An Efficient Optimization Approach for a Cardinality-Constrained Index Tracking Problem
Bibliographic record
Abstract
In the practical business environment, portfolio managers often face business-driven requirements that limit the number of constituents in their tracking portfolio. A natural index tracking model is thus to minimize a tracking error measure while enforcing an upper bound on the number of assets in the portfolio. In this paper we consider such a cardinality-constrained index tracking model. In particular, we propose an efficient nonmonotone projected gradient (NPG) method for solving this problem. At each iteration, this method usually solves several projected gradient subproblems. We show that each subproblem has a closed-form solution, which can be computed in linear time. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the NPG method is a local minimizer of the cardinality-constrained index tracking problem. We also conduct empirical tests to compare our method with the hybrid evolutionary algorithm and the hybrid half thresholding algorithm \cite{L1/2} for index tracking. The computational results demonstrate that our approach generally produces sparse portfolios with smaller out-of-sample tracking error and higher consistency between in-sample and out-of-sample tracking errors. Moreover, our method outperforms the other two approaches in terms of speed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".