Optimal risky portfolio and the optimal investor portfolio

In short

• Combining the risk-free asset with any efficient portfolio gives a CAL; the best one is the steepest, tangent to the efficient frontier.
• The tangency portfolio is the optimal risky portfolio; its CAL dominates every other CAL and the efficient frontier (except at the tangency point).
• Two-fund separation: all investors hold the risk-free asset and the same optimal risky portfolio.
• Step 1, the investment decision, ignores preferences; step 2, the financing decision, uses each investor's indifference curves.
• Highly risk-averse investors sit near $R_f$ (lending); less risk-averse investors sit at or beyond the optimal risky portfolio (borrowing).