Final answer:
The expected return of stock A is 23% using the CAPM formula. However, without the expected return of stock B, we cannot calculate the beta of stock B, the expected return, and the beta of an equally weighted portfolio Z, or the alphas for stock A and portfolio Z, as these calculations require additional information not provided in the question.
Step-by-step explanation:
The Capital Asset Pricing Model (CAPM) helps to calculate the expected return on an asset when all its assumptions are true. In this case, the market portfolio has an expected return of 15% with a risk-free rate of 5%.
1. Estimate the expected return of stock A
Using the CAPM formula:
Expected Return of A = Risk-Free Rate + Beta of A * (Market Return - Risk-Free Rate)
Expected Return of A = 5% + 1.8 * (15% - 5%) = 5% + 1.8 * 10% = 5% + 18% = 23%
2. Estimate the beta of stock B
We rearrange the CAPM formula to solve for Beta:
Beta of B = (Expected Return of B - Risk-Free Rate) / (Market Return - Risk-Free Rate)
We need additional information to calculate this as the expected return of B is not given in the question.
3. Estimate the expected return of the optimal risky portfolio
This typically refers to the market portfolio, which is already provided as 15%.
4. Estimate the alpha of stock A
Alpha = Actual or Expected Return of the stock - CAPM Expected Return
Without the actual or an alternative expected return for A, we cannot calculate the alpha.
5. Estimate the expected return and the beta of an equally weighted portfolio Z consisting of stocks A and B
Expected Return of Z = (Expected Return of A + Expected Return of B) / 2
Beta of Z = (Beta of A + Beta of B) / 2
Again, without the expected return of B and its beta, we cannot calculate these values for Portfolio Z.
6. Estimate the alpha of portfolio Z
Alpha of Z = Actual or Expected Return of Z - CAPM Expected Return of Z
As we don't have the necessary values, we cannot estimate the alpha of portfolio Z.