Proper Conditioning for Coherent VaR in Portfolio Management
Why this work is in the frame
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Bibliographic record
Abstract
Value at risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999, Coherent measures of risk, Math. Finance 9(3) 203–228), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, eliciting proper conditioning information may restore VaR rationale for decentralized risk management. The argument is threefold. First, since individual traders are hired because they possess a richer information on their specific market segment than senior management, they just have to follow consistently the prudential targets set by senior management to ensure that decentralized VaR control will work in a coherent way. The intuition is that if one could build a fictitious conditioning information set merging all individual pieces of information, it would be rich enough to restore VaR subadditivity. Second, in this decentralization context, we show that if senior management has access ex post to the portfolio shares of the individual traders, it amounts to recovering some of their private information. These shares can be used to improve backtesting to check that the prudential targets have been enforced by the traders. Finally, we stress that tail thickness required to violate subadditivity, even for small probabilities, remains an extreme situation because it corresponds to such poor conditioning information that expected loss appears to be infinite. We then conclude that lack of coherence of decentralized VaR management, that is VaR nonsubadditivity at the richest level of information, should be an exception rather than a rule.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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 it