The efficient frontier of risky assets is:

Question

BlackTom AI · Accepted Answer

Here we evaluate what the efficient frontier of risky assets represents in portfolio theory.
Option a: 'the portion of the investment opportunity set that lies above the global minimum variance portfolio.' This is a correct description because the efficient frontier consists of portfolios that offer the highest expected return for a given level of risk, and, when plotted in mean-variance space, these portfolios lie above the global minimum-variance portfolio (GMVP) on the boundary of the feasible set.
Option b: 'the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation.' While the GMVP has the lowest variance, the efficient frontier is not simply all portfolios with the lowest standard deviation; it focuses on best return for risk, and includes portfolios with higher standard deviation as long as they offer superior returns. So this is incomplete or mischaracterizes the frontier.
Option c: 'both the portion of the investment opportunity set that lies above the global minimum variance portfolio and the portion of the investment opportunity set that represents the highest standard deviations.' This is misleading because the frontier is defined by the trade-off between risk and return; it does not separately consist of portfolios solely at the highest standard deviations, and the boundary is determined by the efficient set, not by merely listing high-variance portfolios.
Option d: 'the portion of the investment opportunity set that represents the highest standard deviations.' This ignores the return dimension and implies the frontier consists only of extreme risk, which is incorrect since many high-variance portfolios may offer poor (or inferior) risk-adjusted returns relative to on-frontier portfolios.
Option e: 'the set of portfolios that have zero standard deviation.' Zero-risk portfolios lie at a single point (the risk-free or near-risk-free case) and are not part of the efficient frontier for risky assets. The efficient frontier for risky assets considers portfolios with positive risk as well, so this is incorrect.
Overall, the only option that correctly characterizes the efficient frontier of risky assets is option a, which identifies it as the portion of the investment opportunity set lying above the GMVP, representing the best trade-offs between risk and return among risky portfolios.

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