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Estimate the return equity holders require with both the market model and the CAPM

CFA® Level I · Equity Investments · The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models · EQ.18.a

The idea

The capital asset pricing model estimates the required return on equity as the risk-free rate plus beta times the equity risk premium: r = Rf + beta x (E(Rm) - Rf). With Rf at 3%, beta at 1.2 and an equity risk premium of 5%, the required return is r = 3% + 1.2 x 5% = 9%. Only systematic risk, measured by beta, earns a premium, because diversifiable risk can be removed. Beta is usually estimated with the market model, a regression of the stock's returns on the market's returns, Ri = alpha + beta x Rm + error, where the slope is beta. Estimates depend on the index, period and return frequency chosen, and a historical beta may not describe the future, so analysts often adjust it or use peers' betas.

A practice question

From the question bank, with the reason each wrong option is wrong.

The risk-free rate is 3%, the expected market return is 8% and a stock's beta is 1.2. Its required return under the CAPM is:

  1. 9.0% — correct
  2. 12.6%Why not: Multiplies beta by the market return rather than by the market risk premium.
  3. 6.0%Why not: Gives only the risk premium (1.2 × 5%) and forgets to add the risk-free rate.

Required return = 3% + 1.2 × (8% − 3%) = 3% + 6% = 9.0%.

A harder one

A stock's returns have a covariance with the market of 0.024, the market's standard deviation is 20%, the risk-free rate is 4% and the expected market return is 10%. The stock's CAPM required return is:

  1. 4.72%Why not: Divides the covariance by the market's standard deviation rather than its variance, giving a beta of 0.12.
  2. 10.0%Why not: Multiplies beta by the market return (10%) rather than the market risk premium (6%).
  3. 7.6% — correct

Beta = 0.024 / 0.20² = 0.024 / 0.04 = 0.60. Required return = 4% + 0.60 × (10% − 4%) = 7.6%.

The hardest tier

A stock's correlation with the market is 0.6, its standard deviation is 30% and the market's is 20%. With a risk-free rate of 3.5% and an expected market return of 9%, the CAPM required return is closest to:

  1. 11.75%Why not: Takes beta as the ratio of standard deviations (1.5), ignoring the correlation.
  2. 5.70%Why not: Inverts the volatility ratio (0.6 × 20% / 30%), giving a beta of 0.4.
  3. 8.45% — correct

Beta = ρ × σ_i / σ_m = 0.6 × 30% / 20% = 0.9. Required return = 3.5% + 0.9 × 5.5% = 8.45%.

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