Lesson 7 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 7 of 14 · 12 min

Minimum-variance and efficient frontiers

Of all the portfolios risky assets can form, only those on the upper half of the minimum-variance frontier, the efficient frontier, are worth holding.

In short

  • The investment opportunity set is every risk–return combination that can be built from the available assets.
  • Adding an asset class that is not perfectly correlated pushes the opportunity set northwest.
  • The minimum-variance frontier holds the lowest-risk portfolio for each level of expected return.
  • Its leftmost point is the global minimum-variance portfolio: no risky-asset portfolio has less risk.
  • The part of the frontier above the global minimum-variance portfolio is the Markowitz efficient frontier; the part below is inefficient.
  • Along the efficient frontier, each extra unit of risk buys less and less extra return.

Unlock this lesson free for 7 days

Create a free account to get 7 days free: every lesson, video and flashcard, and the question bank. No card needed.

Start your 7-day free trialLog in