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.