Math & Analytics

Alpha

Risk-adjusted excess return of an investment above what would be predicted by its beta (CAPM).

S65S66CFP

Alpha (α) measures a portfolio or security's risk-adjusted excess return compared to what CAPM (Capital Asset Pricing Model) would predict given its beta.

Formula: > Alpha = Actual Return − Expected Return (per CAPM) > Expected Return = Risk-free rate + Beta × (Market return − Risk-free rate)

Interpretation:

| Alpha | Meaning | |---|---| | α > 0 | Manager outperformed on a risk-adjusted basis (added value) | | α = 0 | Performance exactly as expected for the risk taken | | α < 0 | Underperformed on a risk-adjusted basis (destroyed value) |

Example: Risk-free rate = 3%, market return = 10%, portfolio beta = 1.2. - Expected return = 3% + 1.2 × (10% − 3%) = 3% + 8.4% = 11.4%. - Actual return = 13%. - Alpha = 13% − 11.4% = +1.6% (positive alpha — manager added value).

Alpha vs. returns: A portfolio can have high returns and negative alpha (if it took excessive risk). Alpha isolates the manager's skill from market exposure.

Jensen's alpha: A specific version of alpha used in performance measurement; calculated as above. A positive Jensen's alpha suggests genuine skill.

Efficient Market Hypothesis (EMH): In a truly efficient market, alpha should be zero on average. Most actively managed funds have negative alpha after fees.

> Exam tip: Positive alpha = outperformance vs. risk-adjusted expectation = good. Negative alpha = underperformance. Alpha and beta are the two most important performance attribution metrics for the Series 65/66 and CFP® exams.

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