For stock A, we have
𝛽
𝑖
= 0.70.

Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM?

(Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

Question

For stock A, we have 
𝛽
𝑖
 = 0.70.

Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM?

(Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

BlackTom AI · Accepted Answer

E[Ri] = Rf + βi × (market risk premium).

1. Relevant knowledge points and concepts
- CAPM (Capital Asset Pricing Model) expresses expected return on a security as the risk-free rate plus the security’s beta times the market risk premium: E[Ri] = Rf + βi*(E[Rm] − Rf).
- β (beta) measures the stock’s sensitivity to market movements.
- Market risk premium is E[Rm] − Rf (given here directly as 9%).
- All percentages must be handled consistently (convert to decimals for multiplication, then convert back to percent).

2. Step-by-step reasoning
- Identify inputs: βi = 0.70, market risk premium = 9% (0.09), risk-free rate Rf = 3% (0.03).
- Apply the CAPM formula, substituting the values.

3. Calculations with intermediate steps
- Compute β × market risk premium: 0.70 × 0.09 = 0.063 (which is 6.3%).
- Add the risk-free rate: 0.03 + 0.063 = 0.093.
- Convert to percent: 0.093 = 9.30%.

4. Why the correct answer is correct
- CAPM requires using the market risk premium (not the total expected market return). Multiplying beta by the 9% premium yields the risk premium attributable to the stock (6.3%), and adding the 3% risk-free rate gives the stock’s expected return of 9.30%. This directly follows the model’s definition and arithmetic.

5. Why other potential answers would be incorrect
- Using β × total market return (instead of β × market premium) would overstate the premium.
- Omitting the risk-free rate or failing to convert percentages to decimals would produce arithmetic errors.
- Rounding too early (e.g., rounding 6.3% improperly) could slightly distort the result, but proper calculation gives 9.30%.

6. Conclusion and confirmation
- The expected return per CAPM is 9.30%, which matches the provided answer of 9.30.

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)数值题

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