Beta Risk Calculator
Calculate a stock's beta and CAPM-based expected return using correlation, volatility, and market return data. Use it to assess whether a stock's potential return adequately compensates for its market risk.
About this calculator
Beta measures a stock's systematic risk relative to the market and is derived from the relationship between the stock's volatility and its co-movement with the market. The formula used here combines beta with the Capital Asset Pricing Model (CAPM): Expected Return = Risk-Free Rate + β × (Market Return − Risk-Free Rate), where β = Correlation × (Stock Volatility ÷ Market Volatility), also written as β = ρ × (σ_s / σ_m). The term (Market Return − Risk-Free Rate) is the equity risk premium — the extra return demanded for bearing market risk. A beta of 1.5 means the stock is 50% more volatile than the market, so CAPM demands a proportionally higher expected return. This model assumes markets are efficient and that only systematic risk is rewarded; unsystematic (company-specific) risk is presumed diversifiable.
How to use
Assume a stock has a correlation with the market of 0.75 and a volatility ratio (stock σ ÷ market σ) of 1.6, giving a beta of 0.75 × 1.6 = 1.20. The risk-free rate is 4% and the market's average annual return is 10%. Plug into the CAPM formula: Expected Return = 4 + (0.75 × 1.6 × (10 − 4)) = 4 + (1.20 × 6) = 4 + 7.2 = 11.2%. This means CAPM suggests the stock should return at least 11.2% annually to justify its level of systematic risk. If the stock is expected to return less, it may be unattractive on a risk-adjusted basis.
Frequently asked questions
What is the difference between beta calculated from correlation versus regression?
Beta can be estimated in two equivalent ways: via regression of stock returns against market returns, or as the product of the stock-market correlation and the ratio of their standard deviations (β = ρ × σ_s/σ_m). Both methods yield the same result when applied to the same historical return dataset. The regression approach is more common in financial software, while the correlation-and-volatility method makes the components of beta more transparent and intuitive for manual analysis. In practice, published betas from data providers use 60 months of monthly returns regressed against a benchmark like the S&P 500.
How does the risk-free rate affect the CAPM expected return calculation?
The risk-free rate serves as the baseline return an investor can earn with zero risk, typically proxied by the current yield on 3-month U.S. Treasury bills or 10-year Treasury bonds. A higher risk-free rate raises the required expected return for every risky asset, making stocks relatively less attractive all else equal — this is a core reason why rising interest rates often pressure equity valuations. Changes in the risk-free rate directly shift the CAPM output: if the risk-free rate rises from 3% to 5%, a stock with a beta of 1.2 and a market premium of 6% sees its required return jump from 10.2% to 12.2%.
When is CAPM not a reliable model for estimating expected stock returns?
CAPM has well-documented limitations: it assumes a single risk factor (market beta), normally distributed returns, and frictionless markets, none of which hold perfectly in reality. Empirical research shows that factors like company size, book-to-market ratio, momentum, and profitability also explain cross-sectional return differences — the basis for multi-factor models like Fama-French. CAPM tends to underperform as a predictor for small-cap stocks, value stocks, and stocks with low or negative beta. It remains widely used as a starting framework and cost-of-equity estimate in discounted cash flow models, but practitioners often supplement it with judgment and alternative models.