The efficient frontier of risky assets is:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

In mean–variance portfolio theory, the efficient frontier is the locus of portfolios that offer the highest expected return for each level of risk (standard deviation) or, equivalently, the lowest risk for each level of expected return. The investment opportunity set is the cloud of all achievable risk–return combinations from risky assets; the efficient frontier is the upper boundary of that cloud.

Step-by-step reasoning:
1. Define the global minimum variance portfolio (GMVP): it is the single portfolio on the opportunity set that attains the lowest possible variance (lowest standard deviation) among all risky-asset portfolios.
2. For any given level of risk above the GMVP’s risk, there is a portfolio that maximizes expected return. These maximal-return portfolios form the upper portion of the feasible region.
3. Portfolios on the lower boundary (below the GMVP or below the upper boundary) are dominated: there exists another portfolio with equal or lower risk and strictly higher expected return (or equal return and lower risk). Such dominated portfolios are not efficient.
4. Therefore, the efficient frontier consists of the portion of the investment opportunity set that lies above the GMVP (the upward-sloping/upper boundary), because those portfolios are undominated in the mean–variance sense.

Why option b is correct:
- It correctly identifies the efficient frontier as the upper portion of the set starting at the GMVP and extending upward/right where expected return is maximized for each risk.

Why the other choices are incorrect:
- a) “represents the highest standard deviations” is wrong — efficiency is about best return for a given risk, not highest risk.
- c) “includes portfolios with the lowest standard deviation” is misleading — only the GMVP has the lowest standard deviation; the frontier includes that point but is not defined by lowest SD alone.
- d) “set of portfolios that have zero standard deviation” is wrong — risky-asset efficient frontier excludes a zero-risk condition (unless a risk-free asset is included).
- e) “lies below the GMVP” is wrong — portfolios below the GMVP are dominated and therefore inefficient.

Conclusion: The correct answer is b.

The efficient frontier of risky assets is:[Fill in the blank]单项选择题

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