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2 October, 21:48

Assume that both portfolios A andB are well diversified, that E (rA) = 12%, and E (rB) = 9%. Assume the economy has only one risk factor, thebeta of A = 1.2 and the beta of B = 0.8. Using the expected return-beta relationship, what must be the riskfreerate?

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  1. 2 October, 21:52
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    The risk free rate (Rf) is 28,2%

    Explanation:

    We will substituting the portfolio expected return (Er) and the betas of the portfolio in the expected return & beta relationship, that is:

    E[r] = Rf + Beta * (Risk Premium)

    On doing this we get 2 equations in which the risk free rate (Rf) and the risk premium [P] are not known to use:

    12% = Rf + 1 * (P - Rf)

    9% = Rf + 1.2 * (P - Rf)

    On solving first equation (of Portfolio A) for P (risk premium), we get:

    12% = Rf + 1 * (P - Rf)

    12% = Rf + P - Rf

    (Rf and Rf cancels each other)

    P = 12%

    Now, on using the value of P in second equation (of Portfolio B), and solving for Rf (risk free rate), we get:

    9% = Rf + 1.2 * (12.2% - Rf)

    9% = Rf + 14.64% - 1.2Rf

    1.2Rf - Rf = 14.64% - 9%

    0.2Rf = 5,64%

    Rf = 5.64% / 0.2

    Rf = 28,2%

    So, the risk free rate (Rf) is 28,2%
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