An investor observes the following portfolios in the portfolio frontier:

Portfolio A: E[R] = 8%, SD[R] = 45%

Portfolio B: E[R] = 9%, SD[R] = 30%

Portfolio C: E[R] = 10%, SD[R] = 30%

Portfolio D: E[R] = 15%, SD[R] = 45%

Which portfolios are inefficient?

Question

An investor observes the following portfolios in the portfolio frontier:

Portfolio A: E[R] = 8%, SD[R] = 45%

Portfolio B: E[R] = 9%, SD[R] = 30%

Portfolio C: E[R] = 10%, SD[R] = 30%

Portfolio D: E[R] = 15%, SD[R] = 45%

Which portfolios are inefficient?

BlackTom AI · Accepted Answer

We start by comparing the portfolios on the frontier in terms of risk (SD) and expected return (E[R]). A portfolio is inefficient if there exists another portfolio that has at most the same risk and at least the same return, with at least one of these being strict.

Option A: Portfolio A has E[R] = 8% and SD = 45%. Portfolio B offers E[R] = 9% with SD = 30%. Since B delivers a higher return and uses significantly less risk than A, A is strictly dominated by B. Therefore, A is inefficient.

Option B: Portfolio B has E[R] = 9% and SD = 30%. Portfolio C has E[R] = 10% and the same SD = 30%. C offers the same risk but a higher return, so B is strictly dominated by C. Thus, B is inefficient.

Option C: Portfolio C has E[R] = 10% and SD = 30%. There exists Portfolio D with E[R] = 15% but a higher SD = 45%. You cannot say C is dominated by D since D carries more risk, and while D has higher return, it does not provide the same or lower risk with at least as much return. However, compare C with A: A has higher risk (45%) and lower return (8%), so A does not dominate C. Since we already found B dominated by C, C remains efficient in the sense of not being dominated by any portfolio with lower or equal risk and higher or equal return. So C is not inefficient on the frontier.

Option D: Portfolio D has E[R] = 15% and SD = 45%. Compare with A: A has 8% at 45% risk; D offers higher return at the same risk, so A is dominated by D. That suggests nothing about D being inefficient; it is capable of dominating A. Since D does not have another portfolio with lower risk and at least the same return, D is not dominated and remains on the efficient frontier.

To summarize these relationships: A is dominated by B, which makes A inefficient. B is dominated by C, which makes B inefficient. C is not dominated by any portfolio with equal or lower risk and higher return, and D is not dominated either, though it dominates A. Among the given options, the portfolios identified as inefficient are A and B. The portfolio C remains non-dominated by any Pareto-lower-risk, higher-return alternative among the listed options, and D does not suffer from a clear dominating portfolio within the set.

An investor observes the following portfolios in the portfolio frontier: Portfolio A: E[R] = 8%, SD[R] = 45% Portfolio B: E[R] = 9%, SD[R] = 30% Portfolio C: E[R] = 10%, SD[R] = 30% Portfolio D: E[R] = 15%, SD[R] = 45% Which portfolios are inefficient?Multiple choice

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