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 need to evaluate each portfolio in the frontier to see if there is any other portfolio that provides a higher return for the same or lower risk, or a lower risk with the same or higher return.

Option A: Portfolio A = 8% return, 45% risk. This is unattractive because there are portfolios with higher return and lower risk. For example, Portfolio B offers 9% at 30% risk, and Portfolio C offers 10% at 30% risk. In both cases, A is worse on both dimensions (higher risk and lower return) than these portfolios, so A is inefficient.

Option B: Portfolio B = 9% return, 30% risk. Here, Portfolio C at the same risk level (30%) provides a higher return of 10%. Since C dominates B on risk-return (same risk, higher return), B is inefficient. The same logic applies when comparing B to any combination that yields a higher return at or below 30% risk—B fails the efficiency test because a portfolio with equal or lower risk gives a greater return.

Option C: Portfolio C = 10% return, 30% risk. There is no portfolio among A, B, or D that offers at most 30% risk with a return of 10% or more; A and B have lower returns for the same risk, and D has higher risk (45%) with a much higher return. But for dominance, we look for equal or lower risk with greater or equal return; since neither A nor B achieves 10% at 30% risk, and D’s higher return comes with higher risk, C is not dominated and is on the efficient frontier at its risk level. Therefore, C is efficient.

Option D: Portfolio D = 15% return, 45% risk. To deem D inefficient, we would need a portfolio with risk ≤ 45% and return ≥ 15%, or risk < 45% with return ≥ 15%. Among the given portfolios, none provides 15% or more return at risk ≤ 45%, and mixing the available portfolios does not produce a portfolio that dominates D with the information provided. Thus D is not dominated by any single portfolio here and is considered efficient on the frontier.

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?多项选择题

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