Alpha Calculator
Calculate Jensen's alpha to measure the excess return of an investment above what would be predicted by the Capital Asset Pricing Model (CAPM). Alpha represents the value added by active portfolio management.
Alpha Results
CAPM Breakdown
Alpha Benchmarks
Excellent: > 3%
Good: 1-3%
Fair: -1% to 1%
Poor: < -1%
Note: Positive alpha indicates outperformance
Understanding Jensen's Alpha
Jensen's alpha, named after Michael Jensen, measures the excess return of an investment above what would be predicted by the Capital Asset Pricing Model (CAPM). It represents the value added or subtracted by active portfolio management.
Alpha Formula
Jensen's alpha is calculated as:
a = R_p - [R_f + ß_p × (R_m - R_f)]
Where: R_p = portfolio return, R_f = risk-free rate, ß_p = beta, R_m = market return
Interpreting Alpha
| Alpha Value | Performance Level | Interpretation |
|---|---|---|
| > 3% | Excellent | Strong outperformance |
| 1-3% | Good | Moderate outperformance |
| -1% to 1% | Fair | Market performance |
| -3% to -1% | Poor | Moderate underperformance |
| < -3% | Very Poor | Strong underperformance |
Components of Alpha
- Expected Return: Return predicted by CAPM based on systematic risk
- Actual Return: Realized return of the portfolio
- Excess Return: Difference between actual and expected returns
- Active Management: Skill in security selection and market timing
- Luck Factor: Random events that may inflate or deflate alpha
Alpha vs. Other Metrics
- Sharpe Ratio: Risk-adjusted return using total volatility
- Sortino Ratio: Risk-adjusted return using downside deviation
- Information Ratio: Active return per unit of tracking error
- Beta: Measure of systematic risk, not excess return
Applications
- Fund Manager Evaluation: Assess active management skill
- Portfolio Performance: Measure against market expectations
- Investment Strategy: Identify successful investment approaches
- Risk Management: Understand sources of excess returns
- Attribution Analysis: Decompose portfolio performance
Positive vs. Negative Alpha
- Positive Alpha: Portfolio outperformed expectations (good active management)
- Zero Alpha: Portfolio performed as expected by CAPM
- Negative Alpha: Portfolio underperformed expectations
- Statistical Significance: Alpha should be tested for significance
- Time Horizon: Alpha can vary significantly over different periods
Limitations
- CAPM Assumptions: Relies on CAPM being an accurate model
- Beta Estimation: Historical beta may not predict future
- Market Proxy: Choice of market index affects results
- Transaction Costs: Doesn't account for trading expenses
- Survivorship Bias: Only considers surviving funds
Alpha in Practice
Institutional investors and fund managers use alpha to evaluate performance. A consistent positive alpha indicates skill in generating excess returns, while negative alpha suggests the portfolio would be better off in a passive index fund.
- Hedge Funds: Often target high alpha generation
- Mutual Funds: Most have negative or zero alpha after fees
- Index Funds: Typically have zero alpha by design
- Private Equity: Alpha measured over long investment horizons
Tip: Alpha measures the value added by active management. Positive alpha indicates the portfolio manager is generating returns above what would be expected given the risk taken. However, alpha should be evaluated over multiple periods and tested for statistical significance.