Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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![**Problem Statement:**
Stock R has a beta of 2.0, Stock S has a beta of 0.35, the required return on an average stock is 9%, and the risk-free rate of return is 3%. By how much does the required return on the riskier stock exceed the required return on the less risky stock? Round your answer to two decimal places.
**Solution Explanation:**
To calculate the required return on each stock, we use the Capital Asset Pricing Model (CAPM), which is given by the formula:
\[ \text{Required Return} = \text{Risk-free Rate} + \beta \times (\text{Market Return} - \text{Risk-free Rate}) \]
**For Stock R:**
- Beta (\(\beta_R\)) = 2.0
- Risk-free Rate = 3%
- Market Return = 9%
- Required Return for Stock R = \(3\% + 2.0 \times (9\% - 3\%) = 3\% + 2.0 \times 6\% = 3\% + 12\% = 15\%\)
**For Stock S:**
- Beta (\(\beta_S\)) = 0.35
- Risk-free Rate = 3%
- Market Return = 9%
- Required Return for Stock S = \(3\% + 0.35 \times (9\% - 3\%) = 3\% + 0.35 \times 6\% = 3\% + 2.1\% = 5.1\%\)
**Difference in Required Returns:**
The difference in the required return between the riskier stock (Stock R) and the less risky stock (Stock S) is:
\[ 15\% - 5.1\% = 9.9\% \]
Thus, the required return on the riskier stock exceeds the required return on the less risky stock by **9.9%**.](https://content.bartleby.com/qna-images/question/00e39c23-5382-4320-a2d9-cf042c74097f/cfab0816-d83f-4772-af8c-188a04fc95bb/zyoro2_processed.png)
Transcribed Image Text:**Problem Statement:**
Stock R has a beta of 2.0, Stock S has a beta of 0.35, the required return on an average stock is 9%, and the risk-free rate of return is 3%. By how much does the required return on the riskier stock exceed the required return on the less risky stock? Round your answer to two decimal places.
**Solution Explanation:**
To calculate the required return on each stock, we use the Capital Asset Pricing Model (CAPM), which is given by the formula:
\[ \text{Required Return} = \text{Risk-free Rate} + \beta \times (\text{Market Return} - \text{Risk-free Rate}) \]
**For Stock R:**
- Beta (\(\beta_R\)) = 2.0
- Risk-free Rate = 3%
- Market Return = 9%
- Required Return for Stock R = \(3\% + 2.0 \times (9\% - 3\%) = 3\% + 2.0 \times 6\% = 3\% + 12\% = 15\%\)
**For Stock S:**
- Beta (\(\beta_S\)) = 0.35
- Risk-free Rate = 3%
- Market Return = 9%
- Required Return for Stock S = \(3\% + 0.35 \times (9\% - 3\%) = 3\% + 0.35 \times 6\% = 3\% + 2.1\% = 5.1\%\)
**Difference in Required Returns:**
The difference in the required return between the riskier stock (Stock R) and the less risky stock (Stock S) is:
\[ 15\% - 5.1\% = 9.9\% \]
Thus, the required return on the riskier stock exceeds the required return on the less risky stock by **9.9%**.
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