Question

Assume that the risk-free rate is 5.5% and the required return on the market is 8%. What is the required rate of return on a stock with a beta of 2? Round your answer to two decimal places.

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Assume that the risk-free rate is 4.5% and the market risk premium is 6%. What is the required return for the overall stock market? Round your answer to one decimal place.

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What is the required rate of return on a stock with a beta of 1.9? Round your answer to one decimal place.

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Answer 1

Using the CAPM formula, a stock with a beta of 2 has a required rate of return of 10.5%. The required return for the overall stock market is also 10.5%. A stock with a beta of 1.9 has a required rate of return of 15.9%.

Step-by-step explanation:

To answer the first question, we use the Capital Asset Pricing Model (CAPM), which calculates the expected return on an asset based on its risk compared to the market. The formula is:

Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)

For a stock with a beta of 2, the required rate of return would be:

5.5% + 2 * (8% - 5.5%) = 5.5% + 2 * 2.5% = 10.5%

For the second question, the required return for the overall stock market can be found using the risk-free rate plus the market risk premium:

4.5% + 6% = 10.5%

And finally, using the CAPM formula again for a stock with a beta of 1.9 and using the risk-free rate and market risk premium from the second question, we calculate:

4.5% + 1.9 * 6% = 15.9%

Answer 2

Using the Capital Asset Pricing Model, the required rate of return on a stock with a beta of 2 is 10.5%. The required return for the overall stock market is also 10.5%. For a stock with a beta of 1.9, the required rate of return is 15.9%.

Step-by-step explanation:

To calculate the required rate of return on a stock using the Capital Asset Pricing Model (CAPM), you can use the following formula:

Required rate of return = Risk-free rate + (Beta × (Required return on the market - Risk-free rate))

For a stock with a beta of 2 and given a risk-free rate of 5.5% and a required return on the market of 8%, the required rate of return is:

5.5% + (2 × (8% - 5.5%)) = 5.5% + (2 × 2.5%) = 10.5%.

For the market as a whole with a risk-free rate of 4.5% and a market risk premium of 6%, the required return is:

4.5% + 6% = 10.5%.

For a stock with a beta of 1.9 and the same market conditions as above, the required rate of return is:

4.5% + (1.9 × 6%) = 4.5% + 11.4% = 15.9%.