Question

Suppose that all the unrealistic assumptions of the CAPM are true (the CAPM is valid)!!! The market portfolio has an expected return equal to 15% and the risk free rate is 5%. We are mainly interested in 2 securities in the market; stocks A and B. The beta of stock A is 1.8 and the expected return of stock B is 10%. 1. Estimate the expected return of stock A. 2. Estimate the beta of stock B. 3. Estimate the expected return of the optimal risky portfolio. 4. Estimate the alpha of stock A.

Answer 1

The expected return of stock A is 23%, the beta of stock B is 0.5, the expected return of the optimal risky portfolio is the market portfolio's return of 15%, and alpha of stock A cannot be determined without the actual return data.

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) allows us to estimate various financial metrics when market conditions follow certain assumptions. Given the information, we can calculate the expected return for stock A and the beta for stock B.

1. Expected return of stock A: Using the CAPM formula, we can calculate this as follows: Expected Return(A) = Risk-Free Rate + Beta(A) * (Market Return - Risk-Free Rate) = 5% + 1.8 * (15% - 5%) = 23%.
2. Beta of stock B: This can be found by rearranging the CAPM formula: Beta(B) = (Expected Return(B) - Risk-Free Rate) / (Market Return - Risk-Free Rate) = (10% - 5%) / (15% - 5%) = 0.5.
3. The optimal risky portfolio is typically the market portfolio in the context of CAPM, which has an expected return of 15%.
4. The alpha of stock A represents the stock's performance relative to the return predicted by CAPM, which would be Alpha(A) = Actual Return(A) - Expected Return(A). Without actual return data, alpha cannot be calculated.