## Centrality-based Capital Allocations

_IMF Working Papers, December 24, 2014_

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## Bibliographic details
- Authors: Adrian Alter, Ben Craig, Peter Raupach
- Published: December 24, 2014
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781498315548.001

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### Summary and research question
- Objective: Analyze the effect of capital rules on a banking system connected through correlated credit exposures and interbank lending.
- Approach: Design capital rules that combine individual bank characteristics and interconnectivity measures of interbank lending to minimize a measure of system‑wide losses.
- Data: Detailed German Credit Register used for estimation.
- Authors and date: Adrian Alter, Ben Craig, Peter Raupach, December 24, 2014.

### Key findings
- Capital rules based on eigenvectors dominate any other centrality measure evaluated.
- Closeness centrality is the second‑best performing centrality measure.
- Compared to the baseline case, capital reallocation based on the Adjacency Eigenvector saves about 15% in system losses as measured by expected bankruptcy costs.

### Methodology and model features
- The analysis models a banking system with:
  - Correlated credit exposures across banks.
  - Interbank lending links that generate interconnectivity.
- Capital allocation rules incorporate:
  - Individual bank characteristics (e.g., bank PDs, bank equity holder implications).
  - Network centrality measures derived from interbank exposure matrices (including eigenvector and closeness measures).
- Objective function: Minimize a system‑wide loss metric (expected bankruptcy costs).

### Policy implications and recommendations
- Incorporating network centrality, particularly eigenvector centrality from the interbank adjacency matrix, into capital allocation rules can materially reduce system losses.
- Regulatory capital reallocation that weights banks by their position in the interbank exposure network (Adjacency Eigenvector) is a superior policy lever relative to allocations that ignore network centrality or rely on weaker centrality measures.
- Policymakers should consider network‑aware capital requirements as a tool to mitigate systemic risk arising from interconnected credit exposures and interbank markets.

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/31/centrality-based-capital-allocations-42560_