Answer: a capital allocation line.

## Explanation In portfolio theory, when we combine a risk-free asset with a risky asset, the resulting set of portfolios forms a **Capital Allocation Line (CAL)**. ### Key Concepts: 1. **Capital Allocation Line (CAL)**: This is a straight line that shows all possible combinations of the risk-free asset and a risky portfolio. It represents the risk-return trade-off available to investors when they can invest in both risk-free assets and risky assets. 2. **Markowitz Efficient Frontier**: This is the set of optimal portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of expected return. It is derived from combinations of **only risky assets**, not including the risk-free asset. 3. **Indifference Curves**: These represent an investor's preferences for risk and return. They show combinations of risk and return that provide the same level of utility to a particular investor. ### Why Option A is Correct: - When you combine a risk-free asset (with zero risk and a certain return) with a risky asset, the resulting portfolios lie on a straight line in risk-return space. - This line starts at the risk-free rate on the vertical axis (zero risk) and extends upward and to the right as you allocate more to the risky asset. - The slope of this line represents the **Sharpe ratio** (excess return per unit of risk). ### Why Other Options are Incorrect: - **Option B (Markowitz efficient frontier)**: This is formed from combinations of risky assets only, not including the risk-free asset. - **Option C (investor's indifference curve)**: This represents investor preferences, not the actual investment opportunities available in the market. ### Mathematical Representation: The equation for the CAL is: $$E(R_p) = R_f + \frac{E(R_m) - R_f}{\sigma_m} \times \sigma_p$$ Where: - $E(R_p)$ = Expected return of the portfolio - $R_f$ = Risk-free rate - $E(R_m)$ = Expected return of the risky asset - $\sigma_m$ = Standard deviation of the risky asset - $\sigma_p$ = Standard deviation of the portfolio This linear relationship is only possible when combining a risk-free asset with a risky asset.

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