Lesson 10 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 10 of 14 · 14 min

Indifference curves and the capital allocation line

Indifference curves show what an investor wants, the capital allocation line shows what is available, and the optimal portfolio is where the two just touch.

In short

  • An indifference curve links risk–return pairs that give one investor the same utility.
  • Risk-averse curves slope upward and are convex; steeper curves mean more risk aversion. Utility rises toward the northwest. One investor's curves never cross.
  • Risk-neutral curves are horizontal; risk-seeker curves slope downward.
  • Combining a risk-free asset with a risky portfolio gives the capital allocation line (CAL): E(Rp)=Rf+E(Ri)−RfσiσpE(R_p) = R_f + \frac{E(R_i) - R_f}{\sigma_i}\sigma_p.
  • Left of the risky portfolio the investor lends at RfR_f; right of it the investor borrows at RfR_f to invest more than 100%.
  • The optimal portfolio is the tangency point between the CAL and the highest indifference curve that touches it.

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