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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%.

a. Estimate the expected return of the optimal risky portfolio.
b. Estimate the alpha of stock A.
c. Estimate the expected return and the beta of an equally weighted portfolio Z consisting of stocks A and B.
d. Estimate the alpha of portfolio Z.

User Hok
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1 Answer

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Final answer:

The expected return of the optimal risky portfolio aligns with the market portfolio at 15%. The reliable calculation of alpha for stock A, the expected return and beta for portfolio Z, and the alpha of portfolio Z cannot be performed with the information provided as critical data for stock A is missing.

Step-by-step explanation:

The student's question pertains to the use of the Capital Asset Pricing Model (CAPM) to evaluate the expected returns and the alpha values of two stocks, A and B, as well as an equally weighted portfolio consisting of the two stocks.

Expected Return of the Optimal Risky Portfolio

The expected return of the optimal risky portfolio is not provided in the question directly. However, in CAPM, if all assumptions hold true, the optimal risky portfolio would align with the market portfolio. Therefore, the expected return of the optimal risky portfolio is given as the expected return of the market, which is 15%.

Alpha of Stock A

To calculate the alpha of stock A, we would use the CAPM formula: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Since we do not have the expected return of stock A, we cannot calculate alpha without additional information.

Expected Return and Beta of Portfolio Z

The expected return and beta of an equally weighted portfolio Z consisting of stocks A and B would be the average of the individual expected returns and betas of stocks A and B. Without the expected return of stock A, we cannot compute the expected return of portfolio Z. The beta of portfolio Z, as an equally weighted portfolio, would be the average of the betas of stocks A and B.

Alpha of Portfolio Z

The alpha of portfolio Z is a measure of the portfolio's performance relative to the expected performance as per CAPM. Without the expected return of portfolio Z and stock B's beta, alpha cannot be calculated.

User Lutz Prechelt
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