Jensen’s Measure

Jensen’s Measure (Jensen’s Alpha)

Jensen’s measure, commonly called Jensen’s alpha, quantifies the excess return of an investment or portfolio relative to its expected return as predicted by the Capital Asset Pricing Model (CAPM). It adjusts for the level of systematic risk (beta) and the prevailing risk-free rate to determine whether a manager or strategy delivered returns beyond what risk exposure alone would explain.

Formula and variables

Alpha = R(i) – [R(f) + B × (R(m) – R(f))]

Where:
* R(i) = realized return of the portfolio or investment
* R(m) = realized return of the chosen market benchmark
* R(f) = risk-free rate for the same period
* B = portfolio beta relative to the benchmark

Interpretation:
* Positive alpha: the investment outperformed its CAPM‑predicted return (value added).
* Negative alpha: the investment underperformed relative to its risk.
* Zero alpha: performance in line with CAPM expectation.

How it’s used

• Evaluating active managers: Determines whether a manager’s returns exceed what would be expected for the portfolio’s market risk.
• Comparing funds: Helps compare funds with different volatility profiles by adjusting for beta.
• Performance attribution: Isolates manager skill (stock selection/timing) from market-driven returns.

Example

Assume:
* Portfolio return R(i) = 15%
* Market return R(m) = 12%
* Risk-free rate R(f) = 3%
* Beta B = 1.2

Calculation:
Alpha = 15% – [3% + 1.2 × (12% − 3%)]
Alpha = 15% − [3% + 1.2 × 9%] = 15% − 13.8% = 1.2%

A positive alpha of 1.2% indicates the fund earned 1.2 percentage points more than its CAPM-expected return for the period.

Limitations and criticism

• Relies on CAPM assumptions: single-factor model, constant beta, and market efficiency—assumptions often unrealistic in practice.
• Beta estimation error: Measured beta can change over time and depends on the chosen lookback period and benchmark.
• Ignores other risk sources: Style, sector exposure, leverage, and idiosyncratic risks are not captured by CAPM beta.
• Attribution to skill vs. luck: Under the efficient market hypothesis, positive alpha may reflect chance rather than persistent skill. Many active managers fail to produce consistent positive alpha net of fees.

Related concepts

• Alpha vs. Beta:
• Alpha measures excess return (performance relative to expectation).
• Beta measures sensitivity to market movements (systematic risk).
• Use with other metrics: Combine Jensen’s alpha with Sharpe ratio, Information ratio, and tracking error for a fuller assessment of risk-adjusted performance.

Bottom line

Jensen’s alpha is a straightforward way to assess whether a portfolio’s returns exceed what would be expected for its market risk. It is useful for evaluating active management but should be interpreted cautiously due to its reliance on CAPM and sensitivity to inputs. Use it alongside other risk-adjusted measures and qualitative assessment when judging investment performance.