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According to the CAPM relation, a security has an expected return that is equal to the risk - free rate when: ( a ) The beta of the stock is lower than 1 ( b ) The beta of the stock is zero ( c ) The beta of the stock is negative ( d ) The risk - free rate is positive give the correct answer and explanation and why other options are not correct and summary. give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.

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According to the CAPM relation, a security has an expected return that is equal to the risk - free rate when: ( a ) The beta of the stock is lower than 1 ( b ) The beta of the stock is zero ( c ) The beta of the stock is negative ( d ) The risk - free rate is positive give the correct answer and explanation and why other options are not correct and summary. give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.

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Asked by: Test User 100079
Created at: 2025-05-11 00:11:19

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**Question:** According to the CAPM relation, a security has an expected return that is equal to the risk-free rate when: (a) The beta of the stock is lower than 1 (b) The beta of the stock is zero (c) The beta of the stock is negative (d) The risk-free rate is positive --- **Step 1: State the CAPM Formula and Define Parameters** The Capital Asset Pricing Model (CAPM) formula is: \[ E(R_i) = R_f + \beta_i \left[E(R_m) - R_f\right] \] **Definition of Parameters:** - \( E(R_i) \): Expected return of security \( i \) - \( R_f \): Risk-free rate - \( \beta_i \): Beta of security \( i \) (measure of sensitivity to market) - \( E(R_m) \): Expected return of the market portfolio **Explanation:** CAPM relates a security's expected return to the risk-free rate, its beta, and the expected market return. The term \( \beta_i \left[E(R_m) - R_f\right] \) represents the risk premium for the security. --- **Step 2: Apply the Condition for Expected Return Equal to Risk-Free Rate** Set \( E(R_i) = R_f \) in the CAPM equation: \[ E(R_i) = R_f + \beta_i \left[E(R_m) - R_f\right] \] \[ R_f = R_f + \beta_i \left[E(R_m) - R_f\right] \] \[ 0 = \beta_i \left[E(R_m) - R_f\right] \] **Explanation:** For this equation to hold, either \( \beta_i = 0 \) or \( E(R_m) = R_f \). However, in normal market conditions, \( E(R_m) > R_f \), so the only practical way for the expected return to equal the risk-free rate is when \( \beta_i = 0 \). --- **Option Analysis:** - **(a) The beta of the stock is lower than 1** *Incorrect.* Beta lower than 1 means the stock is less volatile than the market, but unless beta is exactly zero, the expected return still includes some risk premium. - **(b) The beta of the stock is zero** *Correct.* As shown above, only when beta is zero, the expected return equals the risk-free rate. - **(c) The beta of the stock is negative** *Incorrect.* Negative beta would make the expected return less than the risk-free rate (assuming \( E(R_m) > R_f \)), not equal. - **(d) The risk-free rate is positive** *Incorrect.* The risk-free rate being positive does not guarantee that expected return equals the risk-free rate for any security—that depends on beta. --- **Final Answer Summary:** **Correct answer:** (b) The beta of the stock is zero. According to CAPM, only securities with zero beta (no market risk) have expected returns exactly equal to the risk-free rate. All other options do not satisfy this condition. --- **Review based on 6 Parameters:** - **Relevancy:** Directly addresses CAPM and the question asked. - **Completeness:** Includes formula, parameter definitions, calculation, and explanation. - **Accuracy:** Correct application of CAPM logic and mathematics. - **Clarity:** Clearly structured steps and explanations. - **Structure:** Logical progression from formula to answer. - **Voice:** Human, instructive, and precise.

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