The risk free rate is 4%, and the required return on the market is 12%.
What is the required return on an asset A with a beta of 1.5?

Question

The risk free rate is 4%, and the required return on the market is 12%. 
What is the required return on an asset A with a beta of 1.5?

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
The Capital Asset Pricing Model (CAPM) gives the required return on an asset as: Required return = Risk-free rate + Beta × Market risk premium. The market risk premium equals (Required return on the market − Risk-free rate). CAPM captures that a security’s expected excess return is proportional to its systematic risk (beta).

2. Step-by-step reasoning
- Risk-free rate (rf) = 4%
- Required return on the market (rm) = 12%
- Beta (β) for asset A = 1.5
Compute the market risk premium first, then apply beta, then add the risk-free rate.

3. Calculations with intermediate steps
- Market risk premium = rm − rf = 12% − 4% = 8%
- Beta × Market risk premium = 1.5 × 8% = 12%
- Required return on asset A = rf + (β × market risk premium) = 4% + 12% = 16%

4. Why the correct answer is correct
CAPM is designed to separate the risk-free component (4%) from the compensation for systematic market risk. The asset’s beta of 1.5 means it requires 1.5 times the market premium. Since the market premium is 8%, multiplying by 1.5 gives 12% of extra return above the risk-free rate, so total required return is 4% + 12% = 16%.

5. Why common alternative calculations are incorrect
- Using rf + β × rm (i.e., 4% + 1.5 × 12% = 22%) is wrong because it double-counts the risk-free component; CAPM uses the market risk premium (rm − rf), not rm itself.
- Using β × rm (1.5 × 12% = 18%) and omitting the risk-free rate fails to include the guaranteed baseline return.
- Using rf × β (4% × 1.5 = 6%) confuses scaling of the guaranteed return with the risk premium.

6. Conclusion
Following CAPM, the required return on asset A is 16%, which matches the provided answer.

The risk free rate is 4%, and the required return on the market is 12%. What is the required return on an asset A with a beta of 1.5? 数值题

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