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Let's go through the multiple-choice questions (MCQs) shown in the image and try to answer them based on finance theory concepts.

### 3. MCQ - The separation theorem
The separation theorem states that the investment decision (selection of a portfolio of risky assets) can be separated from the financing decision (how much to allocate between risky assets and risk-free assets).
- **Correct Answer: (d)** allows the construction of an efficient portfolio by separating efficient assets from inefficient assets.

### 4. MCQ - Using the Sharpe single-index model with a random portfolio of U.S. common stocks, as one increases the number of stocks in the portfolio, the total risk of the portfolio will:
As the number of stocks in a portfolio increases, the unsystematic risk is diversified away, leaving only systematic risk.
- **Correct Answer: (b)** approach the portfolio's systematic risk.

### 5. MCQ - The CAPM implies that:
CAPM (Capital Asset Pricing Model) shows the relationship between the expected return of an asset and its risk as measured by beta. It implies that the expected return on an efficient portfolio may be lower than the riskless interest rate under certain conditions.
- **Correct Answer: (d)** the expected return on an efficient portfolio may be lower than the riskless interest rate.

### 6. MCQ - The beta of an efficient portfolio:
An efficient portfolio's beta is 1 since it represents the market portfolio, and by definition, the market has a beta of 1.
- **Correct Answer: (a)** must be 1 since an efficient portfolio is perfectly positively correlated with the market portfolio.

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Would you like more details on any of these concepts?

### Here are 5 related questions to consider:
1. How does the CAPM model help in portfolio diversification?
2. What is the relationship between beta and systematic risk?
3. Can the separation theorem be applied to portfolios with no risk-free assets?
4. How does increasing the number of stocks affect unsystematic risk?
5. What factors influence the efficient frontier in portfolio theory?

### Tip:
In portfolio theory, understanding the difference between systematic and unsystematic risk is key to managing and optimizing your investments.

MCQs related to finance theory: separation theorem, Sharpe single-index model, CAPM, and beta of an efficient portfolio.

Learn about key finance concepts including the Separation Theorem, Sharpe single-index model, CAPM, and the role of beta in an efficient portfolio. These topics are essential for undergraduate studies in finance and investment.

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