Jensen's Alpha in Portfolio Performance

SUMMARY

Jensen's Alpha measures a portfolio manager's ability to generate returns above what would be predicted by systematic risk alone. This risk-adjusted performance metric compares actual returns against those expected based on the Capital Asset Pricing Model (CAPM), providing insight into active management skill.

Understanding Jensen's Alpha

Jensen's Alpha, developed by Michael Jensen in 1968, quantifies the excess return of a portfolio relative to the return predicted by the market risk (beta). The metric is calculated as:

$\alpha = R_p - [R_f + \beta(R_m - R_f)]$

Where:

$\alpha$ = Jensen's Alpha
$R_p$ = Portfolio return
$R_f$ = Risk-free rate
$\beta$ = Portfolio beta
$R_m$ = Market return

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Interpreting Jensen's Alpha

The interpretation of Jensen's Alpha is straightforward:

Positive Alpha ( $\alpha > 0$ ): Portfolio manager has outperformed the market on a risk-adjusted basis
Zero Alpha ( $\alpha = 0$ ): Portfolio performance aligns with market expectations
Negative Alpha ( $\alpha < 0$ ): Portfolio manager has underperformed on a risk-adjusted basis

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Statistical significance and limitations

Statistical testing

Jensen's Alpha should be tested for statistical significance using:

$t_{stat} = \frac{\alpha}{\sigma_{\alpha}}$

Where $\sigma_{\alpha}$ is the standard error of the alpha estimate.

Key limitations

Market benchmark dependency
- Results vary based on chosen market index
- Benchmark selection can bias results
Beta stability assumption
- Assumes constant systematic risk
- May not hold during market regime changes