Question
If a security's expected return is equal to the risk-free rate of return, and the market-risk premium is greater than zero, what can you conclude about the value of the security's beta based on CAPM?
Multiple choice question.
It is equal to –1.
It is equal to the market portfolio's beta.
It is equal to 1.
It is equal to 0.
Multiple choice question.
It is equal to –1.
It is equal to the market portfolio's beta.
It is equal to 1.
It is equal to 0.
Answers
GPT-4o mini
According to the Capital Asset Pricing Model (CAPM), the expected return of a security can be expressed as follows:
\[ E(R_i) = R_f + \beta_i (E(R_m) - R_f) \]
Where:
- \( E(R_i) \) is the expected return of the security.
- \( R_f \) is the risk-free rate of return.
- \( \beta_i \) is the beta of the security.
- \( E(R_m) - R_f \) is the market risk premium.
Given that the expected return of the security \( E(R_i) \) is equal to the risk-free rate \( R_f \), we can substitute that into the equation:
\[ R_f = R_f + \beta_i (E(R_m) - R_f) \]
Subtracting \( R_f \) from both sides:
\[ 0 = \beta_i (E(R_m) - R_f) \]
Since the market risk premium ( \( E(R_m) - R_f \) ) is greater than zero, the only way for the equation to hold is if \( \beta_i \) is equal to 0.
Therefore, the correct conclusion is:
**It is equal to 0.**
\[ E(R_i) = R_f + \beta_i (E(R_m) - R_f) \]
Where:
- \( E(R_i) \) is the expected return of the security.
- \( R_f \) is the risk-free rate of return.
- \( \beta_i \) is the beta of the security.
- \( E(R_m) - R_f \) is the market risk premium.
Given that the expected return of the security \( E(R_i) \) is equal to the risk-free rate \( R_f \), we can substitute that into the equation:
\[ R_f = R_f + \beta_i (E(R_m) - R_f) \]
Subtracting \( R_f \) from both sides:
\[ 0 = \beta_i (E(R_m) - R_f) \]
Since the market risk premium ( \( E(R_m) - R_f \) ) is greater than zero, the only way for the equation to hold is if \( \beta_i \) is equal to 0.
Therefore, the correct conclusion is:
**It is equal to 0.**