BIS国际清算银行-Contagion-Accounting_41页_1mb

Contagion Accounting: A Stress-Testing Framework for the Banking Sector

Core Content

This paper introduces a simple and tractable accounting-based stress-testing framework to assess loss dynamics in the banking sector, particularly in the context of leverage targeting. The framework accounts for both direct interbank exposures and indirect contagion through overlapping portfolios and fire sales. The key focus is on how price dynamics from fire sales amplify the initial shock to the banking system.

Main Viewpoints

• Contagion in the banking sector can occur through two main channels:

  1. Direct interbank exposures, where banks are directly affected by the financial health of their counterparties.
  2. Indirect contagion via overlapping portfolios, where banks hold similar assets and a shock to one asset can lead to simultaneous losses across multiple banks.

• Fire sales play a crucial role in amplifying losses. They introduce price dislocations that affect not only the banks directly holding the asset but also those indirectly connected through overlapping portfolios.

• Leverage targeting is a key assumption in the model. Banks aim to restore their leverage ratios after a shock by selling assets, rather than raising equity.

• Empirical evidence shows that direct interbank contagion has a negligible effect on overall system losses, while fire sales and overlapping portfolios contribute significantly to the total loss.

Key Information

1. Framework Overview

• The model is built on a balance sheet representation of the banking system and incorporates interbank exposures and overlapping portfolios.
• The framework is flexible and can be adapted to real data, including securities-level data.
• The model is iterative, with the ability to trace multiple rounds of contagion and amplification effects.

2. Mathematical Representation

• The basic balance sheet equation is:

$$
\mathbf{e} + \mathbf{d} + \mathbf{X'} \mathbf{i} = \mathbf{X} \mathbf{i} + \mathbf{l} \tag{1}
$$

• This is rewritten as:

$$
\mathbf{q} = \mathbf{B l} \tag{3}
$$

Where $\mathbf{B}$ is the Leontief inverse, representing the direct and indirect connections between banks.

• The shock transmission process is decomposed as:

$$
\Delta \mathbf{q} = \Delta \mathbf{l} + \mathbf{A} \Delta \mathbf{l} + \mathbf{A A} \Delta \mathbf{l} + \dots \tag{7}
$$

• The introduction of prices and fire sales modifies the framework to:

$$
\Delta \mathbf{q} = \mathbf{W} \hat{\mathbf{h}} \Delta \mathbf{p} + \mathbf{A} \mathbf{W} \hat{\mathbf{h}} \Delta \mathbf{p} + \mathbf{A A} \mathbf{W} \hat{\mathbf{h}} \Delta \mathbf{p} + \dots \tag{13}
$$

• The price impact matrix $\hat{\Theta}$ is crucial in modeling the effect of fire sales on asset prices, and thus on the total losses of the banking system.

3. Empirical Application

• The framework is applied to three granular ECB datasets for 26 large euro area banks.
• 5% shock to the price of assets in the trading book leads to:
  • An initial loss of 30% of system equity.
  • An additional loss of 1.3% due to fire sales spillovers.
• Direct interbank contagion is found to be negligible, and the majority of losses stem from common exposures and fire sales.
• Fire sales significantly contribute to systemic risk, as they trigger price dislocations and amplify losses across the network.

4. Assumptions in the Fire Sales Model

• Assumption 1: Banks target leverage.
• Assumption 2: Banks sell assets to restore leverage, not raise equity.
• Assumption 3: Banks sell assets proportionally to their initial holdings.
• Assumption 4: Price impact is proportional to the amount of assets sold.
• Assumption 5: Banks stop selling after the first round of fire sales, as further rounds provide minimal additional insights.

Conclusion

The framework highlights the importance of accurately modeling fire sales and overlapping portfolios in stress-testing. It provides a systematic approach to analyzing contagion effects in the banking sector and emphasizes that indirect contagion via fire sales is a dominant factor in systemic losses. The model is data-driven and can be applied to real-world financial data, offering a practical tool for regulators and financial institutions to assess systemic risk and contagion dynamics.