## 2. Pay-Off Structure with Risky Deposits

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---

### I. Introduction
- Focus: determinants and effects of conflict among claimants after bankruptcy or resolution for banks with multiple financing sources.
- Core argument:
  - Contested claims raise bankruptcy/resolution costs and, via funding costs, raise the probability of bankruptcy.
  - Pre-assignment of rights (collateralization, preferred creditor status) can reduce contest costs but generate limits/costs.
- Scope and assumptions:
  - Emphasis on solvency (not liquidity); simple depositor preference considered.
  - “Collateralized lending” includes repurchase operations, covered bonds, securitized loans with retained exposure.
  - Time horizon: one funding period and one distribution period.

### II. Background

#### A. Bankruptcy Costs — empirical evidence and characteristics
- Typical empirical magnitudes and examples:
  - Nonfinancial firms (well-developed frameworks): direct costs and loss of value totally 10 to 30 percent of gross assets (typical).
  - U.S. bond defaults: average losses about 60 percent of face value; secured senior debt losing about 45 percent of its value in default.
  - Typical high-income country insolvency resolution (World Bank, 2013): direct costs of 9 percent of the estate, takes 1.7 years, and achieves a 70 percent recovery rate.
  - FDIC experience resolving mostly smaller banks: direct administrative costs typically about 7 percent of pre-resolution assets; losses on assets about another 18 percent.
  - KAMCO example (post-1997 Korea): purchased NPLs face value won 110 billion; operating expenses amounted to about 20 percent of this stock, of which direct administrative and selling expenses made up 4.2 percentage points.
  - Lehman Brothers (start September 2008 to end–2012): fees to receivers/administrators reportedly US$2 billion against nominal US$639 billion of assets at bankruptcy; 67,000 payment demands for US$1.2 trillion were received; average creditor expected to ultimately receive 18 percent of face value; process likely to take until 2016.
- Key mechanisms increasing costs:
  - Litigation, multi-jurisdictional insolvency proceedings, and uncertainty over claims.
  - Lobbying/contending efforts by claimants; drawn-out “war of attrition” dynamics.
  - Negative externalities from one claimant’s actions (delays, others’ litigation costs, asset deterioration).

#### B. Depositor Preference — roles, empirical evidence, and debate
- Legal adoption examples:
  - Depositor preference established by law in countries including the United States, Australia, China, Switzerland; European Council (June 2013) agreed to introduce tiered depositor preference into the EU bank resolution framework.
- Purposes and effects:
  - Enhances recoveries by depositors and the DGS; reduces contagion when DGS funded ex post; reduces runs by uninsured depositors; shifts monitoring incentives to non-preferred creditors.
  - In special resolution regimes (purchase and assumption), depositor preference facilitates transfer of deposits without splitting.
- Empirical findings (U.S. experience):
  - Introduction of depositor preference had little systemic effect on FDIC resolution-related costs or bank funding costs; evidence mixed and disentangling effects is difficult.
- Criticisms and counterarguments:
  - May be offset by creditors obtaining collateral or increased cost of unsecured financing.
  - Possible incentive for non-deposit creditors to “run” if depositors are preferred.
  - When no depositor preference, DGS must ensure other unsecured creditors are no worse off than depositors—difficult without delay.

#### C. Asset Encumbrance — concerns and dynamics
- Drivers of recent concern:
  - Greater reliance on collateralized refinancing (e.g., ECB operations), more covered bonds, regulatory incentives favoring secured funding (Basel III), and possible depositor preference extension.
- Principal concerns:
  - Encumbrance reduces assets available to unsecured creditors/DGS in resolution, potentially increasing LGD and pricing for unsecured funding.
  - If pricing of unsecured funding is not risk sensitive (e.g., insured deposits not priced to risk), moral hazard and undue risk-shifting may arise.
- Dynamic considerations:
  - Self-fulfilling expectations and multiple equilibria: low encumbrance → collateral not valuable; high encumbrance → creditors demand high yields or collateral.
  - Encumbrance affects ability to obtain funding in stress; banks with unencumbered eligible assets can obtain liquidity (including central bank refinancing).
- Policy implication:
  - Holdings of unencumbered eligible assets should be included in liquidity buffer measures; level of encumbrance can be symptomatic rather than causal.

### III. Bankruptcy Costs and Claimants’ Lobbying — stylized contest model
- Setup and payoffs:
  - Failed bank: residual assets R; total claims S, with claims s_i for i = 1,...,N and S > R.
  - Claimant i expends c_i on contesting claims; aggregate contest C = Σ c_i.
  - Contest technology g_i(.) with g_i′>0, g_i′′<0; claimant i payoff net:
    - g_i(c_i/C · s_i/S)·(s_i/S)·R − c_i (diminishing returns).
- First-order condition (small claimant takes aggregate as fixed):
  - g_i′(c_i/C · s_i/S) = C/R.  (equation (2))
- Symmetric case (equal claims and technologies):
  - C = g′(1)·R.  (equation (3)) with g(1) = 1 by assumption.
  - Each claimant receives R/N (1 − g′(1)).  (equation (4))
- Implications:
  - Contests destroy value proportional to residual assets; higher residual assets → more lobbying.
  - Drawn-out contest dynamics can create further asset deterioration.
  - Negative externalities: individual claimants do not internalize others’ costs nor asset deterioration, magnifying social bankruptcy costs.

### IV. Optimal Collateralization and Asset Encumbrance

#### A. Depositor preference and funding costs (simple model)
- Model primitives:
  - Return on bank investment q + r; q fixed parameter; r uniformly distributed on [0,1].
  - Balance sheet size normalized to unity; deposits d and market-based financing (1 − d).
  - Deposits pay interest i_d; market funding pays i_m when solvent; reservation safe return i_s.
  - Tractability assumption: bank always has enough assets to pay preferred depositors in full: q − i_d d > 0.
- Break-even return where bank insolvent:
  - r_b = −(q − i_d d − i_m (1 − d)).  (equation (5))
- Bankruptcy costs for unsecured claimants:
  - c_1 (q + r − i_d d) with c_1 ∈ (0,1).
- No-arbitrage / market-clearing for unsecured funding:
  - i_s (1 − d) = ∫_{0}^{r_b} i_m (1 − d) dr + ∫_{r_b}^{1} [q + r − i_d d − c_1 (q + r − i_d d)] dr.  (equation (6))
  - Closed form: i_s (1 − d) = (1 − r_b) i_m (1 − d) + r_b (1 − c_1) (q − i_d d) + 1/2 (1 − c_1) r_b^2.  (equation (6′))
- Solved break-even return:
  - r_b = [1 − c_1 (q − i_d d) − sqrt{[1 − c_1 (q − i_d d)]^2 + 2 (1 + c_1) (q − i_d d − i_s (1 − d))}] / (1 + c_1).  (equation (7))
- Comparative statics:
  - ∂r_b/∂q < 0.  (equation (8))
  - ∂r_b/∂c_1 > 0.  (equation (10))
  - ∂r_b/∂d ambiguous; if i_d = i_s then ∂r_b/∂d < 0 (more preferred deposits reduce bankruptcy probability).  (equation (11))
- Bank value and welfare:
  - V = ∫_{r_b}^{1} (q + r − i_d d − i_m (1 − d)) dr = 1/2 (1 − r_b)^2.  (equation (12))
  - W = V + i_d d + i_s (1 − d).  (equation (13))
- When interest rates invariant (extreme case), welfare expression:
  - W = V + i_d d + (1 − r_b) i_m (1 − d) + r_b (1 − c_1) (q − i_d d) + 1/2 (1 − c_1) r_b^2.  (equation (15))
  - Then ∂W/∂d = −c_1 (1 − d) i_m (i_d − i_m) + c_1 i_d r_b.  (equation (16))
- Key intuition:
  - Depositor preference reduces expected contestable residual assets, lowering bankruptcy costs and funding costs; benefits accrue to bank owners and possibly to other creditors through reduced contest intensity.
  - Effectiveness depends on risk-sensitive pricing of funding; if suppliers ignore LGD reductions, benefits may not materialize.

#### B. Funding costs with collateralization
- Collateralized financing:
  - Bank can obtain collateralized financing share e at yield i_e, with collateralization cost f(e), f′>0, f′′>0.
- Break-even return:
  - r_b = −(q − i_d d − i_e e − i_m (1 − d − e) − f(e)).  (equation (18))
- Bank value:
  - V = 1/2 (1 − r_b)^2.
- First-order condition for optimal e (dV/de = 0) leads to:
  - f′ = [(1 + c_1) (i_s − i_e) + c_1 i_e r_b] / [(1 + c_1) (1 − r_b)].  (equation (21))
- Interpretation:
  - f′ trades off marginal cost of making assets eligible vs. market segmentation advantage (i_s − i_e) and reduction in bankruptcy costs (term c_1 i_e r_b / [(1 + c_1)(1 − r_b)]).
  - Collateralization and statutory depositor preference act as partial substitutes from the bank’s perspective.
- Interaction with deposit share d:
  - de/dd = c_1 (f′ + i_e) f′′^−1 [1 + c_1 (1 + r_b)] ∂r_b/∂d (formula structure).  (equation (22))
  - Since ∂r_b/∂d < 0 in many cases, higher d tends to reduce bank’s incentive to collateralize (substitutability).

#### C. Limits of preferred depositor status and collateralized borrowing
- Feasibility condition for full bankruptcy remoteness:
  - q > i_d d + i_e e + f(e).  (text condition)
- If very bad returns:
  - If q + r < i_d d + i_e e − f(e), preferred depositors and secured creditors must contest pari passu with others → many contestants for few residual assets → possibly large bankruptcy costs.
- Depositor shortfall and contest among depositors:
  - Define r_d = −q + i_d d (rate below which depositors cannot be fully met).  (equation (23))
  - If r < r_d, depositors contest among themselves with marginal bankruptcy costs c_2; other claimants drop out.
- No-arbitrage conditions with risky deposits:
  - Depositor condition: i_s d = ∫_{0}^{r_d} i_d d dr + ∫_{r_d}^{1} [(q + r) − c_2 (q + r)] dr.  (equation (24))
  - Unsecured condition: i_s (1 − d) = ∫_{0}^{r_b} i_m (1 − d) dr + ∫_{r_b}^{1} [q + r − i_d d − c_1 (q + r − i_d d)] dr with integration limits r_b, r_d.  (equation (25))
- Break-even yield for depositors:
  - r_d = [1 − c_2 q − sqrt{[1 − c_2 q]^2 + 2 (1 + c_2) (q − i_s d)}] / (1 + c_2).  (equation (26))
  - ∂r_d/∂d > 0 (increasing deposits increases probability residual assets insufficient).  (equation (27))
- Effect of increasing deposit share d on r_b:
  - dr_b/dd given by a complex expression (equation (28) and expansion (28′)) showing trade-off between increased contest costs from preferred depositors (if they become short) and reduced contest costs among unsecured creditors.
- Optimal deposit share:
  - The deposit share d that minimizes probability of failure depends on relative magnitudes of c_1, c_2, i_m, i_d (implicit condition structure in text).

### V. Conclusions and Next Steps — policy implications and research agenda
- Main conclusions:
  - Conflicts among claimants add substantially to bankruptcy/resolution costs; these prospective costs influence optimal financing composition and motivate making some claims “bankruptcy remote” via statute (depositor preference) or private contract (collateralization).
  - Asset encumbrance can be desirable when it reduces expected bankruptcy contest costs and thus overall funding costs and the probability of distress; full benefits require risk-sensitive pricing of funding and legal certainty of enforcement.
  - Collateralization and depositor preference are near substitutes from the bank’s perspective; collateralization can be increased at the bank’s initiative at increasing marginal cost.
  - If preferred/collateralized claims cannot be met ex post, conflict may intensify and the supposed benefits reverse; regulatory/supervisory frameworks should account for funding composition and aim for prompt intervention.
- Operational policy implications:
  - Supervisory authorities should consider limits on total asset encumbrance (preferred deposits + collateralized borrowing) relative to likely minimum residual assets.
  - Early corrective action raises q (floor on returns) and expands scope for collateralization and depositor preference to be effective.
  - Legal certainty (e.g., dedicated covered bond regimes) is crucial for achieving bankruptcy remoteness.
- Suggested avenues for further research:
  - Systematic empirical investigation of how bankruptcy costs depend on intensity of conflict over residual assets and who bears costs ex ante (market price reactions to regulatory innovations).
  - Reasons for limited transparency on bank asset encumbrance and whether regulation should require greater disclosure (noting confidentiality of central bank refinancing).
  - Implications of heterogeneity among creditors in litigating/lobbying ability and incentives; depositor preference may aggregate many weak atomistic depositors into a single dominant effective claimant.
  - Symmetries between statutory bail-in of unsecured creditors and depositor preference; similarities between CoCos (contingent capital) and collateralized credit.
  - Extension of framework to incorporate liquidity risk and interaction with solvency risk.

*IMF Working Paper — section "2. Pay-Off Structure with Risky Deposits" (text supplied).*

### 1. Pay-Off Structure with Safe Deposits ................................................................................

### 1. Pay-Off Structure with Safe Deposits

### Section reference
- Page: 14

*Source: _wp13172 - 1. Pay-Off Structure with Safe Deposits ................................................................................*

### 2. Pay-Off Structure with Risky Deposits................................................................................

### 2. Pay-Off Structure with Risky Deposits

### I. Introduction
- Focus: determinants and effects of conflict among claimants after bankruptcy or resolution, especially for banks with multiple financing sources.
- Core argument: contested claims raise bankruptcy/resolution costs and, via funding costs, raise the probability of bankruptcy. Pre-assignment of rights (collateralization, preferred creditor status) can reduce these costs but generate their own limits/costs.
- Scope: emphasis on solvency (not liquidity); simple depositor preference considered; “collateralized lending” includes repurchase operations, covered bonds, securitized loans with retained exposure.
- Time horizon: one funding period and one distribution period (solvency-focused).

### II. Background

#### A. Bankruptcy Costs — empirical evidence and characteristics
- Direct and indirect costs can be very high; examples and typical figures:
  - Nonfinancial firms (well-developed frameworks): direct costs and loss of value totally 10 to 30 percent of gross assets (typical).
  - U.S. bond defaults: average losses about 60 percent of face value; secured senior debt losing about 45 percent of its value in default.
  - Typical high-income country insolvency resolution (World Bank, 2013): direct costs of 9 percent of the estate, takes 1.7 years, and achieves a 70 percent recovery rate.
  - FDIC experience resolving mostly smaller banks: direct administrative costs typically about 7 percent of pre-resolution assets; losses on assets about another 18 percent.
  - KAMCO example (post-1997 Korea): purchased NPLs face value won 110 billion; operating expenses amounted to about 20 percent of this stock, of which direct administrative and selling expenses made up 4.2 percentage points.
  - Lehman Brothers (start September 2008 to end–2012): fees to receivers/administrators reportedly US$2 billion against nominal US$639 billion of assets at bankruptcy; 67,000 payment demands for US$1.2 trillion were received; average creditor expected to ultimately receive 18 percent of face value; process likely to take until 2016.
- Key mechanisms increasing costs:
  - Litigation, multi-jurisdictional insolvency proceedings, and uncertainty over claims.
  - Lobbying/contending efforts by claimants; drawn-out “war of attrition” dynamics.
  - Negative externalities from one claimant’s actions (delays, others’ litigation costs, asset deterioration).

#### B. Depositor Preference — roles, empirical evidence, and debate
- Depositor preference established by law in countries including the United States, Australia, China, Switzerland; European Council (June 2013) agreed to introduce tiered depositor preference into the EU bank resolution framework.
- Purposes and effects:
  - Enhances recoveries by depositors and the DGS; reduces contagion when DGS funded ex post; reduces runs by uninsured depositors; shifts monitoring incentives to non-preferred creditors.
  - In special resolution regimes (purchase and assumption), depositor preference facilitates transfer of deposits without splitting.
- Empirical findings (U.S. experience):
  - Introduction of depositor preference had little systemic effect on FDIC resolution-related costs or bank funding costs; mixed evidence on cost increases; disentangling effects is difficult.
- Criticisms and counterarguments:
  - May be offset by creditors obtaining collateral or increased cost of unsecured financing.
  - Possible incentive for non-deposit creditors to “run” if depositors are preferred.
  - When no depositor preference, DGS must ensure other unsecured creditors are no worse off than depositors—difficult without delay.

#### C. Asset Encumbrance — concerns and dynamics
- Recent increases in concern due to:
  - Greater reliance on collateralized refinancing (e.g., ECB operations), more covered bonds, regulatory incentives favoring secured funding (Basel III), and possible depositor preference extension.
- Principal concerns:
  - Encumbrance reduces assets available to unsecured creditors/DGS in resolution, potentially increasing LGD and pricing for unsecured funding.
  - If pricing of unsecured funding is not risk sensitive (e.g., insured deposits not priced to risk), moral hazard and undue risk-shifting may arise.
- Dynamic considerations:
  - Self-fulfilling expectations and multiple equilibria: low encumbrance → collateral not valuable; high encumbrance → creditors demand high yields or collateral.
  - Encumbrance affects ability to obtain funding in stress; banks with unencumbered eligible assets can obtain liquidity (including central bank refinancing).
- Policy implication: holdings of unencumbered eligible assets should be included in liquidity buffer measures; level of encumbrance can be symptomatic rather than causal.

### III. Bankruptcy Costs and Claimants’ Lobbying — stylized contest model
- Setup:
  - Failed bank: residual assets R; total claims S, with claims s_i for i = 1,...,N and S > R.
  - Claimant i expends c_i on contesting claims; aggregate contest C = Σ c_i.
  - Contest technology g_i(.) with g_i′>0, g_i′′<0; payoff net for i:
    - g_i(c_i/C · s_i/S)·(s_i/S)·R − c_i  (as represented in text; diminishing returns).
- First-order condition (claimant small, takes aggregate as fixed):
  - g_i′(c_i/C · s_i/S) = C/R.  (equation (2))
- Symmetric case (equal claims and technologies):
  - C = g′(1)·R.  (equation (3)) with g(1) = 1 by assumption.
  - Each claimant receives R/N (1 − g′(1)).  (equation (4))
- Implication: contests destroy value proportional to residual assets; higher residual assets → more lobbying; drawn-out time dimension can create war-of-attrition dynamics and further asset deterioration.
- Negative externalities: individual claimants do not internalize other claimants’ costs nor asset deterioration, magnifying social bankruptcy costs.

### IV. Optimal Collateralization and Asset Encumbrance

#### A. Depositor preference and funding costs (simple model)
- Setting:
  - Return on bank investment q + r; q fixed parameter; r uniformly distributed on [0,1].
  - Balance sheet size normalized to unity; deposits d and market-based financing (1 − d).
  - Deposits pay (one plus) interest i_d; market funding pays i_m when solvent; reservation safe return i_s.
  - Assumption for tractability: bank always has enough assets to pay preferred depositors in full: q − i_d d > 0.
- Break-even return r_b where bank insolvent:
  - r_b = −(q − i_d d − i_m (1 − d)).  (equation (5))
- Bankruptcy costs for unsecured claimants assumed linear in residual assets:
  - c_1 (q + r − i_d d) with c_1 ∈ (0,1).
- No-arbitrage / market-clearing condition for unsecured funding:
  - i_s (1 − d) = ∫_{0}^{r_b} i_m (1 − d) dr + ∫_{r_b}^{1} [q + r − i_d d − c_1 (q + r − i_d d)] dr.  (equation (6))
  - Closed form: i_s (1 − d) = (1 − r_b) i_m (1 − d) + r_b (1 − c_1) (q − i_d d) + 1/2 (1 − c_1) r_b^2.  (equation (6′))
- Solved break-even return:
  - r_b = [1 − c_1 (q − i_d d) − sqrt{[1 − c_1 (q − i_d d)]^2 + 2 (1 + c_1) (q − i_d d − i_s (1 − d))}] / (1 + c_1).  (equation (7))
- Comparative statics:
  - ∂r_b/∂q < 0.  (equation (8))
  - ∂r_b/∂c_1 > 0.  (equation (10))
  - ∂r_b/∂d ambiguous; if i_d = i_s then ∂r_b/∂d < 0 (more preferred deposits reduce bankruptcy probability).  (equation (11))
- Value of bank owners:
  - V = ∫_{r_b}^{1} (q + r − i_d d − i_m (1 − d)) dr = 1/2 (1 − r_b)^2.  (equation (12))
- Social welfare:
  - W = V + i_d d + i_s (1 − d).  (equation (13))
  - When interest rates are risk-sensitive, depositor preference reduces r_b and increases W (capitalized into bank value).
- If interest rates invariant (extreme case), welfare expression modified:
  - W = V + i_d d + (1 − r_b) i_m (1 − d) + r_b (1 − c_1) (q − i_d d) + 1/2 (1 − c_1) r_b^2.  (equation (15))
  - Then ∂W/∂d simplifies to: −c_1 (1 − d) i_m (i_d − i_m) + c_1 i_d r_b.  (equation (16))
- Key intuition:
  - Depositor preference reduces expected contestable residual assets, lowering bankruptcy costs and funding costs; benefits accrue to bank owners and possibly to other creditors through reduced contest intensity.
  - Effectiveness depends on risk-sensitive pricing of funding; if suppliers ignore LGD reductions, benefits may not materialize.

#### B. Funding costs with collateralization
- Bank can obtain collateralized financing share e at yield i_e, with collateralization cost f(e), f′>0, f′′>0.
- Break-even return becomes:
  - r_b = −(q − i_d d − i_e e − i_m (1 − d − e) − f(e)).  (equation (18))
- Bank value V = 1/2 (1 − r_b)^2 as before.
- First-order condition for optimal e (dV/de = 0) implies collateralization chosen until it has no marginal effect on r_b. Rearranged condition:
  - f′ = [(1 + c_1) (i_s − i_e) + c_1 i_e r_b] / [(1 + c_1) (1 − r_b)].  (equation (21))
- Interpretation:
  - f′ trades off marginal cost of making assets eligible vs. market segmentation advantage (i_s − i_e) and reduction in bankruptcy costs (term c_1 i_e r_b / (1 + c_1)(1 − r_b)).
  - Collateralization and statutory depositor preference act as partial substitutes from the bank’s perspective.
- Interaction with deposit share d:
  - de/dd = c_1 (f′ + i_e) f′′^−1 [1 + c_1 (1 + r_b)] ∂r_b/∂d (formula structure).  (equation (22))
  - Since ∂r_b/∂d < 0 in many cases, higher d tends to reduce bank’s incentive to collateralize (substitutability).

#### C. Limits of preferred depositor status and collateralized borrowing
- Assumption examined: residual assets always sufficient to meet preferred/collateralized claims may fail.
- Full bankruptcy remoteness achieved if:
  - q > i_d d + i_e e + f(e).  (text condition)
- If q + r < i_d d + i_e e − f(e) (very bad returns), preferred depositors and secured creditors must contest pari passu with others → many contestants for few residual assets → possibly large bankruptcy costs.
- Consider case with depositor preference but no collateralization and deposits may be insufficient:
  - Define r_d = −q + i_d d (rate below which depositors cannot be fully met).  (equation (23))
  - If r < r_d, depositors contest among themselves with marginal bankruptcy costs c_2; other claimants drop out.
- No-arbitrage conditions with risky deposits:
  - For depositors: i_s d = ∫_{0}^{r_d} i_d d dr + ∫_{r_d}^{1} [(q + r) − c_2 (q + r)] dr.  (equation (24))
  - For unsecured: i_s (1 − d) = ∫_{0}^{r_b} i_m (1 − d) dr + ∫_{r_b}^{1} [q + r − i_d d − c_1 (q + r − i_d d)] dr with integration limits r_b, r_d.  (equation (25))
- Break-even yield for depositors:
  - r_d = [1 − c_2 q − sqrt{[1 − c_2 q]^2 + 2 (1 + c_2) (q − i_s d)}] / (1 + c_2).  (equation (26))
  - ∂r_d/∂d > 0 (increasing deposits increases probability residual assets insufficient).  (equation (27))
- Effect of increasing deposit share d on r_b is ambiguous; expression for dr_b/dd given with complex numerator and denominator showing trade-off between increased contest costs from preferred depositors (if they become short) and reduced contest costs among unsecured creditors.  (equation (28) and expansion (28′))
- Optimal deposit share d that minimizes probability of failure depends on relative magnitudes of c_1, c_2, i_m, i_d (text gives implicit condition structure).

### V. Conclusions and Next Steps — policy-relevant implications and research agenda
- Main conclusions:
  - Conflicts among claimants add substantially to bankruptcy/resolution costs; these prospective costs influence optimal financing composition and motivate making some claims “bankruptcy remote” via statute (depositor preference) or private contract (collateralization).
  - Asset encumbrance can be desirable when it reduces expected bankruptcy contest costs and thus overall funding costs and the probability of distress; full benefits require risk-sensitive pricing of funding and legal certainty of enforcement.
  - Collateralization and depositor preference are near substitutes from the bank’s perspective; collateralization can be increased at the bank’s initiative at increasing marginal cost.
  - If preferred/collateralized claims cannot be met ex post, conflict may intensify and the supposed benefits reverse; regulatory/supervisory frameworks should account for funding composition and aim for prompt intervention.
- Operational policy implications:
  - Supervisory authorities should consider limits on total asset encumbrance (preferred deposits + collateralized borrowing) relative to likely minimum residual assets.
  - Early corrective action raises q (floor on returns) and expands scope for collateralization and depositor preference to be effective.
  - Legal certainty (e.g., dedicated covered bond regimes) is crucial for achieving bankruptcy remoteness.
- Suggested avenues for further research/questions:
  - Systematic empirical investigation of how bankruptcy costs depend on intensity of conflict over residual assets and who bears costs ex ante (market price reactions to regulatory innovations).
  - Reasons for limited transparency on bank asset encumbrance and whether regulation should require greater disclosure (noting confidentiality of central bank refinancing).
  - Implications of heterogeneity among creditors in litigating/lobbying ability and incentives; depositor preference may aggregate many weak atomistic depositors into a single dominant effective claimant.
  - Symmetries between statutory bail-in of unsecured creditors and depositor preference; similarities between CoCos (contingent capital) and collateralized credit.
  - Extension of framework to incorporate liquidity risk and interaction with solvency risk.

*Italicized source attribution: IMF Working Paper — section "2. Pay-Off Structure with Risky Deposits" (text supplied).*

### introduction.php

### _wp13172 - introduction.php

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### Key themes and topics covered by the references
- Depositor preference laws and depositor protection
- Bank capitalization and capital structure signaling
- Bank risk-shifting, bankruptcy costs, and the cost of debt capital
- Bail-out to bail-in mechanisms and mandatory debt restructuring of systemic financial institutions
- Asset encumbrance and covered bonds
- Bank restructuring, resolution, and nonperforming loans
- Legal and legislative impacts on credit risk and financial stability

*Source: _wp13172 - introduction.php*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13172.pdf_