Financial Modeling
Jensen’s Alpha (CAPM Abnormal Return) & Systematic Beta Return Attribution
Decompose realized portfolio return into risk-free carry, systematic market-beta exposure, and manager selection skill (Jensen’s Alpha = R_p - [R_f + beta * (R_m - R_f)]).
Why raw excess return over the index misstates high-beta manager skill
Comparing a portfolio’s 14.8% return directly against an 11.2% equity index return suggests +3.60% of outperformance. However, if the portfolio ran a systematic beta of 1.20 while the risk-free Treasury yield was 4.2%, Capital Asset Pricing Model (CAPM) equilibrium already required 4.2% + 1.20 * (11.2% - 4.2%) = 12.6% just to compensate investors for amplified market exposure.
Michael Jensen’s (1968) Alpha isolates risk-adjusted selection skill by subtracting the beta-adjusted CAPM benchmark from realized portfolio return: alpha_J = R_p - (R_f + beta * (R_m - R_f)). In our example, true selection alpha is +2.20% (+220 bps), while +8.40% came from systematic market beta and +4.20% from the risk-free floor.
| Attribution Layer | Formula | Example Value | Share of 14.8% Return |
|---|---|---|---|
| Risk-Free Carry (R_f) | B3 | 0.0420 (4.20%) | 28.38% |
| Systematic Beta Return | B5 * (B4 - B3) | 0.0840 (8.40%) | 56.76% |
| CAPM Required Benchmark | B3 + B5 * (B4 - B3) | 0.1260 (12.60%) | 85.14% |
| Jensen’s Alpha (Skill) | B2 - (B3 + B5 * (B4 - B3)) | 0.0220 (+220 bps) | 14.86% |
CAPM Required Return & Jensen’s Alpha Formula
Subtract R_f + beta * (R_m - R_f) from realized portfolio return R_p, and multiply by 10,000 when reporting institutional basis points.
=ROUND(B2 - (B3 + B5 * (B4 - B3)), 4)Sample Beta & Alpha from Periodic Return Columns
When computing directly from periodic excess return columns, SLOPE(excess_port, excess_mkt) estimates beta and INTERCEPT(excess_port, excess_mkt) estimates periodic Jensen’s Alpha directly.
=ROUND((B2 - (B3 + B5 * (B4 - B3))) * 10000, 1)Try the example
Use the original values or change them to test your understanding.