Which of the following statements is true? Risky assets on the efficient frontier…

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BlackTom AI · Accepted Answer

Kicking off with the overall context, we’re evaluating statements about risky assets that lie on the efficient frontier, i.e., the set of optimal portfolios balancing risk and return among risky assets.
Option A: 'provide returns which are higher than or equal to the Global Minimum Variance Portfolio.' The logic here is that the Global Minimum Variance Portfolio (GMVP) sits at the leftmost, lowest-variance point of the frontier; as you move along the efficient frontier to portfolios with higher risk, the expected return generally increases. Therefore, for portfolios on the frontier that correspond to higher risk levels, the expected return is at least as large as the GMVP’s return. While specific numeric comparisons can depend on data, the typical characterization on the frontier is that higher risk accompanies higher (or at least not-lower) returns relative to the GMVP, making this statement consistent with the standard risk–return ordering.
Option B: 'have risk which is higher than or equal to the Global Minimum Variance Portfolio.' By definition, the GMVP has the minimum possible variance among all portfolios of risky assets. Any other portfolio on the efficient frontier either has greater variance (risk) or, in the degenerate case, exactly the same variance at the same point. Thus, this statement is aligned with the fundamental property of the GMVP as the lowest-variance anchor on the frontier.
Option C: 'are a subset of the Minimum Variance Frontier.' The Minimum Variance Frontier refers to the portion of the frontier that connects the GMVP to portfolios with progressively higher returns at increasing risk. Since the efficient frontier for risky assets generally traces the same curve for portfolios that are optimal at their risk levels, the risky assets on the efficient frontier do indeed lie along or constitute a segment of the Minimum Variance Frontier. This reflects the idea that the locus of optimal risky allocations, as risk increases, traces the minimum-variance boundary for those return targets.
Option D: 'represent the optimal allocations among risky assets at each risk level.' The efficient frontier is defined as the set of portfolios that maximize expected return for a given level of risk (or minimize risk for a given return). At each target risk level along the frontier, there is a corresponding optimal allocation among the risky assets. Hence, this statement captures the core definition of what the frontier represents in portfolio optimization.
Option E: 'All of the above statements are true.' If each of A through D holds under the usual interpretation of the efficient frontier for risky assets, then the comprehensive option that all statements are true is correct. Keeping in mind that the GMVP anchors the frontier, and the frontier is organized so that higher risk aligns with higher (or at least non-decreasing) returns, along with the correspondence between risk levels and optimal allocations, all components align cohesively.
In summary, each individual statement (A through D) can be understood as a natural property of the risky-assets efficient frontier, and coherence among them supports the conclusion expressed in option E. The reasoning reinforces how the GMVP anchors the frontier, how risk and return scale along it, and how the allocations vary to maintain optimality at each risk level.

Which of the following statements is true? Risky assets on the efficient frontier…

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