Title page
Contents
Abstract 2
Non-technical summary 3
1. Introduction 4
1.1. Related literature 5
2. Balance sheet construction and model setup 7
3. A clearing problem for depositor runs 10
4. Case studies based on Silicon Valley Bank 12
4.1. Balance sheet dynamics of SVB 12
4.2. Drivers of bank runs and policy implications 13
5. On the balance between HtM and AfS 15
5.1. Maximising the HtM designation subject to price shocks 16
5.2. Implications for SVB's implied risk tolerance 21
6. Conclusions 22
Appendix 23
A. Proofs of main results 23
B. Additional Sensitivity Analysis 27
References 28
Table 1. Balance sheet evolution of the SVB 13
Figure 1. Stylized book and balance sheet for the bank subject to withdrawal risks where held to maturity assets need not be sold 8
Figure 2. The figure shows equilibrium withdrawal of funding (in USD billion) from SVB for balance sheets observed between Q1 2020 and Q4 2022 and for... 16
Figure 3/Figure 7. Graphical depiction of the one-period model. Given the price shock, the bank suffers realised losses on the AfS assets, while the value of the HtM assets... 16
Figure 4/Figure 3. The figure shows equilibrium liquidation of securities by SVB (in USD billion) for balance sheets observed between Q1 2020 and Q4 2022 and for... 17
Figure 5/Figure 4. The figure shows equilibrium funding withdrawals from SVB (in USD billion) in a hypothetical scenario of unrealised losses in AfS and HtM portfolios... 18
Figure 6/Figure 5. The figure shows equilibrium funding withdrawals from SVB (in USD billion) in a hypothetical scenario of unrealised losses in AfS and HtM portfolios... 19
Figure 7/Figure 6. The figure shows equilibrium funding withdrawals from SVB (in USD billion) in a hypothetical scenario of unrealised losses in AfS and HtM portfolios... 20
Figure 8. The figure shows theoretically optimal HtM portfolios of SVB for maximum accepted leverage ratios of 7.5 (upper pane) and 6.5 (lower pane).... 21
Figure 9. Smallest value of λmax that, for a balance sheet of SVB with all securities held in the HtM portfolio (= s + h), implies no selling of securities in equilibrium 22
Figure 10. The figure shows equilibrium liquidation of assets (in USD billion) from SVB for balance sheets observed as of Q1 2022 for various calibrations of... 28
Figure 11. The figure shows equilibrium withdrawal of funding (in USD billion) from SVB for balance sheets observed between Q1 2020 and Q4 2022 and... 29