Alpha Beta Calculator
Alpha Beta Calculator
Calculate portfolio beta, CAPM expected return, and alpha from matched portfolio and benchmark return periods. Use the result as an educational risk-adjusted performance estimate, not as a buy or sell signal.
Inputs
Enter monthly/quarterly/annual returns (same period as market)
Use S&P 500 or relevant index (must match portfolio periods)
Use a rate that matches your analysis period, such as a Treasury yield for the same horizon.
Performance Metrics
⚠️ Higher volatility than market
✅ Outperforming risk-adjusted expectations
Interpretation:
Your portfolio has a beta of 1.33 (33% more volatile than market) and generated +0.77% alpha (outperformance) after risk adjustment.
Educational estimate only. Alpha and beta are backward-looking statistics and can change when the benchmark, time window, fees, portfolio holdings, or market regime changes.
How to Use This Calculator
- Enter portfolio returns for past 12-36 months (comma-separated)
- Enter market benchmark returns for same periods (e.g., S&P 500 for US stocks)
- Set a risk-free rate that matches your analysis period
- Use beta as a benchmark sensitivity estimate and alpha as a model-based excess-return estimate
Alpha and Beta Formula Guide
| Metric | Formula | What it means | Main caution |
|---|---|---|---|
| Beta | Covariance(portfolio, benchmark) / Variance(benchmark) | Historical sensitivity to benchmark moves | Depends heavily on benchmark choice and sample period |
| CAPM expected return | Risk-free rate + beta x (benchmark return - risk-free rate) | Return implied by market exposure in the sample | A model estimate, not a forecast |
| Alpha | Portfolio average return - CAPM expected return | Return above or below the model-implied return | Can reflect luck, fees, timing, or benchmark mismatch |
Method and Worked Example
Direct answer: beta is calculated as covariance of portfolio and benchmark returns divided by benchmark variance. Alpha is calculated as actual portfolio return minus the CAPM expected return: risk-free rate plus beta times the benchmark risk premium.
Worked example: if the portfolio average return is 8.02%, the benchmark average return is 6.57%, the risk-free rate is 4.5%, and beta is 1.22, the CAPM expected return is 4.5% + 1.22 x (6.57% - 4.5%) = 7.03%. Alpha is then 8.02% - 7.03% = 0.99%.
Official Investor Resources
FAQ
What does beta measure?
Beta estimates how much a portfolio has moved with a benchmark over the return periods you enter. A beta above 1 has historically moved more than the benchmark; a beta below 1 has moved less.
What does alpha measure?
Alpha is the difference between actual portfolio return and the CAPM expected return after accounting for the risk-free rate, market return, and beta. Positive alpha is not a guarantee of future outperformance.
How much data should I use?
Use matched return periods for the portfolio and benchmark. More periods usually make the estimate less noisy, but old data may not reflect the current portfolio.
Is this investment advice?
No. This is an educational calculator. It does not recommend buying, selling, or holding any security or fund.
About This Calculator
Calculate portfolio alpha and beta from matched portfolio and benchmark return periods. Estimate CAPM expected return and risk-adjusted excess return for educational portfolio review.
Frequently Asked Questions
What is alpha in investing?
Alpha is the difference between actual portfolio return and the CAPM expected return after accounting for the risk-free rate, benchmark return, and beta. Positive alpha means the portfolio beat the model estimate in the sample period; it does not prove future outperformance.
What is beta and how does it measure risk?
Beta estimates how closely a portfolio has moved with a benchmark over the return periods you enter. A beta above 1 means the portfolio moved more than the benchmark in the sample; a beta below 1 means it moved less. Beta is backward-looking and depends on the benchmark and time window.
What return data should I enter?
Enter matched portfolio and benchmark returns for the same periods, such as monthly portfolio returns and monthly S&P 500 returns. The calculator requires the same number of observations for both series.
Which benchmark should I use?
Use a benchmark that matches the portfolio exposure. A broad U.S. equity portfolio might use the S&P 500, while small-cap, international, bond, or sector portfolios should use a more relevant benchmark.
Is alpha or beta a recommendation?
No. Alpha and beta are analytical statistics, not investment recommendations. They can help review historical risk-adjusted performance, but they do not determine whether you should buy, sell, or hold an investment.
Alex specializes in personal finance modeling with experience in investment analysis and tax optimization. He reviews calculator logic, source notes, and assumptions so finance and tax pages explain their limits clearly.
- CFA Level II Candidate
- B.S. in Finance, University of Michigan
- 8 years in financial planning tools