Compared to a traditional index-based portfolio, an index-based portfolio constructed by excluding meaningful sectors or industries in an index will most likely a lower:

Question

BlackTom AI · Accepted Answer

Excluding meaningful sectors reduces the level of diversification because you remove groups of holdings that lower portfolio concentration and idiosyncratic risk.

1. Relevant knowledge points and concepts
- Diversification: spreading investments across many sectors/industries reduces idiosyncratic (unsystematic) risk and portfolio variance.
- Tracking error: standard deviation of the difference between portfolio and benchmark returns; it rises with active deviations from the index.
- Fee structure: management fees and trading costs are determined by strategy complexity and manager, not directly by excluding sectors.

2. Step-by-step reasoning
- An index-based portfolio normally replicates the index’s sector weights, capturing the index’s broad exposure and diversification.
- If you construct an index-based portfolio that excludes one or more meaningful sectors, the portfolio no longer holds those sector exposures. The remaining holdings must be up-weighted or fewer securities held, increasing concentration.
- Increased concentration means fewer independent return sources and higher sensitivity to the remaining sector/stock-specific risks, so diversification falls.

3. Intermediate conceptual “calculation” steps (variance logic)
- Portfolio variance depends on weights, variances, and covariances: Var(Rp) = ΣiΣj wi wj Cov(Ri,Rj).
- Removing a sector alters weights w_i and reduces the number of terms that diversify covariance effects, typically increasing Var(Rp) for a given risk profile.
- Tracking error, TE = sqrt(Var(Rp − Rb)). Excluding sectors creates systematic deviations from the benchmark (active bets), so Var(Rp − Rb) increases and TE typically rises, not falls.

4. Why the correct answer is correct
- Removing sectors removes diversification benefits (fewer independent exposures and greater concentration risk). Therefore the portfolio will most likely have a lower level of diversification.

5. Why the other options are incorrect
- Tracking error: excluding sectors increases differences from the benchmark and thus generally increases tracking error rather than lowers it.
- Fee structure: fees depend on provider, management style, and trading; exclusion of sectors does not inherently lower fees and can increase trading or management complexity, so you cannot conclude fees will be lower.

6. Conclusion
The portfolio constructed by excluding meaningful sectors will most likely have a lower level of diversification, which matches the provided answer.

Compared to a traditional index-based portfolio, an index-based portfolio constructed by excluding meaningful sectors or industries in an index will most likely a lower: 单项选择题

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