Explanation

The two-fund separation theorem is a fundamental concept in modern portfolio theory. It states that:

1. All investors, regardless of their risk preferences, will hold a combination of just two assets:

   • The risk-free asset (such as government bonds or Treasury bills)
   • The optimal risky portfolio (also known as the tangency portfolio)

2. The optimal risky portfolio is the portfolio that lies at the point where the capital allocation line (CAL) is tangent to the efficient frontier. This portfolio maximizes the Sharpe ratio.

3. Why not the other options?

   • Option B: The global minimum-variance portfolio is not necessarily the optimal risky portfolio. While it has the lowest variance among all risky portfolios, it doesn't maximize the Sharpe ratio.
   • Option C: Investors combine the risk-free asset with the optimal risky portfolio, not two risky portfolios.

4. Key implications:

   • All investors face the same optimal risky portfolio
   • Differences in investor risk preferences are reflected only in the proportion allocated to the risk-free asset versus the optimal risky portfolio
   • More risk-averse investors allocate more to the risk-free asset
   • Less risk-averse investors allocate more to the optimal risky portfolio

This theorem simplifies portfolio construction by separating the investment decision into two steps: (1) identifying the optimal risky portfolio, and (2) determining the appropriate mix between this portfolio and the risk-free asset based on individual risk tolerance.