Alpha and Beta Calculator
Free alpha and beta calculator. Measure your portfolio's market sensitivity (beta) and excess risk-adjusted return (alpha) against a benchmark index.
CAPM Calculator
Calculate expected return using the Capital Asset Pricing Model (CAPM). Visualize the Security Market Line and project investment growth.
Usually the 10-year Treasury yield
Historical S&P 500 ≈ 10-12%
Overrides Market Return − Rf calculation
Expected Return (CAPM)⧉
13.40%
Rf(5%) + β(1.2) × MRP(7.00%)
Risk Premium⧉
8.40%
Additional return demanded for bearing systematic risk
Market Risk Premium⧉
7.00%
Excess return of market over risk-free rate
Projected Value⧉
$187,528
$100000 invested for 5 years at CAPM rate
Risk-Free Value⧉
$127,628
Same amount invested at the risk-free rate
Excess Value⧉
$59,899
Additional value earned by taking market risk
Security Market Line (SML)
β = 0β = 1 (Market)β = 2.5
Year-by-Year Projection
| Year | CAPM Value | Risk-Free Value | Excess Return |
|---|---|---|---|
| 1 | $113,400 | $105,000 | $8,400 |
| 2 | $128,596 | $110,250 | $18,346 |
| 3 | $145,827 | $115,763 | $30,065 |
| 4 | $165,368 | $121,551 | $43,818 |
| 5 | $187,528 | $127,628 | $59,899 |
Planning notes, formulas, and examples
About the CAPM Calculator
The Capital Asset Pricing Model (CAPM) is a cornerstone of modern finance. It describes the relationship between systematic risk (measured by beta) and expected return for an asset. In essence, CAPM says that investors deserve to be compensated for two things: the time value of money (risk-free rate) and the risk they take (beta times the market risk premium).
The formula is elegantly simple: Expected Return = Risk-Free Rate + β × Market Risk Premium. This relationship defines the Security Market Line (SML), where every fairly priced asset should lie. Assets above the SML offer better returns for their risk level (positive alpha), while assets below it underperform.
This calculator lets you compute expected returns for any beta, compare multiple risk profiles on the SML, and project how your investment grows versus a risk-free alternative. It is essential for equity valuation (determining the cost of equity), setting hurdle rates for corporate projects, and evaluating whether a stock's historical returns justify its risk.
When This Page Helps
Use this to estimate the return an asset should earn for its beta relative to the market. It is useful for cost-of-equity work, hurdle-rate setting, and checking whether a stock's return is high enough for its systematic risk.
How to Use the Inputs
- Enter the current risk-free rate — typically the 10-year US Treasury yield.
- Enter the beta of the stock or portfolio you are evaluating.
- Enter the expected market return (S&P 500 historical average is 10-12%).
- Optionally override the market risk premium if you have a separate estimate.
- Enter the investment amount and time horizon for growth projection.
- Review the expected return, risk premium, projected values, and SML chart.
Formula used
Expected Return = Rf + β × (Rm − Rf)
Risk Premium = β × Market Risk Premium
Future Value = Investment × (1 + Expected Return)^Years
Where Rf = risk-free rate, β = beta, Rm = market return.Example Calculation
Result: Expected Return = 13.4%
With a risk-free rate of 5%, beta of 1.2, and market return of 12%, the expected return is 5% + 1.2 × (12% − 5%) = 5% + 8.4% = 13.4%. A $100,000 investment would grow to about $188,000 in 5 years at this rate.
Tips & Best Practices
- Use a market risk premium of 5-7% for developed markets, higher for emerging markets.
- Remember that CAPM only prices systematic (market) risk — it ignores company-specific risk.
- Compare the CAPM expected return with the stock's actual historical return to identify alpha.
- For project evaluation, use CAPM to set the hurdle rate above which to invest.
- Combine CAPM with multi-factor models (Fama-French) for more robust analysis.
How It Helps
CAPM links expected return to beta, the risk-free rate, and the market risk premium. This makes it a quick way to estimate the cost of equity or compare securities on a common risk-adjusted basis.
What To Check
Use a risk-free rate that matches your horizon, and make sure beta and expected market return come from the same market context. Small changes in the market risk premium can move the result materially, so it is worth testing more than one assumption set.
Usefully Interpreted
CAPM is a single-factor model, so it captures market risk but not company-specific risk. Treat the output as a benchmark for required return, not as a full valuation model on its own.
Sources & Methodology
Last updated:
Methodology
This calculator applies the CAPM formula expected return = risk-free rate + beta × market risk premium. The Security Market Line chart visualizes that same relationship across different betas.
The page is a benchmark worksheet for required return, not a guarantee of future performance.
Sources
- Capital Asset Pricing Model (CAPM) (Investor.gov / U.S. Securities and Exchange Commission)
- Beta (Investor.gov / U.S. Securities and Exchange Commission)
- Risk and Return (Investor.gov / U.S. Securities and Exchange Commission)
Frequently Asked Questions
It is the return on a theoretically zero-risk investment, usually proxied by a government bond yield. Match the tenor to your analysis horizon where possible instead of treating one Treasury maturity as universal.
Beta measures a stock's sensitivity to market movements. β=1 means market-level risk; β>1 means more volatile than the market.
It is the expected return of the market minus the risk-free rate — the extra return investors demand for bearing market risk. Historically, it has been 5-7%.
CAPM assumes rational investors, efficient markets, and that beta captures all risk. In reality, size, value, and momentum factors also affect returns.
CAPM provides the cost of equity for discounted cash flow (DCF) models. It sets the discount rate used to calculate the present value of future cash flows.
Yes. By comparing actual return with CAPM-predicted return, you can calculate alpha — the portfolio's risk-adjusted outperformance.
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