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4 November, 18:42

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 6.9 percent and a standard deviation of 9.9 percent. The risk-free rate is 3.9 percent, and the expected return on the market portfolio is 11.9 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a. 44 correlation with the market portfolio and a standard deviation of 54.9 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

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  1. 4 November, 21:24
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    11.22%

    Explanation:

    We need beta coefficient of the security to determine the expected return.

    beta = (correlation * standard deviation) : market standard deviation

    The share of risk free asset is =

    (the market portfolio - portfolio of expected return) : (the market portfolio - risk-free rate)

    The share of risk free asset is = (11.9 - 6.9) % : (11.9 - 3.9) %

    The share of risk free asset is = 0.625.

    As the portfolio has a standard deviation of 9.9%, the standard deviation of market value = Standard deviation : (1 - the share of risk free asset)

    The market standard deviation = 9.9% : (1 - 0.625)

    The market standard deviation = 26.4%

    As we get all the values for beta, we now input the values -

    beta = (0.44 * 54.9%) : 26.4%

    beta = 0.915

    Now we will use Capital asset pricing model to determine the expected return

    expected return = Risk free return + (expected market return - risk free return) * beta

    expected return = 3.9% + (11.9% - 3.9%) * 0.915

    expected return = 3.9% + 7.32%

    expected return = 11.22%
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