AN ANALYSIS OF CLOSURE POLICY UNDER ALTERNATIVE REGULATORY STRUCTURES

1. AN ANALYSIS OF CLOSURE POLICY UNDER ALTERNATIVE REGULATORY STRUCTURES GREG CALDWELL BANK OF CANADA September 2005

2. Purpose of this paper • To identify (using a theoretical model) the welfare tradeoffs of closure and resolution policy under (1) a dual regulatory regime (separate supervisor and deposit insurer); and (2) a “meta-regulatory” regime (single entity) .

3. Why is this of interest? • Limited research done on the tradeoffs of separating the supervisor and deposit insurer. • Canada: recent debate over the balance of roles between OSFI and CDIC.

4. Theoretical literature • Closure Policy. Acharya and Dreyfus (1989); Dreyfus, Saunders and Allen (1994); Mailath and Mester (1992); Freixas (1999). • LOLR and Optimal Regulatory Structure. Repullo (2000); Kahn and Santos (2001); Goodhart (2000), (2004). • Deposit Insurance and Prudential Supervision. Little. Garcia (1999), on the policy side discussion.

5. Methodology • Consider three hierarchies: • (1) Unregulated with no deposit insurance (1st best benchmark). • (2) Dual regulatory regime with a separate supervisor and deposit insurer. • (3) Meta-regulatory regime. For (1) measure the ex ante expected welfare and characterize the equilibrium then compare (2) and (3).

6. Model Highlights • Participants: Bank, Uninsured Depositors, Insured Depositors, Supervisor and Deposit Insurer • Exogenous Participants: Nature, risk-free market and merger candidate. • 2-period model. • Endogenization of both ex ante and ex post decision making of authorities.

7. Timing: t=0 • Supervisor/Meta-regulator sets capital requirement: ω • Nature decides bank profitability: μ • Bank of type μ maximizes expected return ρ choosing riskiness of loan portfolio, v, facing an uninsured deposit rate schedule, R(v). These choices are observed.

8. Timing: t=1 • Supervisor observes signal of period 2 realization of A • If NW/A < ω bank is closed and resolution policy implemented. This defines a closure threshold: Ac=(Φ +(1- Φ)∙R)/(1-ω) ≡ A0/(1-ω) ≥ A0 • If merger is chosen, bank’s shortfall is recapitalized immediately. • If liquidation, insured depositors are refunded and bank’s assets are sold for λA. Proceeds are shared equiproportionately.

9. Timing: t=2 • If bank is healthy, A is realized and creditors are reimbursed. • If bank was merged, A is realized but shortfall was made up by recapitalization and all creditors are reimbursed.

10. Bank Type Distribution • Nature decides bank profitability μ from uniform distribution.

11. Loan Distribution • Assume loan is uniformly distributed on interval [μ-v,μ+v].

12. Typical Bank Balance Sheet Before After Note: A0 ≡ Φ+ (1- Φ)R(v)

13. Uninsured deposit rate equilibrium • Uninsured depositors are risk neutral. • Main source of market discipline. • R equates the gross return an uninsured depositor can guarantee itself for sure in an alternative risk free market, with their expected gross return from depositing funds at the bank. (no arbitrage condition) R∙(1-P(L)) + P(L)∙E(recovery|L) = 1 L : liquidation R = f(μ,v,ω,λ,Φ,θ)

14. Where is the market failure? Two sources: (1) Risk-Shifting (deposit insurance combined with limited liability; inefficient lending opportunities). (2) Disintermediation (caused by capital requirements).

15. Metric for ex ante welfare comparison • For a given ωdetermine the ex ante expected welfare. Then determine the expected welfare gross return. Eμ[W(ω)] ------------------ (1+ω)

16. (1) Unregulated Benchmark • Key Characteristic driving results: All Uninsured Depositors. • Disciplinary Mechanics: R’(v)>0. Leading to ρ’(v)<0. Consequently v*=0, for all μ≥1. • Result: (a) Market discipline leads to no risk-shifting by any bank type. • Result: (b) Proper intermediation/disintermediation mix at μ=1. • Result: (c) Ex ante expected welfare is maximized.

17. (2) And (3) Regulated Banking Economies • Now bank has Φ in insured deposits ( 1- Φuninsured deposits ) • For both regulatory structures we: • Characterize the uninsured deposit rate. • Characterize each bank type’s optimal risk choice: v*є{0,μ}. (binary simplification) • Determine ex ante expected welfare.

18. Dual Regulation. • Deposit insurer implements least costly resolution (LCR) • Cost of liquidation is the amount paid to insured depositors minus their proportion of claims on liquidated funds. CL(A)= Φ - λA∙ (Φ / (Φ +(1- Φ) ∙R)) • Cost of Merger is the amount necessary to bring the bank back to zero net worth plus additional capital needed to make the bank healthy. Cm(A)=-NW(A)+ωA=Φ +(1- Φ)∙R-(1-ω)A

19. Cost Curves for Deposit Insurer open

20. Optimal capital requirements under dual regulatory regime

21. Meta Regulation Same methodology as under 2 regulators. Now the resolution decision is based on what is ex post optimal. (EPOR) Liquidation: surplus is the amount that insured depositors receive, the fraction of liquidated funds allocated to uninsured depositors and the social cost of liquidation process government: WL(A)= φ +λA [(1- φ)R / (φ+(1- φ) ∙R)] + (1+θ)(-CL(A)) Merger: both uninsured and insured depositors get their funds in full, there is a social cost of merger and the banking sector gets new recapitalization funds: Wm(A) = φ +(1- φ )R+ (1+θ)(-Cm(A))+ωA

22. Ex post Welfare for Meta-Regulator

23. Result: For λ<1 and Φ <1, A*<Am however as θ increases A* approaches Am. EPOR is more prone to merger relative to LCR but this effect dissipates as the shadow cost of government bailout increases. Relationship between merger and liquidation regions for two regimes

24. Optimal capital requirements and ex ante expected welfare comparison (Low θ) (θ=0.1, λ=0.7)

25. Optimal capital requirements and ex ante expected welfare comparison (High θ) (θ=0.5, λ=0.7)

26. Summary of results: • Although LCR (dual) regime has poorer ex post attributes than EPOR (meta): (a) When market discipline is present: LCR (dual) generally dominates EPOR (meta) and LCR as an ex post policy imposes lower ex ante optimal capital requirements than EPOR. (b) When market discipline is not present neither regime dominates • Generally, EPOR is more likely to merge a failed bank than LCR. However, as the shadow cost of public funds increases, EPOR policy converges towards LCR.