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Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 12% and 16%, respectively. The beta of A is 0.7, while that of B is 1.4. The T-bill rate is currently 5%, whereas the expected rate of return of the S&P 500 index is 13%. The standard deviation of portfolio A is 12% annually, that of B is 31%, and that of the S&P 500 index is 18%. a. Calculate the alphas for the two portfolios. (Round your answers to 1 decimal place.)

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Answer:

Alpha for A is 1.40%; Alpha for B is -0.2%.

Explanation:

First, we use the CAPM to calculate the required returns of the two portfolios A and B given the risks of the two portfolios( beta), the risk-free return rate ( T-bill rate) and the Market return rate (S&P 500) are given.

Required Return for A: Risk-free return rate + Beta for A x ( Market return rate - Risk-free return rate) = 5% + 0.7 x (13% - 5%) = 10.6%;

Required Return for A: Risk-free return rate + Beta for B x ( Market return rate - Risk-free return rate) = 5% + 1.4 x (13% - 5%) = 16.2%;

Second, we compute the alphas for the two portfolios:

Portfolio A: Expected return of A - Required return of A = 12% - 10.6% = 1.4%;

Portfolio B: Expected return of B - Required return of B = 16% - 16.2% = -0.2%.

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