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13 July, 19:33

what is the standard deviation of returns on a well-diversified portfolio with a beta of 1.25 if the standard deviation of the market portfolio equals 18%?

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  1. 13 July, 21:18
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    the standard deviation of the portfolio is σP = 22.5%

    Step-by-step explanation:

    since the variance of the portfolio σP² is

    σP² = β²*σM²+σ² (e)

    where

    β = Portfolio's beta

    σM = standard deviation of the market portfolio

    σ² (e) = variance of the unexpected returns of the portfolio (diversifiable risk)

    for a well-diversified portfolio σ² (e) = 0, then

    σP² = β²*σM²

    σP=β*σM

    replacing values

    σP = β*σM = 1.25*0.18 = 0.225 = 22.5%

    σP = 22.5%
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