The market is expected to generate a 12% return and the risk free rate is 4%. A portfolio manager has 70% of her capital allocated to stock A with a beta of 0.8, which generated a total return of 11%. 30% of her capital is allocated to stock B with a beta of 1.1, which generated a total return of 12%. What Alpha was generated by the manager by allocating more capital to stock A?
A) 0.11%
B) 0.18%
C) 0.25%
D) 0.38%

Question

Quizplus · Accepted Answer

The expected return of the portfolio can be calculated using the Capital Asset Pricing Model (CAPM) for each stock and then finding the weighted average of these expected returns. For stock A, the expected return is $4\% + 0.8(12\% - 4\%)$ = $10.4\%$. For stock B, it is $4\% + 1.1(12\% - 4\%)$ = $12.8\%$. The expected return of the portfolio is $70\%\times10.4\% + 30\%\times12.8\%$ = $11.12\%$. The actual return of the portfolio is $70\%\times11\% + 30\%\times12\%$ = $11.3\%$. The alpha, or the excess return, is $11.3\% - 11.12\% = 0.18\%$.

The Market Is Expected to Generate a 12% Return and the Risk