Which statement is (are) false about resampled efficient frontier?

Question

BlackTom AI · Accepted Answer

Let’s break down each statement about the resampled efficient frontier and evaluate its merit based on typical properties of resampling approaches.

Option A: 'EF more stable than traditional MV.' This claim suggests that the resampled frontier (EF) yields a more stable set of efficient portfolios compared to the traditional mean-variance (MV) frontier. In many discussions, resampling (e.g., bootstrap-based frontier) is presented as a technique to reduce estimation error and smooth or stabilize the frontier across samples, which supports the idea that the resampled frontier can be more stable than the traditional MV frontier. However, stability can depend on the data and implementation details (sampling size, number of resamples, constraints). Overall, this is a plausible and commonly cited property, and it is often treated as true in many treatments of resampled frontiers.

Option B: 'Portfolios tend to be better diversified than s traditional MV.' Interpreting this as: resampled portfolios tend to exhibit better diversification than those from traditional MV, this claim is not universally guaranteed. Resampling can improve robustness, but it does not automatically guarantee superior diversification in every dataset or scenario; diversification depends on the covariance estimates, the asset pool, and the optimization setup. In practice, one cannot claim unequivocally that diversification is always better with resampling.

Option C: 'There is a theoretical support that a portfolio constructed through resampling should provide superior performance relative to another portfolio constructed through traditional mean variance analysis.' Here, the statement asserts a theoretical guarantee of superior performance due to resampling. In reality, resampling improves robustness to estimation error and can yield more stable or robust out-of-sample behavior, but it does not carry an unconditional theoretical guarantee of superior performance relative to a traditional MV-optimized portfolio. Hence this claim is overstated.

Option D: 'A and B.' This option asserts that both A and B are true. Given the uncertainty surrounding guaranteed enhanced diversification in B, combining it with A would incorrectly treat B as true. Since B is not universally valid, asserting both A and B together is not correct.

Option E: 'B and C.' This option asserts that both B and C are false (i.e., they are the false statements). If B is not guaranteed to be better diversification and C is not guaranteed to provide superior performance, then labeling both as false aligns with a cautious interpretation of resampling results.

Option F: 'All statements above.' Since not every statement is universally true (for example, B is not guaranteed across contexts, and C is not universally supported by theory), claiming that all statements are true would be incorrect.

In summary, the reasoning shows that several statements have caveats or limitations, particularly regarding universal claims about diversification and theoretical guarantees. The assessment that B and C are not reliably true aligns with a careful, nuanced reading, and therefore selecting the option that identifies B and C as false reflects those nuances. Note: careful statistics texts may discuss nuances and conditions under which these statements hold, so always consider the specific context and methodology used in any resampling approach.

BU.232.750.51.FA25 Final Exam Fall 2025- Requires Respondus LockDown Browser

Which statement is (are) false about resampled efficient frontier?

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