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.