Portfolio performance under benchmarking relative loss and portfolio insurance: From omega ratio to loss aversion
Bibliographic record
Abstract
Abstract We study an optimal investment problem under a joint limited expected relative loss and portfolio insurance constraint with a general random benchmark. By making use of a static Lagrangian method in a complete market setting, the optimal wealth and investment strategy can be fully determined along with the existence and uniqueness of the Lagrangian multipliers. Our numerical demonstration for various commonly used random benchmarks shows a trade-off between the portfolio outperformance and underperformance relative to the benchmark, which may not be captured by the widely used Omega ratio and its utility-transformed version, reflecting the impact of the benchmarking loss constraint. Furthermore, we develop a new portfolio performance measurement indicator that incorporates the agent’s utility loss aversion relative to the benchmark via solving an equivalent optimal asset allocation problem with a benchmark-reference-based preference. We show that the expected utility performance is well depicted by looking at this new portfolio performance ratio, suggesting a more suitable portfolio performance measurement under a limited loss constraint relative to a possibly random benchmark.
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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 | 0.006 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".