The Effect of Constraint on Portfolio Construction Using the Index Model
Bibliographic record
Abstract
This study examines the performance and characteristics of the Single Index Model under different constraint regimes. Utilizing the S&P 500 index and 21 of its constituent stocks across five sectors, we construct and compare optimal portfolios and efficient frontiers for an unconstrained scenario and a "box" constraint scenario where the absolute weight of any asset is limited to 100%. The analysis confirms the theoretical prediction that the unconstrained model generates an efficient frontier that dominates the constrained one, offering a higher maximum Sharpe ratio (1.537 vs. 1.519) and a lower minimum variance (11.48% vs. 12.03%). The unconstrained model achieves this through more concentrated allocations, including significant short positions and leverage, which are restricted under the box constraint. However, the constraint effectively eliminates impractical, high-risk portfolios that rely on excessive short selling, resulting in a more parabolic and realistic efficient frontier. The findings validate core portfolio theories, demonstrating that while constraints limit optimization potential and reduce efficiency, they also curb firm-specific risk and produce more implementable portfolio strategies.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".