Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios a and b are 11% and 14%, respectively. the beta of a is .8, while that of b is 1.5. the t-bill rate is currently 6%, while the expected rate of return of the s&p 500 index is 12%. the standard deviation of portfolio a is 10% annually, while that of b is 31%, and that of the index is 20%.
a. if you currently hold a market index portfolio, what would be the alpha for portfolios a and b? (negative values should be indicated by a minus sign. do not round intermediate calculations. round your answers to 1 decimal place.)

Answer 1

Answer:

∝ for portfolio A = E(rA) - Required return predicted by CAPM

                           = 0.11 - [0.06 + 0.8 × (0.12 - 0.06)]

                           = 0.11 - [0.06 + 0.048]

                           = 0.11 - 0.108

                           = -0.002      ≈ -0.2%  to 1 decimal place

∝ for portfolio B = E(rB) - Required return predicted by CAPM

                           = 0.14 - [0.06 + 1.5 × (0.12 - 0.06)]

                           = 0.14 - [0.06 + 0.09]

                           = 0.14 - 0.15

                           = -0.01         ≈ -1.0% to 1 decimal place