Practice Question
Your personal opinion is that a security has an expected rate of return of 11%. It has a beta of 1.5.
The risk-free asset has a beta of zero and the market expected rate of return is 9%.
According to the Capital Asset Pricing Model, this security is:
A) Underpriced
B) Overpriced
C) Fairly priced
D) Cannot be determined from data provided
Step 1: Define Variables
- Expected return \( E(R_i) = 11\% = 0.11 \)
- Beta \( \beta_i = 1.5 \)
- Market return \( E(R_m) = 9\% = 0.09 \)
- Risk-free rate \( R_f \) = not provided
Step 2: CAPM Formula
\[ E(R_i) = R_f + \beta_i \cdot (E(R_m) - R_f) \] This formula gives the required rate of return based on systematic risk (beta).
Step 3: Determine the Missing Input
Since the risk-free rate \( R_f \) is not provided, we cannot compute the required return using the CAPM formula. As a result, we cannot compare the required return to the expected return to determine if the security is underpriced, overpriced, or fairly priced.
Conclusion: The correct answer is D) Cannot be determined from data provided because the essential input — the risk-free rate — is missing from the question.