Jensen's Alpha Calculator
Measure portfolio performance and risk-adjusted returns compared to the market
Calculate Jensen's Alpha
The total return of your investment portfolio
Typically 10-year US Treasury bond yield (e.g., 2%)
Measure of portfolio volatility relative to market (e.g., 1.12)
Typically S&P 500 annual return (e.g., 11%)
Jensen's Alpha Results
Formula: α = Rp - (Rf + β × (Rm - Rf))
Calculation: 0.00% - (0% + 0 × (0% - 0%)) = 0.00%
Interpretation Guide
Example Calculation
Investment Portfolio Example
Beginning Portfolio Value: $1,000,000
Ending Portfolio Value: $1,200,000
Portfolio Return: 20%
Portfolio Beta: 1.12
Risk-Free Rate: 2%
Market Return (S&P 500): 11%
Step-by-Step Calculation
1. Portfolio Return = (1,200,000 - 1,000,000) / 1,000,000 = 20%
2. Expected Return = 2% + 1.12 × (11% - 2%) = 2% + 1.12 × 9% = 12.08%
3. Jensen's Alpha = 20% - 12.08% = 7.92%
Result: Portfolio outperformed by 7.92 percentage points! 💰
Alpha Interpretation
Positive Alpha
Outperformed market expectations
Generated excess returns above risk level
Zero Alpha
Met market expectations
Performed as predicted by CAPM
Negative Alpha
Underperformed market expectations
Generated lower returns than risk justified
Key Components
Portfolio Return (Rp)
Total return of your investment portfolio
Risk-Free Rate (Rf)
Return on risk-free investment (10-year Treasury)
Beta (β)
Volatility relative to market (1.0 = market volatility)
Market Return (Rm)
Return of broad market index (S&P 500)
Investment Tips
Positive alpha doesn't guarantee future performance
Track alpha over multiple periods for consistency
Consider luck vs. skill when analyzing results
Use appropriate benchmark for comparison
Account for transaction costs and fees
Understanding Jensen's Alpha
What is Jensen's Alpha?
Jensen's Alpha is a performance metric that measures a portfolio's excess return when compared to the market on a risk-adjusted basis. Unlike simple return calculations, it accounts for the risk level of your investments to provide a fair comparison.
Why is it Important?
- •Adjusts returns for risk level taken
- •Enables fair comparison between portfolios
- •Identifies skill vs. luck in investment performance
- •Helps evaluate fund manager performance
Formula Explanation
α = Rp - (Rf + β × (Rm - Rf))
- α (Alpha): Excess return above expected
- Rp: Portfolio return
- Rf: Risk-free rate
- β (Beta): Portfolio volatility vs. market
- Rm: Market return
- (Rm - Rf): Market risk premium
Note: Alpha is based on the Capital Asset Pricing Model (CAPM) and assumes efficient markets. Results should be analyzed over multiple periods.
Interpretation Guidelines
Positive Alpha
Your portfolio beat the market after adjusting for risk. This suggests skillful management or beneficial investment decisions.
Zero Alpha
Your portfolio performed exactly as expected given its risk level. This aligns with efficient market theory predictions.
Negative Alpha
Your portfolio underperformed relative to its risk level. This may indicate poor investment decisions or higher fees.
Limitations and Considerations
Limitations
- • Based on historical data, not predictive
- • Assumes market efficiency and CAPM validity
- • Single-factor model (only considers market risk)
- • Sensitive to benchmark choice
- • May not account for all risk factors
Best Practices
- • Analyze alpha over multiple time periods
- • Use appropriate market benchmarks
- • Consider transaction costs and fees
- • Supplement with other performance metrics
- • Account for market conditions and cycles