Diversification Can Control Probability of Default or Risk, but Not Both
Bibliographic record
Abstract
One of the controversies of diversification is that it may not be beneficial to banks, as it tends to increase systemic risk. Recent theoretical and empirical work have addressed this problem. We argue, from a theoretical perspective, that this controversy ultimately depends on how risk is assessed or measured. In particular, we observe that when one talks about random losses (risk) there are two intertwined approaches. On the one hand, one can fix the loss level and ask with what probability does that occur. On the other, one can fix a confidence level (or probability of loss) and ask, for example, what is the smallest loss with that probability. In a banking system, a systemic crisis occurs when all banks default simultaneously. Using the theoretical work of Wagner, where he proposed a simple model of a banking system in which a systemic crisis increases with diversification, we extend his analysis to show that if one allows for short positions; then the probability of default decreases, but the risk, measured by the value at risk (a non-coherent risk measure) increases. This brings up an interesting methodological question for risk management: Should we consider the probability of a given (acceptable) loss or, should we consider the minimum loss with an acceptable probability? We show that, within Wagner’s model and depending on which question is asked, a different answer can be obtained. This, in turn, lead us to discuss some implications of these results for risk managers and regulators.
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 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 | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".