The efficient frontier of risky assets is

Question

BlackTom AI · Accepted Answer

The efficient frontier is the upper part of the risk–return locus where, for any given level of risk (standard deviation), no other portfolio offers a higher expected return. This is a core result of mean–variance (Markowitz) portfolio theory.

1) Relevant knowledge points and concepts
- Investment opportunity set: all achievable combinations of expected return and standard deviation from risky assets.
- Global minimum variance portfolio (GMVP): the single portfolio on that set with the lowest possible variance (leftmost point).
- Efficient frontier: the set of portfolios that maximize expected return for a given risk (equivalently, minimize risk for a given return) — this is the upper branch of the feasible locus above the GMVP.

2) Step-by-step reasoning
- Plot expected return on the vertical axis and standard deviation (risk) on the horizontal axis. The feasible set for combinations of risky assets is typically a curved (parabolic) region.
- Locate the GMVP: the point on the left edge with the smallest standard deviation.
- For any given standard deviation greater than the GMVP’s, there are two possible portfolios on the feasible curve (upper and lower branches). The upper branch has the higher expected return.
- By definition, portfolios on the upper branch above the GMVP are not dominated by any other portfolio (they give the highest return for that risk), so they form the efficient frontier.

3) Intermediate “calculation”/construction steps (conceptual)
- Solve mean–variance optimization: maximize μ_p − λσ_p^2 or minimize σ_p^2 subject to return constraint to get frontier equation.
- Identify the vertex (GMVP) of the parabola; take the branch with increasing return as σ increases — that branch is efficient.

4) Why the correct answer is correct
- The efficient frontier consists of portfolios above the GMVP because below-GMVP points are dominated (for same risk a higher return exists on the upper branch). The GMVP itself is the leftmost boundary; only the portion above it gives the highest returns for given risk levels.

5) Why other options are incorrect
- “Represents the highest standard deviations”: incorrect — efficiency is about best return per risk, not highest risk.
- “Includes portfolios with the lowest standard deviation”: incorrect — only one portfolio (the GMVP) has the absolute lowest standard deviation.
- “Set of portfolios that have zero standard deviation”: incorrect — that would be risk-free assets, not the risky-assets frontier.
- “Set of portfolios that have the highest standard deviation”: incorrect — high standard deviation alone doesn’t imply efficiency.

6) Conclusion
This confirms the correct answer: the efficient frontier of risky assets is the portion of the investment opportunity set that lies above the global minimum variance portfolio.

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