Returns and risk
Estimating beta
Estimate a share's beta from monthly returns, tell it apart from correlation, and turn it into a CAPM required return.
Learning objectives
- Calculate beta as the covariance of stock and market returns divided by the market's variance
- Distinguish beta from correlation and from total volatility
- Use beta in the CAPM to estimate a required return on equity
Not all risk is rewarded. Stock-specific surprises (a product recall, a lost contract) wash out in a diversified portfolio, so investors don't demand extra return for bearing them. What can't be diversified away is exposure to the market as a whole. Beta measures that exposure: how much a share's return tends to move when the market moves 1%.
Beta feeds the cost of equity in the CAPM, which in turn feeds the discount rate in a DCF and the hurdle an investor sets for a share. Bustan Foods Co. is a fictional listed food producer, and its share prices, the market index and all other figures are invented for teaching. Examples are educational and illustrative, not investment advice.
β = Cov(Rₛ, Rₘ) ÷ Var(Rₘ) = ρ × σₛ ÷ σₘ · Required return = r_f + β × ERP
- Cov(Rₛ, Rₘ)
- sample covariance of the stock's and the market's returns: Σ(rₛ − r̄ₛ)(rₘ − r̄ₘ) ÷ (n − 1)
- Var(Rₘ)
- sample variance of the market's returns (VAR.S), same n − 1
- ρ
- correlation between the two return series (−1 to +1)
- σₛ, σₘ
- standard deviations of the stock's and the market's returns
- r_f, ERP
- risk-free rate and equity risk premium (annual)
Included with a Formula Quest membership
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