Jensen's Alpha Calculator
Calculate Jensen's Alpha to measure a portfolio's excess returns relative to its expected returns based on the Capital Asset Pricing Model (CAPM). Alpha indicates whether a portfolio manager is adding value.
Jensen's Alpha Results
CAPM Analysis
Alpha Interpretation
Alpha > 0: Outperforming market
Alpha = 0: Market performance
Alpha < 0: Underperforming market
Note: Positive alpha indicates skill
Understanding Jensen's Alpha
Jensen's Alpha, named after Michael Jensen, measures the excess return of a portfolio relative to the expected return predicted by the Capital Asset Pricing Model (CAPM). It quantifies whether a portfolio manager is adding value beyond what would be expected given the portfolio's risk.
Jensen's Alpha Formula
Alpha is calculated as:
a = R_p - [R_f + ß_p × (R_m - R_f)]
Where: a = alpha, R_p = portfolio return, R_f = risk-free rate, ß_p = portfolio beta, R_m = market return
Interpreting Alpha
| Alpha Value | Interpretation | Manager Skill |
|---|---|---|
| a > 0 | Outperforming | Adding value |
| a = 0 | Market performance | No excess return |
| a < 0 | Underperforming | Destroying value |
CAPM Foundation
Jensen's Alpha is based on the Capital Asset Pricing Model (CAPM), which describes the relationship between risk and expected return.
CAPM Expected Return:
E(R_p) = R_f + ß_p × (E(R_m) - R_f)
Expected return = Risk-free rate + Beta × Market risk premium
Applications
- Portfolio Manager Evaluation: Assess skill in generating excess returns
- Fund Selection: Compare actively managed funds
- Performance Attribution: Understand sources of excess returns
- Risk-Adjusted Performance: Measure performance relative to risk taken
- Investment Strategy: Guide portfolio construction decisions
Limitations
- CAPM Assumptions: Relies on CAPM being accurate
- Market Efficiency: Assumes efficient markets
- Beta Stability: Beta may change over time
- Single Factor Model: Only considers market risk
- Short-term Focus: May not reflect long-term skill
Alpha vs. Other Metrics
Jensen's Alpha differs from other performance measures in its risk-adjustment approach.
- Sharpe Ratio: Measures risk-adjusted returns using total volatility
- Information Ratio: Compares excess returns to tracking error
- Sortino Ratio: Focuses on downside risk only
- Jensen's Alpha: Measures excess returns relative to CAPM expectations
Tip: Jensen's Alpha helps determine whether a portfolio manager is truly adding value beyond what would be expected given the portfolio's risk. Positive alpha indicates skill in security selection or market timing, while negative alpha suggests the portfolio would be better off in a passive index fund.