2010年-BIS国际清算银行_Attributing_systemic_risk_to_individual_institutions_34页_780kb

Summary of BIS Working Paper No 308: Attributing systemic risk to individual institutions

Core Content

This BIS Working Paper introduces a methodological framework for attributing systemic risk to individual financial institutions. It emphasizes the need for a macroprudential approach to financial stability, especially in light of the recent financial crisis, where the failure of individual institutions had widespread systemic consequences. The paper proposes a general methodology based on the Shapley value, a concept from game theory, to fairly allocate systemic risk among institutions.

The Shapley value is defined as the average marginal contribution of an institution to the total risk of the system, across all possible subsets of institutions. It ensures that the sum of the systemic importance measures of individual institutions equals the total systemic risk, and it is flexible enough to accommodate various risk measures and models. The methodology also allows for the handling of model and parameter uncertainty by combining information from different risk models.

The paper demonstrates how the Shapley value can be used to assess the impact of different drivers on systemic risk, including the size of institutions, their individual risk profiles, and their exposure to common risk factors. It also explores the implications of this methodology for prudential policy, such as the calibration of macroprudential capital rules.

Main Points

• Systemic importance is defined as the contribution of an individual institution to the overall systemic risk.

• The Shapley value is introduced as a fair and efficient method to allocate systemic risk among institutions.

• The Shapley value methodology has the following desirable properties:

  • Additivity: The sum of the Shapley values of all institutions equals the total systemic risk.
  • Symmetry: The order of institutions does not affect the Shapley value.
  • Dummy axiom: Institutions that do not contribute to systemic risk have a Shapley value of zero.
  • Linearity: The Shapley value is linear with respect to the characteristic function, which allows for robustness to model uncertainty.

• Key drivers of systemic risk include:

  • The size of institutions.
  • The probability of default (PD) of each institution.
  • The exposure to common risk factors.

• The paper highlights that:

  • Size alone does not fully determine systemic importance; the ratio of systemic importance between institutions is greater than the ratio of their sizes when PDs and common factor exposures are controlled for.
  • ES (expected shortfall) is a more comprehensive measure of systemic risk than VaR (value-at-risk), as it accounts for the severity of losses in the tail of the distribution.
  • VaR is less noisy in estimation compared to ES, but ES is more intuitive for capturing systemic risk.

Policy Applications

• The Shapley value methodology can be used to:

  • Calibrate macroprudential capital rules, ensuring that capital requirements reflect the systemic importance of institutions.
  • Design fair and efficient risk allocation mechanisms, particularly in the context of systemic risk mitigation and supervisory interventions.
  • Derive actuarially fair premia for systemic risk insurance, by focusing on the expected share of an institution in the cost of systemic events.

• The paper considers three stylised policy interventions:

  1. Equalising individual riskiness while maintaining the same level of systemic risk.
  2. Equalising systemic importance while maintaining the same level of systemic risk.
  3. Minimising aggregate capital holdings given a target level of systemic risk.

  It shows that equalising systemic importance leads to lower aggregate capital compared to equalising individual riskiness, and that the capital charges are close to the constrained minimum of aggregate capital.

Key Findings

• The Shapley value is a general and robust methodology for attributing systemic risk to individual institutions.
• Systemic importance is not solely determined by size; it is influenced by default probability and exposure to common risk factors.
• The relationship between size and systemic importance is non-linear, with systemic importance increasing faster than size.
• The methodology accommodates uncertainty, making it suitable for use in real-world applications where model assumptions may vary.
• ES is a more appropriate measure of systemic risk than VaR, but VaR is more robust to estimation noise.

Conclusion

The paper concludes that the Shapley value approach provides a methodologically sound and operationally useful framework for understanding and attributing systemic risk. It supports the development of macroprudential policies that can better address the risks posed by systemic events, particularly by incorporating the interconnectedness of financial institutions and their contribution to systemic risk.

References

• Acharya, V. V., Richardson, M. (2009)
• Adrian, T., Brunnermeier, M. K. (2008)
• BIS (2008, 2009)
• Geluk, et al. (2009)
• Goodhart, C., Segoviano, M. (2008)
• Gordy, G. B., Lütkebohrmert, T. (2007)
• Heyde, C. C., et al. (2006)
• Kuritzkes, A., et al. (2005)
• Kurth, A., Tasche, D. (2003)
• Koyluoglu, H., Stoker, J. M. (2002)
• Martin, A., Wilde, D. (2002)
• Praschnik, A., et al. (2001)
• IMF (2008, 2009)

Appendix Summary

The paper includes an appendix that formally derives the impact of size on systemic importance using the Shapley value methodology. It shows that the Shapley value is a function of the characteristic function of the system, which is defined for all possible subsystems of institutions. The characteristic function is used to compute the marginal contribution of each institution to the total systemic risk. The results demonstrate the non-linear relationship between size and systemic importance, which is derived in the context of expected shortfall (ES).

The Shapley value is also shown to be linear with respect to the characteristic function, which allows for the combination of different risk models and the derivation of robust systemic importance measures.