Math Problem Statement
The risk-free rate is 1.91% and the expected return on the market 12.23%. A stock with a β of 1.14 will have an expected return of ____%.
Solution
To calculate the expected return of the stock, we can use the Capital Asset Pricing Model (CAPM) formula:
Where:
- = Expected return of the stock
- = Risk-free rate = 1.91% = 0.0191
- = Expected return on the market = 12.23% = 0.1223
- = Beta of the stock = 1.14
Step-by-step calculation:
-
Calculate the market risk premium:
-
Multiply the market risk premium by the beta of the stock:
-
Add the risk-free rate to the result:
Final Answer:
The expected return of the stock is approximately 13.67%.
Would you like a breakdown of related concepts or further clarification?
Here are 5 related questions you might explore:
- What does the beta () of a stock represent in CAPM?
- How would a change in the market's expected return affect the stock's expected return?
- Can a stock have a negative beta, and what does it imply for expected returns?
- How does the CAPM compare to other models like the Fama-French three-factor model?
- What are the limitations of using CAPM for estimating expected returns?
Tip: Always double-check the risk-free rate and market return assumptions, as small errors can significantly impact the result.
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Math Problem Analysis
Mathematical Concepts
Finance
Expected Return
CAPM (Capital Asset Pricing Model)
Formulas
E(R_i) = R_f + β × (E(R_m) - R_f)
Theorems
CAPM Theory
Suitable Grade Level
Undergraduate/Finance Students
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