Answer: improves

## Explanation When a risk-free asset with zero expected return is added to the investable universe of risky assets, the investors' risk-return trade-off **improves**. ### Key Concepts: 1. **Capital Allocation Line (CAL)**: The addition of a risk-free asset creates a linear risk-return trade-off line that connects the risk-free rate to the optimal risky portfolio (tangency portfolio). 2. **Zero Expected Return Risk-Free Asset**: Even though the risk-free asset has zero expected return, it still provides diversification benefits and allows investors to: - Lend at the risk-free rate (invest in the risk-free asset) - Borrow at the risk-free rate (leverage the risky portfolio) 3. **Improved Risk-Return Trade-off**: - **Without risk-free asset**: Investors can only choose among risky assets on the efficient frontier - **With risk-free asset**: Investors can achieve any point on the Capital Allocation Line (CAL), which dominates the efficient frontier (except at the tangency point) - This creates a **steeper slope** of the risk-return trade-off, meaning investors get higher expected return for the same level of risk, or lower risk for the same expected return 4. **Mathematical Explanation**: - The CAL equation: E(R_p) = R_f + [E(R_t) - R_f]/σ_t × σ_p - Even with R_f = 0, the slope is E(R_t)/σ_t, which is positive for any risky portfolio with positive expected return - This allows investors to achieve better risk-return combinations than the efficient frontier alone 5. **Practical Implication**: Investors can now: - Create portfolios with lower risk than the minimum variance portfolio - Achieve higher returns through leverage - Customize their risk exposure more precisely **Therefore, the correct answer is C: improves.**

Author: LeetQuiz .