Lesson 12 of 14 · All lessons in this module
  1. Portfolio expected return and varianceVideo lesson
  2. Portfolio returns over time: drift and rebalancing
  3. The covariance matrix and many-asset portfolios
  4. Correlation and diversification
  5. Scenario-based portfolio risk and the many-asset limit
  6. Integrated cases: three-asset risk from volatilities, correlations and scenarios
  7. Minimum-variance and efficient frontiersVideo lesson
  8. Finding the minimum-variance portfolio and optimising weights
  9. Risk aversion and utilityVideo lesson
  10. Indifference curves and the capital allocation lineVideo lesson
  11. Theory assumptions, risk-aversion measures and the Sharpe ratio of the CAL
  12. Optimal risky portfolio and the optimal investor portfolioVideo lesson
  13. The risk-free asset, the market portfolio and the CMLVideo lesson
  14. Beta, the security market line and the CAPM

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 12 of 14 · 14 min

Optimal risky portfolio and the optimal investor portfolio

Adding a risk-free asset turns portfolio choice into two steps: everyone picks the same optimal risky portfolio, then each investor chooses how much to lend or borrow.

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 RfR_f (lending); less risk-averse investors sit at or beyond the optimal risky portfolio (borrowing).

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