Beta for CAPM
Beta measures how much a stock tends to move when the whole market moves. It is the risk number that goes into CAPM. A beta above 1 means the stock swings more than the market; below 1 means it swings less.
What you will learn
- What beta measures and how to read values above and below 1
- The covariance-over-variance formula for beta
- The shortcut using correlation and standard deviations
- How beta changes the CAPM cost of equity
- Why beta only captures market risk, not firm-specific risk
The formulas
- Cov(R_s, R_m)
- covariance of the stock's returns with the market's returns
- Var(R_m)
- variance of market returns (σ_m²)
- ρ_s,m
- correlation between stock and market returns
- σ_s
- standard deviation of the stock's returns
- σ_m
- standard deviation of market returns
Worked example
A stock's returns have a standard deviation of 30%, the market's is 20%, and their correlation is 0.8. What is the stock's beta?
- Covariance = ρ × σ_s × σ_m = 0.8 × 0.30 × 0.20 = 0.048
- Market variance = 0.20² = 0.04
- Beta = 0.048 ÷ 0.04 = 1.2
- Check with the shortcut: 0.8 × 30% ÷ 20% = 1.2
Answer: Beta = 1.2, so the stock tends to move about 1.2 times as much as the market.
Common questions
What is the formula for beta?
Beta equals the covariance between the stock's returns and the market's returns, divided by the variance of the market's returns. An equivalent version is correlation times the stock's standard deviation divided by the market's standard deviation.
What does a beta of 1.5 mean?
A beta of 1.5 means the stock has tended to move about 1.5 times as much as the market. If the market rises 10%, the stock would be expected to rise about 15%, and fall about 15% if the market drops 10%.
Can beta be negative?
Yes. A negative beta means the asset tends to move in the opposite direction to the market. It is rare for ordinary stocks but can show up in assets like gold at times. In CAPM, a negative beta gives a required return below the risk-free rate.
Is a high beta stock riskier?
It carries more market risk, meaning it swings more with the overall market, so CAPM demands a higher return. But beta ignores firm-specific risk, so a low-beta stock can still be volatile for its own reasons.