Assuming answer choices are not numerical, you should always be able to eyeball the right answer, correct, i.e., without doing either attribution calculation?
Want to confirm it’s always true that …
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If portfolio (i) underweights asset X but (ii) performs equal to or better than benchmark’s returns in asset X, then attribution is necessarily security selection?
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If portfolio (i) overweights asset X and (ii) outperforms benchmark’s returns in asset X, then … what do we know for sure? At least some of the outperformance is due to asset allocations? Would you have to do calculations to know for sure is any is attributable to security selection?
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The outperformance must be a result of security selection.
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It depends on the amount of active weight, the benchmark’s return on that particular asset, and your active return on that asset. For example, let’s say your active return on an equity asset allocation is 6% (i.e., the benchmark’s equity allocation generated 30% return, while you generated 36%). 6% is the active return that needs to be attributed between security selection and/or asset allocation. Let’s say your active weights are 10% (you allocated 60% to equities while the benchmark only holds 50%). We know that your active weight * benchmark return (i.e., 10% * 30% = 3%) is attributable to asset allocation. Meaning assuming you held the exact same securities as the benchmark, and you held 10% more equities in your portfolio than the benchmark did, your active return should be 3% over the benchmark (i.e., 33% vs 30%)… but that wasn’t the case, you generated 36%, an extra 3% that isn’t explained by simply holding more equities than the benchmark. So the 3% is attributable to the securities you selected within the equity allocation.
If you’re given returns/weights you might be able to do that calculation in your head, but I don’t know if there’s another way to answer that question without considering the numbers, except for the example you gave in #1 that it couldn’t possibly be because of asset allocation as you’re underweight.
Hope that helps!