Jensen's Alpha Calculator — Portfolio Performance
Calculate Jensen's Alpha to measure portfolio performance vs. the market.
See if your investments beat or lagged the benchmark.
What Is Jensen’s Alpha?
Jensen’s Alpha measures how much better (or worse) an investment portfolio performed compared to what it “should have” earned based on its risk level.
Think of it like a school grading curve. If a student is expected to score 80% based on how hard the test is, but actually scores 90%, they outperformed by 10 points. Jensen’s Alpha does the same thing for investments — it measures outperformance (or underperformance) compared to expectations.
A positive alpha means the portfolio beat the market after adjusting for risk. A negative alpha means it underperformed. An alpha of zero means it performed exactly as expected for its level of risk.
The Formula
Alpha = Rp - [Rf + Beta × (Rm - Rf)]
Where:
- Rp = Actual portfolio return (what you actually earned)
- Rf = Risk-free rate (return on a safe investment like Treasury bills)
- Beta = Portfolio beta (how sensitive the portfolio is to market movements)
- Rm = Market return (what the overall market earned, e.g., S&P 500)
- Rm - Rf = Market risk premium (the extra return the market provided above the risk-free rate)
The part in brackets [Rf + Beta × (Rm - Rf)] is the expected return according to the CAPM (Capital Asset Pricing Model).
Alpha is simply the difference between what you actually earned and what CAPM says you should have earned.
Understanding Beta
Beta measures how much a portfolio moves relative to the market:
| Beta | Meaning | Example |
|---|---|---|
| 1.0 | Moves exactly with the market | Index fund tracking the S&P 500 |
| 1.5 | 50% more volatile than the market | Aggressive growth stocks |
| 0.5 | Half as volatile as the market | Utility stocks, defensive portfolio |
| 0.0 | No correlation with the market | Cash, some hedge fund strategies |
| -0.5 | Moves opposite to the market | Certain inverse ETFs |
Worked Example
Suppose:
- Your portfolio returned 15% last year
- The risk-free rate was 4%
- The S&P 500 returned 12%
- Your portfolio’s beta is 1.2
Step 1 — Expected return: 4% + 1.2 × (12% - 4%) = 4% + 9.6% = 13.6% Step 2 — Alpha: 15% - 13.6% = +1.4%
Your portfolio earned 1.4% more than it “should have” based on the risk you took. This is good — you (or your fund manager) added value beyond what the market risk alone would have provided.
How to Interpret Alpha
| Alpha | Meaning |
|---|---|
| +2% or more | Excellent — significantly beat expectations |
| +0.5% to +2% | Good — modest outperformance |
| -0.5% to +0.5% | Neutral — essentially matched expectations |
| -2% to -0.5% | Below average — underperformed expectations |
| Below -2% | Poor — significantly underperformed |
Why Alpha Matters
Many mutual funds and hedge funds charge high fees, claiming they can “beat the market.” Jensen’s Alpha is a reality check. If a fund charges 1.5% in fees but has an alpha of only 0.5%, the manager is not actually adding enough value to justify the fees.
Academic research consistently shows that most actively managed funds have negative alpha after fees. This is one reason index funds have become so popular — they give you the market return (alpha of zero) at very low cost.
Where to Find the Inputs
| Input | Where to Find It |
|---|---|
| Portfolio Return | Your brokerage statement or portfolio tracker |
| Risk-Free Rate | Current US 10-year Treasury yield (search “10-year Treasury rate”) |
| Market Return | S&P 500 annual return for the same period |
| Portfolio Beta | Your broker may show this, or calculate it from stock betas |
Limitations
- Alpha depends entirely on which benchmark you use — different benchmarks give different alphas
- Past alpha does not guarantee future alpha
- Beta may not be stable over time
- CAPM (which Alpha is based on) assumes markets are efficient, which is debatable