Portfolios on the Capital Market Line

A

The Capital Market Line (CML) is a graphical representation of the risk-return tradeoff for efficient portfolios that consist of both risky assets and the risk-free asset. It helps investors determine the optimal portfolio allocation between risky assets and the risk-free asset.

The CML is derived from the combination of the risk-free rate and the efficient frontier, which represents portfolios with the highest expected returns for a given level of risk. The CML is a tangent line drawn from the risk-free rate to the efficient frontier.

Now let's analyze each answer choice:

A. contain the same mix of risky assets unless only the risk-free asset is held.

This answer choice is incorrect. Portfolios that lie on the CML do not necessarily contain the same mix of risky assets. The CML represents the optimal combination of risky assets and the risk-free asset based on an investor's risk tolerance. It allows for different allocations to risky assets, depending on an investor's preference for risk and return.

B. have some unsystematic risk unless only the risk-free asset is held.

This answer choice is correct. Portfolios on the CML will have some unsystematic risk unless only the risk-free asset is held. Unsystematic risk refers to the risk that is specific to individual assets and can be diversified away by holding a diversified portfolio. Since the CML represents efficient portfolios, it means that the portfolios on the CML have diversified away most of the unsystematic risk. However, they still carry some level of unsystematic risk because the CML includes risky assets that have their own idiosyncratic risks.

C. contain at least some positive allocation to the risk-free asset.

This answer choice is incorrect. Portfolios on the CML can have different allocations to the risk-free asset, including zero allocation. The risk-free asset represents a riskless investment, typically a government bond or treasury bill, that provides a guaranteed return. Investors can choose to allocate all their investments to the risk-free asset if they want to avoid any exposure to risky assets.

To summarize, the correct answer is B. Portfolios on the Capital Market Line (CML) have some unsystematic risk unless only the risk-free asset is held.