A. Banking Units

Each banking unit requires one unit of funds at date 0 to make loans that return a final payoff at date 2. We assume that the payoffs of the two banking units are independent. Units may be ex ante asymmetric, reflecting access to different pools of loans that differ in their payoff and risk characteristics.

A banking unit $ i\in \left\{H,L\right\} $ generates a positive payoff $ {R}_i $ with probability $ {p}_i $ and 0 with probability $ 1-{p}_i $ . Bankers can increase the probability of a positive return of unit $ i $ from $ {p}_i $ to $ {p}_i^m={p}_i+\Delta {p}_i $ by monitoring the unit’s loans between date 1 and date 2. Monitoring is not observable and involves a nonpecuniary cost c per monitored unit.

Banking units are subject to exogenous liquidity shocks at date 1. If a unit suffers a shock, it requires one additional unit of financing to continue operating.Footnote ⁷ If a shocked unit fails to raise the additional funds, its loans are liquidated for a value of 0 and monitoring becomes irrelevant. If a shocked unit succeeds in raising the additional funds, the payoff structure of its loans is the same as in the absence of the shock.

The probability that unit $ i $ suffers a liquidity shock is $ {q}_i $ . We assume that only one unit may suffer a shock at date 1, implying that the probability that one of the two units suffers a shock equals $ q={q}_H+{q}_L $ .Footnote ⁸ We call a shocked unit that does not reinvest “nonperforming.” A unit that does not suffer a shock, or suffers a shock and reinvests, is called “performing.”

B. Assumptions

We impose the following assumptions to ensure that the decision of operating either of the two units, as well as continuing a unit that suffers a shock, is efficient if and only if bankers monitor the unit.

Assumption 1. Each unit generates positive NPV at date 0 if it is monitored, even if there is no reinvestment after a shock at date 1:

(1) $$ \left(1-{q}_i\right)\left({p}_i^m{R}_i-c\right)>1,\hskip1em \forall i\in \left\{H,L\right\}. $$

Assumption 1 implies that continuing a unit if it suffers a shock at date $ 1 $ generates positive NPV if bankers monitor the unit: $ {p}_i^m{R}_i-c>1 $ .Footnote ⁹ These two conditions in turn imply that a monitored unit generates positive NPV at date 0 if there is reinvestment after a shock: $ {p}_i^m{R}_i-c>1+{q}_i $ . Since both units generate positive NPV regardless of whether they continue after a shock, it is efficient to operate both units at date 0 if they are monitored.

Assumption 2. Continuing either unit following a shock at date 1 generates negative NPV if it is not monitored:

(2) $$ {p}_i{R}_i<1,\hskip1em \forall i\in \left\{H,L\right\}. $$

Assumption 2 implies that operating either unit at date 0 is never efficient if it is not monitored. The reason is that, at date 0, the possibility that the unit suffers a shock implies either higher expected costs (if there is reinvestment) or lower expected return (if there is no reinvestment) compared to reinvestment at date 1.

C. Financing

The capital market is competitive, and outside investors provide funds as long as they break even in expectation. We assume that outside investors cannot commit at date 0 to contracts requiring reinvestments at date 1 that are ex post suboptimal from their perspective. This limited commitment friction prevents banking units from using prearranged financing agreements (e.g., irrevocable lines of credit) to finance their operations.Footnote ¹⁰ We also assume that outside investors cannot force banking units to invest in liquid assets at date 0.Footnote ¹¹ This assumption prevents banking units from self-insuring against liquidity shocks by hoarding liquid assets ex ante.

D. Resolution Policy

Resolution gives the regulator the authority to restructure the banking group’s financial contracts and to shut down one or more of its units at date 1. If the regulator prefers to continue a unit, it imposes the minimum losses on outside investors to enable reinvestment at date 1. We abstract from any direct cost of resolution.

Contrary to private contracting, we assume that the regulator can enforce reinvestment at date 1 even when it is privately suboptimal for outside investors.Footnote ¹² Resolution, therefore, allows the regulator to implement contracting outcomes that private parties cannot achieve outside resolution. This assumption reflects a central feature of modern bank resolution regimes. Statutory bail-in and transfer powers allow authorities to impose losses and enforce continuation outcomes that cannot be achieved through voluntary private restructuring, due to coordination problems and/or creditor veto rights.Footnote ¹³ These features are illustrated by the 2017 Banco Popular resolution, where equity, AT1 holders, and subordinated creditors were written down overnight to enable an immediate going-concern transfer without creditor consent, and by the 2023 Credit Suisse case, where losses were imposed on AT1 holders to facilitate an immediate merger despite the absence of unanimous investor agreement.Footnote ¹⁴ We abstract from these legal and institutional details and impose this assumption to capture the expanded set of allocations that resolution policy can implement relative to private restructuring.

E. Resolution Regimes

A resolution regime specifies one or more “entry points,” that is, legal entities at which the regulator is empowered to initiate restructuring. Resolution ensues at an entry point if that entity (or one of its subsidiaries if the entry point is the holding company) suffers a shock at date 1 and is unable to continue operating outside resolution. Resolution regimes and entry points are chosen ex ante at date 0 (i.e., before units suffer a shock), conditional on the units’ observable characteristics.Footnote ¹⁵

We compare, essentially, two different resolution regimes: single point of entry (SPOE) and multiple point of entry (MPOE) regimes. A SPOE regime is one where the holding company is designated as the sole entry point. In this case, resolution is executed at the holding company level. All units are resolved jointly, losses are mutualized across units, and the banking group’s corporate structure does not change after resolution. In contrast, a MPOE regime is one in which, in addition to the holding company, one or more of its units are designated as separate entry points. Resolution at the unit level breaks up the banking group. Units are ring-fenced, which prevents transfers across units, and are operated independently after resolution. If the resolution of one unit undermines the operational efficiency (monitoring incentives) of the other unit, the regulator retains the authority to restructure the other unit.

F. Regulatory Objectives

The objective of the regulator is to maximize the net present value (NPV) of the banking group at any point in time.Footnote ¹⁶ In the main part of the article, we assume that the regulator can commit to a resolution regime at date 0. Continuing a unit following a shock at date 1 always generates positive NPV if bankers monitor (Assumption 1). However, continuation may not be ex ante optimal if reinvestment prevents the operation of the banking group at date 0. As a result, the regulator may face a time-consistency problem if it cannot commit to the resolution regime. We discuss what happens if the regulator cannot commit to a resolution regime in Section V.

Figure 1 summarizes the sequence of events of the model.

FIGURE 1Sequence of Events

Figure 1 summarizes the sequence of events of the model.

FIGURE 1 Long description

The timeline is divided into three distinct intervals marked by vertical ticks on a horizontal axis.

* Date 0 interval. The first section describes two events. First, the Regulator chooses the resolution regime. Second, Bankers need to raise one unit of financing for each banking unit.

* Date 1 interval. The middle section describes two events. First, Liquidity shocks realize. Second, the Bank is resolved if it cannot continue outside of resolution.

* Date 2 interval. The final section describes two events. First, Bankers choose whether to monitor performing units. Second, Returns realize and payments are made.

A. Incentive Contract

We first derive bankers’ optimal incentive payments for standalone units and then for units operating within a banking group under centralized decision-making.

If unit $ i\in \left\{H,L\right\} $ is operated independently and is performing at date 1, the optimal incentive contract given bankers’ limited liability specifies a payment $ {\tau}_i\ge 0 $ to the bankers in case unit $ i $ generates a positive return at date 2, and 0 otherwise. The incentive compatibility constraint for bankers to monitor unit $ i $ is

(3) $$ {p}_i^m{\tau}_i-c\ge {p}_i{\tau}_i,\hskip1em \forall i\in \left\{H,L\right\}. $$

The lowest payment that ensures that bankers monitor unit $ i $ is thus given by

(4) $$ {\tau}_i\equiv \frac{c}{\Delta {p}_i},\hskip1em \forall i\in \left\{H,L\right\} $$

and unit $ i $ ’s pledgeable income at date $ 1 $ equals

(5) $$ {\mathcal{P}}_i^1\equiv {p}_i^m\left({R}_i-{\tau}_i\right),\hskip1em \forall i\in \left\{H,L\right\}. $$

We assume that the date 1 pledgeable income of the $ H $ -unit is weakly higher than that of the $ L $ -unit: $ {\mathcal{P}}_H^1\ge {\mathcal{P}}_L^1 $ . This assumption, which is without loss of generality, allows us to distinguish between the $ H $ - and $ L $ -unit based on their date 1 pledgeable income.

If both units operate within a banking group and are performing at date 1, the optimal incentive contract $ {T}_G\equiv \left({\tau}_L,{\tau}_H,{\tau}_2\right) $ must specify three different payments to bankers depending on whether only the $ L $ -unit, only the $ H $ -unit, or both units generate a positive return at date 2. We denote the banking group’s date 1 pledgeable income by $ {\mathcal{P}}_G^1 $ .Footnote ¹⁸

Proposition 1. The optimal incentive contract $ {T}_G^{\ast } $ for two performing units within a banking group satisfies $ {\tau}_2^{\ast }>0 $ and $ {\tau}_H^{\ast }={\tau}_L^{\ast }=0 $ . The banking group’s date 1 pledgeable income is strictly larger than the sum of the pledgeable incomes of two individual performing units:

(6) $$ {\mathcal{P}}_G^1>{\mathcal{P}}_H^1+{\mathcal{P}}_L^1. $$

We call the additional date $ 1 $ pledgeable income from operating the units within a group, $ {\mathcal{P}}_S^1\equiv {\mathcal{P}}_G^1-{\mathcal{P}}_H^1-{\mathcal{P}}_L^1 $ , the group’s “incentive synergies.”

Proposition 1, which generalizes the main result of Laux (Reference Laux2001) to the case of asymmetric projects, shows that total pledgeable income at date 1 is maximized if both units operate within a banking group.Footnote ¹⁹ Centralized decision-making relaxes bankers’ limited liability constraint by allowing agency rents to be cross-pledged across units, which lowers the incentive payments required to induce monitoring of both units. These cost savings generate additional pledgeable income, which we refer to as “incentive synergies.”

Under the optimal contract $ {T}_G^{\ast } $ , bankers are paid only when both units succeed at date 2 ( $ {\tau}_2^{\ast } $ ) if both units are performing. If one unit becomes nonperforming at date 1, bankers’ incentive pay depends solely on the success of the remaining unit and coincides with the standalone incentive payment, $ {\tau}_H $ or $ {\tau}_L $ .

B. Operation and Reinvestment Decisions

We are interested in studying the resolution of multiunit banking groups. Thus, without loss of generality, we focus on cases where bankers choose to operate both units within a banking group at date 0. Joint operation is strictly more efficient than operating the units as standalone units whenever at least one unit cannot operate independently.Footnote ²⁰

A reinvestment policy for the banking group consists of a choice variable $ \rho \in \left\{2,H,L,0\right\} $ , where $ \rho =2 $ denotes the case where the banking group reinvests in any unit that receives a shock, $ \rho =i\in \left\{H,L\right\} $ the case where the banking group reinvests if and only if unit $ i $ suffers a shock, and $ \rho =0 $ the case where the banking group does not reinvest in any unit that receives a shock.

If the reinvest policy stipulates continuing unit $ i $ , the expected cost of reinvesting one unit of funds in case of a shock (which occurs with probability $ {q}_i $ ) is $ {q}_i $ . In contrast, if the reinvestment policy stipulates closing down unit $ i $ if it suffers a shock, the unit becomes nonperforming with probability $ {q}_i $ . The date 0 pledgeable income of the banking group, given the reinvestment policy $ \rho $ , is thus

(7) $$ {\mathcal{P}}_G^0\left(\rho \right)\equiv \left(\begin{array}{ll}{\mathcal{P}}_G^1-q& \mathrm{if}\;\rho =2,\\ {}\left(1-{q}_L\right){\mathcal{P}}_G^1+{q}_L{\mathcal{P}}_H^1-{q}_H& \mathrm{if}\;\rho =H,\\ {}\left(1-{q}_H\right){\mathcal{P}}_G^1+{q}_H{\mathcal{P}}_L^1-{q}_L& \mathrm{if}\;\rho =L,\\ {}\left(1-q\right){\mathcal{P}}_G^1+{q}_L{\mathcal{P}}_H^1+{q}_H{\mathcal{P}}_L^1& \mathrm{if}\;\rho =0\end{array}\right. $$

The banking group can operate both units at date 0 if and only if outside investors’ participation constraint is satisfied. This requires that the banking group’s date 0 pledgeable income exceeds the initial investment cost, $ {\mathcal{P}}_G^0\left(\rho \right)\ge 2 $ , for some reinvestment policy $ \rho $ . Notice that the banking group’s date 1 pledgeable income is greater than its date 0 pledgeable regardless of the reinvestment policy because there are no liquidity shocks after date 1: that is, $ {\mathcal{P}}_G^1>{\mathcal{P}}_G^0\left(\rho \right) $ for all $ \rho $ .

Lemma 1. Reinvesting in unit $ i $ increases the banking group’s date 0 pledgeable income if and only if unit $ i $ ’s standalone pledgeable income at date 1 plus the investment synergies from operating both units together exceed the reinvestment cost:

(8) $$ {\mathcal{P}}_G^0(2)>{\mathcal{P}}_G^0(j)\iff {\mathcal{P}}_G^0(i)>{\mathcal{P}}_G^0(0)\iff {\mathcal{P}}_i^1+{\mathcal{P}}_S^1\ge 1, $$

where $ j\ne $ i denotes the other banking unit.

Lemma 1 implies that the banking group can always continue the $ H $ -unit after a shock at date 1. Since $ {\mathcal{P}}_H^1\ge {\mathcal{P}}_L^1 $ , condition (8) must hold for the $ H $ -unit if the group can operate both units at date 0. Otherwise, the group’s date 1 (and hence date 0) pledgeable income would be insufficient to cover the initial investment cost. As a result, we can restrict attention to policies that reinvest in both units following a shock $ \left(\rho =2\right) $ or only reinvest if the $ H $ -unit suffers a shock $ \left(\rho =H\right) $ .

Proposition 2. A banking group can operate both units at date 0 if and only if:

(9) $$ \max \left\{{\mathcal{P}}_G^0(2),{\mathcal{P}}_G^0(H)\right\}\ge 2. $$

The banking group always reinvests in the $ H $ -unit after a shock and withholds reinvestment from the $ L $ -unit if and only if $ {\mathcal{P}}_G^0(2)<2\le {\mathcal{P}}_G^0(H) $ .

Figure 2 illustrates Proposition 2. Because the group can transfer resources across units, both the date 0 operation decision and the date 1 reinvestment policy depend only on total pledgeable income. Since continuing the $ H $ -unit after a shock increases the banking group’s date 0 pledgeable income, it is always optimal to reinvest in the $ H $ -unit.

FIGURE 2Constrained Efficient Operation and Reinvestment Decisions

Figure 2 is a visual representation of the concept put forth in Proposition 2.

FIGURE 2 Long description

The graph features a horizontal x-axis labeled P sub G super 0 2 and a vertical y-axis labeled P sub G super 0 H. Both axes have a marked threshold at the value of 2. A vertical line rises from x equals 2 and a horizontal line extends from y equals 2, dividing the space into four main regions.

* Bottom-left quadrant (below 2 on both axes): Labeled cannot operate both units.

* Top-left quadrant (y above 2, x below 2): Labeled operate both units but do not reinvest into the L-unit.

* Bottom-right quadrant (x above 2, y below 2): Labeled L-unit can fund its reinvestment.

* Top-right quadrant (both above 2): Labeled operate and reinvest into both units.

A dotted diagonal line starts at the origin and bisects the graph. In the top-right section, text above this diagonal line reads L-unit receives transfers after shock. To the right of the diagonal line, equations are listed: P sub G super 0 2 equals P sub G super 0 H, which is equivalent to P sub L super 1 plus P sub S super 1 equals 1.

Reinvesting in the $ L $ -unit, by contrast, may require a transfer from the $ H $ -unit when condition (8) fails, reducing the group’s pledgeable income $ \left({\mathcal{P}}_G^0(2)<{\mathcal{P}}_G^0(H)\right) $ . If this reduction is large enough such that $ {\mathcal{P}}_G^0(2)<2 $ , operating both units at date 0 requires withholding reinvestment from the $ L $ -unit following a shock. Otherwise, reinvestment in the $ L $ -unit is optimal, since continuation yields positive NPV if bankers monitor.Footnote ²¹

A. SPOE Resolution

A SPOE regime is one where the regulator specifies a single entry point at the holding company level. In this case, if one of the banking group’s units suffers a shock, all entities are resolved jointly, and losses are mutualized across units. The banking group’s corporate structure does not change after resolution.

The regulator prefers to continue all units at date 1 since a shocked unit generates positive NPV as long as bankers monitor (Assumption 1). To this end, the regulator restructures financial contracts to maximize the banking group’s date 1 pledgeable income, imposing the minimum losses on outside investors to enable reinvestment while preserving bankers’ monitoring incentives. Since the banking group’s date 1 pledgeable income must exceed the reinvestment cost if the banking group can operate at date 0, the regulator can always issue new securities at date 1 under SPOE to finance reinvestment by imposing sufficiently large write-downs on outside investors’ outstanding claims.

B. MPOE Resolution

A MPOE regime, contrary to a SPOE regime, allows the regulator to specify more than one of the banking group’s legal entities as an entry point. In particular, the regulator can specify entry points at the individual unit level (the $ L $ -unit, the $ H $ -unit, or both individual units), in addition to the holding company level.

If unit $ i\in \left\{H,L\right\} $ suffers a shock and is not designated as an entry point, resolution proceeds at the holding company level. In this case, just as under the SPOE regime, the regulator will always finance reinvestment in the unit. In contrast, if unit $ i $ is designated as an entry point, resolution occurs at the individual unit level. In this case, the regulator breaks up the banking group. The shocked unit is ring-fenced from the other unit, implying that the regulator cannot transfer cash flows from the nonshocked unit to the shocked unit. Units operate independently if continued following the shock, which destroys the incentive synergies from operating the two units together. As a result, the regulator can only finance reinvestment in unit $ i $ when it is designated as an entry point if its standalone date 1 pledgeable income exceeds the reinvestment cost $ \left({\mathcal{P}}_i^1\ge 1\right) $ .

Designating a unit with $ {\mathcal{P}}_i^1\ge 1 $ as an entry point does not affect the banking group’s reinvestment policy compared to SPOE. The reason is that the unit can always cover the reinvestment cost if it suffers a shock. However, ring-fencing the unit destroys the incentive synergies, which reduces the banking group’s pledgeable income and may jeopardize its ability to operate at date 0.Footnote ²³ It follows that the regulator will never designate the $ H $ -unit as an entry point since its date 1 pledgeable income always exceeds the reinvestment cost if the banking group can operate both units at date 0 (Lemma 1).

Designating a unit with $ {\mathcal{P}}_i^1<1 $ has two opposing effects on the banking group’s date $ 0 $ pledgeable income. Separately resolving the unit destroys the incentive synergies, $ {\mathcal{P}}_S^1 $ , but also avoids having to make a transfer from the nonshocked unit to cover the shocked unit’s funding shortfall, $ 1-{\mathcal{P}}_i^1>0 $ . The regulator will only designate the $ L $ -unit as an entry point if this transfer exceeds the foregone incentive synergies from separately resolving the unit: that is, if $ {\mathcal{P}}_L^1+{\mathcal{P}}_S^1<1 $ .

If $ {\mathcal{P}}_L^1+{\mathcal{P}}_S^1<1 $ and the $ L $ -unit is designated as an entry point, it must be shut down following a shock. In this case, the regulator must also restructure outside investors’ outstanding claims to ensure that bankers monitor the (nonshocked) $ H $ -unit. This requires that both the $ L $ -unit and the rest of the banking group enter resolution if the $ L $ -unit suffers a shock. The regulator then restructures bankers’ date 0 incentive contract (which specified a positive payment $ {\tau}_2 $ if and only if both units succeed at date 2) such that bankers receive a positive payment $ {\tau}_H $ if and only if the $ H $ -unit succeeds at date 2, and 0 otherwise.

C. Efficient Resolution Regime

Assumption 1 implies that it is efficient to operate and reinvest in both units because both units generate NPV if they are monitored. Thus, the choice of resolution regime depends on how the resolution regime affects the banking group’s date 0 pledgeable income since this determines the banking group’s ability to raise the initial financing needed to operate both units at date 0.

SPOE resolution ensures that the regulator will continue both units following a shock, which is ex post efficient. Hence, the SPOE regime implements the constrained efficient allocation whenever the banking group’s date 0 pledgeable income exceeds the initial investment cost given continuation of both units. However, if continuing the $ L $ -unit requires a sufficiently large transfer from the $ H $ -unit such that $ {\mathcal{P}}_G^0(2)<2 $ , the SPOE regime fails to implement the constrained-efficient allocation by preventing the banking group from efficiently operating both units at date 0.

MPOE resolution can implement the constrained efficient allocation when shutting down the $ L $ -unit following a shock increases the banking group’s date 0 pledgeable income ( $ {\mathcal{P}}_G^0(2)<{\mathcal{P}}_G^0(H) $ ). In this case, the $ L $ -unit cannot operate independently since $ {\mathcal{P}}_L^1<1 $ , implying that designating the $ L $ -unit as an entry point allows the regulator to commit to shutting down the $ L $ -unit if it suffers a shock. At the same time, MPOE resolution allows reinvestment in the $ H $ -unit while preserving the banking group’s incentive synergies as long as the $ H $ -unit is not designated as an entry point.

Figure 3 depicts how to implement the constrained-efficient allocation. If $ 2\le {\mathcal{P}}_G^0(H)\le {\mathcal{P}}_G^0(2) $ , resolution is not needed because outside investors are willing to restructure their claims to allow efficient reinvestment in both units at date 1. However, if $ 2\le {\mathcal{P}}_G^0(2)<{\mathcal{P}}_G^0(H) $ , SPOE resolution is essential since it allows the regulator to enforce reinvestment in the $ L $ -unit. In contrast, if $ {\mathcal{P}}_G^0(2)<2\le {\mathcal{P}}_G^0(H) $ , operating both units at date 0 requires freeing up pledgeable income by shutting down the $ L $ -unit at date 1 if it suffers a shock. As a result, the regulator must designate the $ L $ -unit as an entry point to implement the constrained-efficient allocation. If outside investors prefer not to restructure the incentive contract if the $ L $ -unit is shut down (see Appendix B), MPOE resolution is essential since it allows the regulator to restructure outside investors’ outstanding claims to ensure that bankers monitor the $ H $ -unit if the $ L $ -unit is shut down.

FIGURE 3Efficiency of Resolution Regimes and Private Restructuring

Figure 3 illustrates the implementation of the constrained-efficient allocation.

D. Implementing the Incentive Contract

So far, we have assumed that bankers’ incentive contracts can be implemented both outside and within resolution. We now show how debt securities together with appropriate write-downs can replicate the payoff structure of the optimal incentive contract.

Suppose that the banking group issues debt securities at the holding company level at date 0 with a face value $ {F}_{G0}={R}_H+{R}_L-{\tau}_2^{\ast } $ maturing at date 2. Bankers own the equity of the holding company. If neither of the two units suffers a shock, the banking group reaches date 2 with this financing structure. This financing structure implements the optimal incentive contract $ {T}_G^{\ast } $ as long as

(10) $$ {F}_{G0}\ge \max \left\{{R}_H,{R}_L\right\}. $$

Substituting $ {F}_{G0} $ into condition (10) and solving for $ {\tau}_2^{\ast } $ yield $ {\tau}_2^{\ast}\le \min \left\{{R}_H,{R}_L\right\} $ , implying that the value of bankers’ equity is 0 if just one unit succeeds at date 2 and $ {\tau}_2^{\ast } $ if both units succeed.Footnote ²⁴

If one of the units suffers a shock and it is constrained efficient to continue the unit, the regulator writes down some of the banking group’s outstanding debt to free up pledgeable income for reinvestment at date 1. Consider a write-down $ \Delta $ of the outstanding debt $ {F}_{G0} $ . The write-down must be large enough so that the sum of the face value of the original debt after the write-down $ \left({F}_{G0}-\Delta \right) $ , the face value of the new debt $ {F}_{G1} $ , and bankers’ compensation $ {\tau}_2^{\ast } $ satisfies the following resource constraint:

(11) $$ {F}_{G0}-\Delta +{F}_{G1}+{\tau}_2^{\ast}\le {R}_H+{R}_L. $$

The optimal write-down dilutes outside investors as little as possible to ensure reinvestment and monitoring of the continued units. Thus, condition (11) must hold with equality. Using the definition of $ {F}_{G0} $ , it follows that the optimal write-down satisfies $ {\Delta}^{\ast }={F}_{G1} $ : that is, the write-down should be equal to the face value of new debt. This new financing structure implements the optimal incentive contract $ {T}_G^{\ast } $ as long as

(12) $$ \left({F}_{G0}-{\Delta}^{\ast}\right)+{F}_{G1}\ge \max \left\{{R}_H,{R}_L\right\} $$

which is equivalent to condition (10).

If it is constrained efficient to shut down the $ L $ -unit following a shock, the incentive contract must ensure that bankers still monitor the $ H $ -unit. To this end, the regulator needs to write down the outstanding debt $ {F}_{G0} $ to $ {F}_H={R}_H-{\tau}_H $ so that bankers receive a payment of $ {\tau}_H $ in case the $ H $ -unit succeeds, and 0 otherwise. An alternative way to implement this resolution policy is to require the banking group to issue convertible securities at date 0 whose payoff depends on whether or not the $ L $ -unit is shut down at date 1. In particular, suppose that the banking group issues nonconvertible debt with face value $ {F}_H={R}_H-{\tau}_H $ at date 0, together with convertible debt with face value $ {F}_C={R}_L-{\tau}_2^{\ast }+{\tau}_H $ that is fully written down in case the $ L $ -unit is shut down at date 1. This financing structure implements the incentive contract $ {T}_G^{\ast } $ if the $ L $ -unit does not suffer a shock, and $ {\tau}_H $ otherwise.

A. Choice of Resolution Regime

Corollary 1 implies that units must be sufficiently asymmetric for the regulator to prefer MPOE to SPOE. Asymmetry arises in our model from i) each unit’s shock probability, $ {q}_i $ , and ii) its pledgeable income, $ {\mathcal{P}}_i $ , which depends on its risk and return characteristics ( $ {p}_i^m $ , $ \Delta {p}_i $ , and $ {R}_i $ ).

Low profitability implies limited buffers relative to expected funding needs, making access to external finance particularly sensitive to changes in financing capacity. If units are sufficiently asymmetric—reflecting different scopes, competencies, or geographic focuses—the incentive synergies are small, reducing the loss from separate resolution. If weaker units have large expected financing deficits, continuing them after a shock requires substantial transfers from stronger units, lowering their financing capacity and restricting the group’s ability to raise the funds needed to operate both units.

B. Choice of Entry Points

Lemma 3 implies that a unit should be designated as an entry point under MPOE only if its financing deficit following a shock is sufficiently large. Crucially, stronger units should not be resolved separately in order to preserve incentive synergies.

HSBC (2021) provides an example of a banking group subject to MPOE. The banking group specifies its holding company and its U.S. and Asian subsidiaries as separate entry points, while its other subsidiaries (including its European subsidiaries) are not designated as entry points. As a result, shocks to its U.S. or Asian operations may trigger a separate resolution of these parts of the banking group, while the corporate structure will be preserved if it suffers shocks to its European operations.

Other banks, especially in Europe, are subject to a similar resolution framework. In the case of Santander (2021), the parent bank (which is itself an operating unit) designates its international subsidiaries as separate entry points. A shock to the parent bank will lead to joint resolution of the entire group, while operating subsidiaries will be resolved separately if one of them suffers a shock.

C. Financing and Investment Decisions

A key implication of our model is that resolution regimes affect investment decisions. Investors in SPOE banks are more exposed to risks from future investments, since they are more likely to be bailed-in than investors in MPOE banks.

Given their greater flexibility to shut down failing units following a shock, MPOE banks are less likely to curtail investment in weaker units as they become riskier. This effect will be amplified during economic crises when the profitability of the banking group as a whole is low. In extreme cases, SPOE banks may even find it necessary to divest weaker units to continue operating stronger ones.

D. Cross-Border Banking

As discussed in Section V, MPOE resolution requires regulators to credibly refrain from using the pledgeable income of the $ H $ -unit to support the $ L $ -unit following a shock. Such a resolution framework is ex post inefficient and thus difficult to enforce when a single regulator oversees the entire group. In cross-border settings, regulators can more credibly deny support to units outside of their jurisdiction. Thus, jurisdictional separation can act as a commitment device and make MPOE resolution easier to enforce.

Prediction 4 is consistent with the prevalence of MPOE in cross-border settings. For example, as of 2009, the United States requires foreign banks to establish intermediate holding companies for their U.S. activities to facilitate their separate supervision and resolution (Federal Reserve (2019)).Footnote ²⁷ Prediction 4 is also consistent with the findings of Faia and Weder di Mauro (Reference Faia and di Mauro2015), who argue that MPOE resolution makes banks more inclined to increase their cross-border activities because they can limit their exposure to foreign losses. Our model’s predictions differ from Bolton and Oehmke (Reference Bolton and Oehmke2019), however, who argue that MPOE resolution should only arise as a consequence of coordination failures between different national regulators who fail to implement the more efficient SPOE resolution regime. In our model, coordination failures between regulators may actually be desirable insofar as they make MPOE resolution more credible, which can increase efficiency.