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26 January, 00:17

The market price of a security is $25. Its expected rate of return is 12%. The risk-free rate is 4% and the market risk premium is 6.0%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged) ? Assume that the stock is expected to pay a constant dividend in perpetuity. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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  1. 26 January, 03:13
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    Given Information:

    Market price of security = $25

    Expected rate = 12%

    Risk-free rate = 4%

    Market risk premium = 6%

    Answer:

    New market price of security = $15.03

    Explanation:

    The new market price of security can be calculated by,

    P = Dividend/Expected return

    Where Dividend is given by

    Dividend = Market price*Expected rate

    D = $25*0.12

    D = 3$

    Expected return is given by

    Expected return = Risk-free rate + β * (market risk premium)

    β can be calculated as

    β = (Expected rate - Risk-free rate) / market risk premium

    β = (12 - 4) / 6

    β = 1.33%

    Since it is given that correlation coefficient with the market portfolio doubles, therefore, β will get doubled too because they are directly proportional.

    β = 2*1.33%

    β = 2.66%

    So the Expected return is

    Expected return = 4 + 2.66 * (6)

    Expected return = 19.96%

    So the new market price of security is,

    P = Dividend/Expected return

    P = 3/0.1996

    P = $15.03
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