Beta Calculator
Calculate the beta of an investment to measure its volatility relative to the market. Beta indicates how much an investment's price moves in relation to market movements and is a key component of the Capital Asset Pricing Model (CAPM).
Beta Results
Statistical Analysis
Beta Interpretations
ß < 1: Less volatile than market
ß = 1: Same volatility as market
ß > 1: More volatile than market
Note: Beta measures systematic risk
Understanding Beta
Beta (ß) measures the volatility of an investment relative to the overall market. It quantifies the systematic risk of a security and is a key component of the Capital Asset Pricing Model (CAPM) for determining expected returns.
Beta Formula
Beta is calculated as the covariance of the investment's returns with market returns, divided by the variance of market returns:
ß = Cov(R_i, R_m) ÷ Var(R_m)
Where: R_i = investment returns, R_m = market returns
Interpreting Beta Values
| Beta Range | Risk Level | Typical Investments | Expected Return |
|---|---|---|---|
| ß < 0 | Negative | Inverse ETFs, gold | Moves opposite to market |
| 0 < ß < 1 | Low | Utilities, consumer staples | Less than market |
| ß = 1 | Market | Market index, S&P 500 | Same as market |
| 1 < ß < 2 | High | Technology, small caps | More than market |
| ß > 2 | Very High | Biotech, emerging markets | Much more than market |
Beta in CAPM
Beta is a key input in the Capital Asset Pricing Model (CAPM), which calculates the expected return of an investment based on its systematic risk.
CAPM Expected Return Formula:
E(R_i) = R_f + ß × (R_m - R_f)
Higher beta = higher expected return (for taking more risk)
R-Squared and Correlation
- R-Squared: Percentage of investment's movements explained by market movements
- Correlation: Strength and direction of relationship between investment and market
- High R-Squared: Investment moves closely with market (high systematic risk)
- Low R-Squared: Investment has unique risk factors (more unsystematic risk)
- Perfect Correlation: R-squared = 100% (beta perfectly predicts movements)
Applications
- Portfolio Construction: Balance high and low beta assets
- Risk Assessment: Understand systematic risk exposure
- Asset Allocation: Determine optimal market exposure
- Performance Evaluation: Compare risk-adjusted returns
- Hedging Strategies: Use beta to determine hedge ratios
Historical Beta Examples
- Apple (AAPL): Beta ~1.3 (more volatile than market)
- Johnson & Johnson (JNJ): Beta ~0.7 (less volatile than market)
- SPDR S&P 500 ETF (SPY): Beta = 1.0 (matches market)
- Utilities Sector: Beta ~0.5-0.8 (defensive)
- Technology Sector: Beta ~1.2-1.5 (aggressive)
Limitations
- Historical Data: Past beta may not predict future
- Market Changes: Beta can change with company fundamentals
- Time Period: Beta varies with different time horizons
- Market Proxy: Choice of market index affects beta
- Non-Linear Relationships: Assumes linear relationship with market
Beta vs. Volatility
- Beta: Measures systematic risk (market-related)
- Volatility: Measures total risk (systematic + unsystematic)
- Key Difference: Beta focuses on risk you can't diversify away
- Investment Focus: Beta for market risk, volatility for total risk
- CAPM Relevance: Beta determines expected return, volatility does not
Tip: Beta is a measure of systematic risk that cannot be diversified away. A beta of 1 means the investment moves with the market, while a beta greater than 1 means it's more volatile. Use beta to understand how much market risk you're taking and to build appropriately diversified portfolios.