R_p])

11.85%

Nominal Factor Return

Jensen's Alpha (α)

+0.60%

True Skill Above 6 Factors

CAPM Implied Beta Return

10.03%

Single-Factor Baseline

Factor Excess Spread

+1.82%

Multi-Factor Premium

Portfolio Factor Tilt Polygon (Normalized Style Profile)

Factor Attribution & Variance Decomposition

Factor Name	Factor Sensitivity (β)	Annual Factor Premium	Contribution to E[R]	Style Interpretation

The Mathematics of Fama-French 5-Factor & Momentum Models

In 1993, Eugene Fama and Kenneth French demonstrated that market beta (β_mkt) explains only a fraction of cross-sectional equity returns. They introduced the 3-factor model adding Size (SMB) and Value (HML). In 2015, they expanded to 5 factors by incorporating Operating Profitability (RMW) and Investment Conservatism (CMA). Mark Carhart subsequently added cross-sectional Price Momentum (MOM).

E[R_p] - R_f = α + β_mkt(R_m - R_f) + β_smb(SMB) + β_hml(HML) + β_rmw(RMW) + β_cma(CMA) + β_mom(MOM)

De-Masking Fake Alpha: A common trap in active equity management is confusing factor exposure with managerial skill. An active manager claiming 200 bps of Alpha who is merely holding small-cap value equities (β_smb > 0, β_hml > 0) is capturing systematic factor risk premia—not generating true idiosyncratic α. Once the 6-factor regression is applied, residual α must remain statistically positive (t-stat > 2.0) to confirm authentic alpha.