The efficient frontier of risky assets is:

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Question restatement: The efficient frontier of risky assets is:

Option a: 'the portion of the investment opportunity set that lies above the global minimum variance portfolio.' This is the standard definition: the efficient frontier consists of all portfolios with the best (maximum) expected return for a given level of risk, and for risky assets in the mean-variance framework, this frontier lies above the global minimum variance portfolio on the return–risk (mean–standard deviation) plane.

Option b: 'the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation.' While the global minimum variance portfolio has the lowest variance among all portfolios, the efficient frontier is not merely the set of lowest-variance portfolios. It includes portfolios with varying levels of return for a given risk, and excludes suboptimal portfolios that lie below the frontier.

Option c: 'the portion of the investment opportunity set that represents the highest standard deviations.' High-variance portfolios are not automatically efficient; many high-variance portfolios do not deliver commensurate returns and lie below the frontier. Therefore, this is not the defining characteristic of the efficient frontier.

Option d: 'the set of portfolios that have zero standard deviation.' Zero risk portfolios exist (risk-free assets), but the efficient frontier for risky assets excludes zero-variance portfolios since it concerns combinations of risky assets; the zero-variance point is not on the frontier of risky assets.

Option e: '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 wording is misleading: while the frontier lies above the global minimum variance portfolio, it does not include the highest-variance portfolios as part of the efficient frontier in the standard mean–variance sense; some highly volatile portfolios are inefficient due to disproportionate risk relative to return.

Summary: Option a correctly identifies the efficient frontier for risky assets as the segment of the investment opportunity set that lies above the global minimum variance portfolio, representing the best trade-offs between expected return and risk. The other options describe incorrect or incomplete aspects of the concept, such as confusing the frontier with merely low-variance, high-variance, zero-variance, or mischaracterizing its relation to risk-free assets.

The efficient frontier of risky assets is:

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