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Summary of Incorporating Funding Costs in a Top-Down Stress Test

Core Content

Danmarks Nationalbank has introduced funding cost increases into its top-down stress test framework, which assesses the resilience of 16 banks under three scenarios: baseline, mild, and adverse, over a three-year period. The stress test includes two capital thresholds: "red" (total capital > 8%) and "yellow" (total capital > 8% + buffers). Until recently, funding costs were not considered in these assessments, but this has changed to provide a more comprehensive view of banks' solvency and financial stability.

Main Challenges

One of the key challenges in incorporating funding costs into solvency assessments is the non-linear relationship between a bank's solvency and its funding costs. Aymanns et al. (2016) found that a 1 percentage point drop in the capital ratio leads to a 2 bps increase in average funding costs and a 4 bps increase in wholesale funding costs. However, the magnitudes of these changes are relatively small compared to the differences in funding costs between banks.

Another challenge is that riskier banks may have higher capital ratios as a precautionary measure, which may not be fully reflected in risk weights. This can lead to an underestimation of funding costs, as the Merton model may not be directly applicable to banks due to their unique asset structure and regulatory environment.

Our Approach

Danmarks Nationalbank has developed an adapted version of the distance-to-default (DD) measure that incorporates qualitative features from other models while simplifying the process. The approach avoids the need for numerical estimation of asset values and volatilities, making it more practical for implementation. The adapted DD measure is based on the following steps:

1. Intuitive Definition of DD: $ DD = \frac{E}{\sigma_V V} $, where $ E $ is equity, $ V $ is the value of assets, and $ \sigma_V $ is the volatility of assets.
2. Approximation of V: Use book value of debt to approximate $ V \approx E + D_{book} $.
3. Adjustment for Risk: Incorporate the relationship between asset volatility and equity volatility, using $ \sigma_V = \frac{E}{V} \sigma_E $.
4. Smoothed Measure: Combine the smoothed measure with the "naive" version to avoid underestimating asset volatility.
5. Estimation of Funding Costs: Use regression analysis to estimate the relationship between funding costs and DD, taking into account deposit share as a factor.

Practical Implementation

The adapted DD measure is used in a five-step process to incorporate funding cost increases into the stress test:

1. Calculate the adapted DD from market data.
2. Run a stress test without considering funding cost increases.
3. Measure the loss in market value by comparing cumulative discounted profits in baseline and stress scenarios.
4. Update the DD measure based on the loss in market value.
5. Calculate the change in funding costs based on the updated DD.

This method is flexible and can be extended to include second- and third-order effects.

Effects in Stress Test

The inclusion of funding cost stress has an amplifying effect on the losses experienced by banks, particularly those already under financial strain. The effects vary significantly across institutions, with systemic and non-systemic banks showing different responses. In a severe recession scenario, banks with excess capital adequacy may see their capital position eroded by higher funding costs, while those with capital shortfalls may face even greater losses.

Key Findings

• The adapted DD measure performs as well as other models in explaining CDS premia.
• Funding cost increases are calculated based on changes in the DD measure.
• The method is low-cost, easy to implement, and requires minimal data.
• It incorporates market information and allows for flexibility in modeling.

Caveats and Comments

• The method assumes that banks can access funding in time, thus ignoring liquidity risks.
• Special handling is required for non-traded banks.
• The analysis is based on financial statements from the first half of 2016 and may need updating with current data.

Conclusion

Danmarks Nationalbank has successfully integrated funding cost increases into its top-down stress test framework, enhancing the accuracy of its financial stability assessments. This approach provides a practical and flexible method for incorporating market-based risk measures into stress testing, while acknowledging the limitations of ignoring liquidity risks.