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3 March, 09:38

Consider the multifactor APT with two factors. Stock A has an expected return of 20.70%, a beta of 1.2 on factor 1, and a beta of 0.6 on factor 2. The risk premium on the factor 1 portfolio is 4.00%. The risk-free rate of return is 8.40%. What is the risk premium on factor 2 if no arbitrage opportunities exist?

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  1. 3 March, 12:08
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    12.5%

    Explanation:

    expected return = 20.70%

    risk-free rate of return is 8.40%

    beta of on factor 1 = 1.2

    risk premium on the factor 1 = 4.00%

    beta of on factor 2 = 0.6

    risk premium on factor 2 = x (unknown)

    To calculate for the risk premium on factor 2, we use this formula

    expected return = (beta of on factor 1 * premium on the factor 1) + (beta of on factor 2 * premium on the factor 2) + risk-free rate of return

    20.70% = (1.2 * 4%) + (0.6 x) + 8.40%

    0.207 = 0.048 + 0.6x + 0.084

    0.207 = 0.132 + 0.6x

    0.6x = 0.075

    x = 0.125

    =12.5%
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