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Explain the market portfolio and the idea of two-fund separation

CFA® Level I · Portfolio Management · Portfolio Risk and Return: Part II · PM.2.d

The idea

Two-fund separation is the result that the investment decision splits cleanly in two: which risky portfolio to hold, and how much of total wealth to place in it. The first answer is the same for every investor who shares the same expectations and can borrow and lend at the risk-free rate — the tangency portfolio. Only the second answer depends on risk aversion. If all investors hold the same risky portfolio, it must in equilibrium be the market portfolio, which is the logical step that takes the framework from the capital allocation line to the capital market line and the CAPM.

A practice question

From the question bank, with the reason each wrong option is wrong.

What are the two decisions separated by two-fund separation?

  1. Which securities to buy and when to buy themWhy not: Selection and timing are the active manager's problems. The separation result is about composition against allocation.
  2. Which risky portfolio to hold and how much to allocate to it — correct
  3. Whether to use active or passive management, and which managerWhy not: An implementation choice, which the theory does not address.

The composition of the risky holding is common to all investors; only the allocation between it and the risk-free asset reflects individual preference.

A harder one

Under the assumptions of the model, why must the tangency portfolio be the market portfolio?

  1. Because the market portfolio has the lowest varianceWhy not: That would be the global minimum-variance portfolio, which is a different point on the frontier.
  2. Because index funds are widely availableWhy not: An observation about products. The argument is about market clearing, and it long predates index funds.
  3. Because it must then contain every asset — correct

If every investor holds the same risky portfolio, it must hold every asset in proportion to its market value. Assets must be held by someone: if all investors want identical proportions, those proportions can only be the market's own, or prices would adjust until they were.

The hardest tier

Which assumption, if relaxed, most directly breaks two-fund separation?

  1. Investors have homogeneous expectations — correct
  2. Assets are infinitely divisibleWhy not: Indivisibility makes exact weights hard to hit in practice but leaves everyone aiming at the same portfolio.
  3. Returns are measured over a single periodWhy not: Multi-period extensions complicate the analysis without necessarily giving investors different risky portfolios.

If investors disagree about expected returns and covariances, each computes a different tangency portfolio, and there is no longer one risky fund everyone holds.

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