1. Complex Financial Institutions and Systemic Risk
Elisa Luciano
University of Torino and Collegio Carlo Alberto, Italy
Clas Wihlborg
Chapman University, USA, and University West, Sweden

2. Background
Size and complexity of a bank contribute to Systemic Risk. With greater complexity a bank becomes “too big to fail” at a smaller size.
Complexity is increasing in number and types of activities, number of countries, number of subsidiaries, interconnectedness, lack of correspondence between functional and legal organization, financial linkages among affiliates (Carmassi and Herring, 2015; Barth and Wihlborg, 2015)
Financial reform proposals to reduce systemic risk: Break up the banks, Capital Requirements, Ring-fencing (operational and financial) of subsidiaries , Living Wills, Resolution Procedures.
Costs/benefits of reforms depends on importance of economies of scale and scope, implicit subsidies of state bailouts expectations, systemic effects of bank failures.
What drives size and complexity? Tax systems, regulation, implicit subsidy, exploiting synergies (Carmassi and Herring, 2015)

3. Outline Objectives Organizational structures
Sources of financial synergies
Model characteristics
Value and expected loss with identical parameters across affiliates
Sources of complexity (differences in volatility, size, likelihood of bailout)
Impact on systemic risk of banks’ choice of organizational structure with complexity
A perspective on regulation

4. Objectives
Identify the organizational structures that generate the most systemic risk.
Explain why banks (seeking financial synergies) have incentives to choose systemically risky structures.
Analyze how sources of complexity affect value and systemic risk in different organizational structures. Sources of complexity are represented by differences in volatility, size and other characteristics of affiliates.
Illustrate a trade-off in the choice of organizational structure between a bank’s (private) value and its systemic risk.
Provide a perspective on current reforms.

5. Financial and Operational Ring-fencing
Stand-alone banks = no rescues, complete financial ring-fencing.
Subsidiaries = mutual or one way rescues while preserving limited liability,
Branches = unconditional rescue within bank with common capital base.
Theoretical, Structural Model, extension of Leland (JF, 2007), Luciano and Nicodano (RFS, 2014) with endogenous leverage and interest rate.
Leland (2007), Banal-Estanol, Ottaviani and Winton (2012), Kahn and Winton (2004), Freixas, Loranth and Morrison (2007), Dell’Arricia and Marquez compare financial synergies in branches with stand-alone subsidiaries (complete financial ring-fencing vs financial integration.
Most subsidiary structures have some internal financial arrangements.
Castiglionesi and Wagner (2012) consider liquidity insurance among affiliates.

6. Model: Organizational structures; internal insurance arrangements
A home bank and an affiliate may be organized as
2 stand-alones (SA)-financial independence
2 subsidiaries or parent+subsidiary
One-way rescue conditional on
parent’s survival (OWR)
Mutual rescue conditional on survival
of rescuing affiliate (MR)
2 Branches of one bank; unlimited rescue,
Joint default (BR)

7. Model characteristics
At time 0 banks give loans and collect deposits (debt), at time 1 they pay back deposits and equity holders with the revenues from loans (the risk source)
Costly default occurs if revenues are smaller than the face value of deposits (F), and if there is no rescue and no state bailout.
In case of default of one affiliate, first rescue from the other affiliate or across branches, then (if rescue is not enough) government bailout with some probability.
Perfect, symmetric information; interest on debt reflect default costs and probability of bailout.

8. Sources of financial synergies from bank’s point of view
Reducing default costs (αL(T)) if bank or subsidiary is insolvent at T.
Exploit benefits from probability of bailout by the state (with probability π at T after internal rescue if applicable)
Interest tax shield (k(F-D0)). Interest is the Face value of debt minus the present value of debt.
Limited liability of subsidiaries and stand-alone banks. Joint liability of branches.
Luciano and Wihlborg (2015) analyze how group value (GV) depends on internal default insurance (rescue arrangements) with equal α, π, k, size, volatility of asset return of the two entities; constrained and unconstrained leverage.
Add sources of complexity: differences in parameters across affiliates and jurisdictions. Here we focus on size, volatility and probability of bailout (not yet included in paper).

9. One Stand-alone Bank
The value of one entity as a stand-alone bank at time 0 is
where F is the face value of deposits (debt). The value of assets at time T:
L(T)=k(Value of Loans at T) + k(F-D0)

10. Group values; j=OWR, MR or BR

11. Events affecting expected value of bailouts and expected value of default costs
1{A} denotes event and condition for it.
If one affiliate is insolvent, there is rescue or not depending on structure. In subsidiary structures rescue is conditional on the other affiliate’s survival.
If rescue is insufficient there is a probability of bailout. If there is a bailout there are no creditor losses.
There are no default costs if there is rescue or bailout.
Thus, bailout prevents creditor losses and default costs.

12. Numerical approach to find optimal leverage and GV for each organizational structure
Log returns on loans are Gaussian. L0 =100 for each affiliate.
Time horizon, T=5, riskless interest rate is 5%.
Volatility (standard deviation of returns)=5%; Correlation between affiliates=0.2.
Tax rate k= 0.05, 0.15, 0.25
Default cost parameter α=0.15, 0.25, 0.50
Probability of state bailout π=0.05, 0.07
Base case for both affiliates
Complexity: Differences between affiliates

13. Results with equal paramaters across affiliates Corr. =0
Results with equal paramaters across affiliates Corr.=0.2 (From L-W, 2015)
Private value: with moderate bailout, Mutual> One-way Subsidiary > Branch > 2 Stand-alones (raising deposits optimally makes branches more valuable than ring-fenced banks)
High bailout probability wipes out differences and induces very high leverage (policy discussion irrelevant, but a lot of risk !!)
Branch is never the preferred structure in numerical cases but cannot be ruled out if leverage is constrained and bank can allocate capital between branches (which are not individually constrained).
2 Standalones are preferred only if there are negative operational synergies (diseconomies of scope) or if leverage is constrained and probability of bailout is very high.

14. Strong debt diversity in subsidiary structures

15. Systemic Risk
We express systemic risk as proportional to expected creditor losses (DEL); K(DEL)=K(Fexp(-rT)-D0).
where K depends on bank specific complexity characteristics such as no of subsidiaries, cross-border activities, interbank positions, etc.
In a comparison of organizational structures for one bank we can focus entirely on how the expected loss (DEL) depends on the organizational structure.

18. Next: Expected losses and GV with differences in volatility and size
Panel 1 is the base case with equal parameters across affiliates
Panel 2. Size difference:Lh=100, Ls=50
Panel 3. Volh>Vols: Volh=0.20, Vols=0.05
Panel 4. Vols>Volh: Vols=0.20, Volh=0.05
Increase home probability of bailout to 50%; subsidiary stays at 5%.

19. Base Case: Lh=Ls=100, Vol.=0.05, Corr.=0.2, k=0.05, π=0.05, α=0.15
MRh
MRs MR
OWh
OWs OW
BRh
BRs BR
SAh
SAs F 1
207
201 84
112 90
Exp Loss
2.38
 2.38
1.18
 1.18
0.07
0.03 GV
191.81
191.70
191.64
191.50
Sizeh>Sizes: Lh=100, Ls=50, Vol.=0.05, Corr.=0.2, k=0.05, π=0.05, α=.15 91
301 71
101 45
.048
176.67
176.72
176.70
176.74
2.92
.03
.015
153.48
141.95
Volh>Vols: Lh=Ls=100, Volh=0.20, Vols=0.05, Corr.=0.2, k=0.05, π=0.05, α=.15 63 87
125.34
 125.34
139.52
 139.52
.21
193.28
191.29
191.20
Volh<Vols: Lh=Ls=100, Volh=0.05, Vols=0.20, Corr.=0.2, k=0.05, π=0.05, α=.15
MR=OWR (mirror image of MR Volh>Vols)
Mirror image of Volh>Vols

21. Differences in probability of bailout
Prob Bailout
Home 50%
Sub 5%
OWR MR BR
2SA GV
255.67
254.87
DEL
74.53
214.05
All organizations take advantage of the high bailout probability but the branch
structure pushes its leverage for the whole bank to high level. Small disadvantage
In GV but large difference in expected loss.
Small advantage in operational synergy would induce the bank to choose
Branch structure and thereby add substantially to systemic risk.

22. Trade-off in organizational structure: Change in systemic risk relative to change in bank’s GV
Assume that bank reorganizes from branch structure, BR, to subsidiary with mutual rescue, MR. (ΔDEL/ΔGV)
Base Case: 2.31/0.17=13.6
Size difference: 173.8/11.58=15
Volh>Vols and Vols>Volh: /2.08=60.2
From OWR to MR. (ΔDEL/ΔGV)
Base case: 1.2/0.11=10.9
Size diff.: 0.02/0
Volh>Vols:-13.98/0.01=-1398 (MR dominates OWR)
Vols>Volh: 0/0

23. TAKE-AWAY
With equal parameters subsidiary structures, MR in particular, have greater expected losses and value than BR and stand-alones.
With complexity parameters (differences in size and volatility) the expected losses of the subsidiary structures increase dramatically without value increasing with the same order of magnitude.
Expected losses of branch bank increases as well with differences in volatility but order of magnitude is not comparable. Substantial loss of value as well.
In subsidiary structures leverage concentrated to one. With differences in probability of bailout branch structure increases leverage and expected loss for both affiliates.
High leverage in small subsidiary and in high volatility subsidiary.
Strong case for constraints on leverage (capital requirements), removal of interest tax shield as a source of debt diversity, and removal of probability of bailout.

24. Policy Reforms 1. Capital Requirements
Optimal requirements would depend on all parameters and, therefore, be country- and bank-specific. (Complexity!)
Can they be made binding? Strong incentives to leverage with systemic risk consequences in the presence of complexity as defined here. Are these incentives also incentives to create complex and opaque organizations?
Are capital requirements imposed and enforced on holding company level or subsidiary level? Increased emphasis in Basel on home country and holding company level.
In general, capital requirements on the subsidiary level negates value enhancement of debt diversity in subsidiary structures.

25. Policy Reforms 2. Ring-fencing
UK and EU; Ring-fencing of commercial banking relative to investment banking.
US. Ringfencing of commercial banking from proprietary trading.
Should prevent rescues of investment bank and trading subsidiary using assets of commercial bank. (One way rescues). There are still incentives to create leverage in high risk subsidiaries with potentially systemic consequences.

26. Policy Reforms 3. Insolvency procedures.
Effective and credible insolvency procedures could reduce the probability of bailouts as well as default costs. Debt diversity driven by the interest tax shield remains as a source of incentives for high leverage in one (or some) subsidiaries.
Lack of correspondence between functional and legal organization blurs the distinction between subsidiaries and branches across activities and countries. If subsidiaries cannot be operationally separated in default, a group of subsidiaries function as branches in our terminology.
Within our framework there are costs of operating as branches from the banks point of view although they may reduce systemic risk.
An unresolved question is why banks would want to operate as in branch organizations while legally organize in subsidiaries? A possible answer is that very high bailout expectations make default costs and rescue arrangements irrelevant. More effective insolvency procedures may increase the weight of these considerations in the future and, thereby, contribute to greater organizational transparency.