Prof Sudipto Bhattacharya, LSE

1
Prof Sudipto Bhattacharya, LSE

• Banks, Liquidity Crunches (to Crises) and
  Multiple Dimensions of Moral Hazards in the
  Regulated Economy

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I Liquidity versus Risk-Shifting

• Banks moral hazard w.r.t under-investment in
  liquid (shorter maturity) assets, happens to be
  just QUALITATIVELY DIFFERENT from that vis-à-vis
  Excessive Risk-Taking
• For example, lower Bank borrowing rates encourage
  over-investment in ILLIQUID longer-maturity
  assets, even with perfect secondary markets for
  these, whereas THE

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Some Lessons for Policy Makers

• OPPOSITE IS TRUE for RISK-SHIFTING by banks with
  (in effect) insured depositors it is HIGHER bank
  borrowing rates which lead to more/excessive
  risk-taking by them
• Indeed, there is NO JUSTIFICATION FOR Punitive ex
  post Interest Rates on Loans to Banks judged to
  be suffering from External- caused Liquidity
  Shocks, although there IS

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Re What to Do in out of Crises

• A CLEAR RATIONALE FOR HAVING A CENTRAL-BANK RUN
  INTERBANK
• BORROWING-LENDING FACILITY with
• Clear Pre-committed Borrowing Limits, and
• Reserve Requirements for Internal Liquidity
  Provisions at Each Member Bank, which is
  completely de-linked from Macroeconomic Price
  Stability (Bhattacharya Gale, 1987)

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II. When a Crunch is Systemic

• Based on Diamond and Rajan in JoF, 2005
• Two types of Banks A with 40 of Loans repayable
  early, 60 after one period, and B with the
  opposite. Each (long-term) loan of 1 generates
  investment returns of 1.6 if not liquidated
  early, of which bankers can collect 80, or 1.28
  per loan. On the other hand, if liquidated early,
  each loan yields

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What Should Policymakers Do?

• 0.4 immediately, and 0.5 after one period in
  alternative uses (transfers to other owners)
• A bad (but not necessarily disastrous!) state of
  the economy has 60 of banks in the A category,
  and 40 in the B category, where
• Depositors have Demandable Claims, and come to
  learn about their banks states just before even
  better bank loans can be repaid

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Support Creation of Liquidity, or

• NON-destruction thereof, VIA MARKETS!
• Total available resources in the banking system
  to pay depositors in the first period without
  transfering/restructuring bank loans is 0.60.4
  0.40.61.6 .768, which is INSUFFICIENT TO
  MEET DEPOSITOR DEMANDS OF UNITY, even with banks
  fortunate borrowers investing/re-depositing

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Process of Orderly Restructuring

• Thus 0.232 of additional liquidity MUST be
  created via restructuring of Bank Loans. Is it
  the case that (inter-bank with investors in it
  too) MARKETS WILL DO THAT OK?
• The answer is NO at any interest rate above 1.4,
  A-type banks would be insolvent even after
  restructuring, leading to EARLY (good quality)
  LOANS being RESTRUCTURED

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B-TYPE BANKS WONT HELP

• Via restructuring their loans too to create
  additional short-term liquidity unless inter-
  bank interest rates rise to 1.6, BUT THAT
• IS EXACTLY WHAT THEY WOULD DO because attempted
  (forced) Restructuring by the Run A-type BANKS
  WOULD DRAIN LIQUIDITY AWAY WHEN B-banks try to
  PARTIALLY restructure, which they must

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IN THEIR MYOPIC ACTIONS

• ALBEIT IN A SMALL way only in that as 60 of
  their loans realised early, their loan base, of
  repayments PLUS investment by the lucky
  borrowers, CAN contribute THE AMOUNT 0.61.6
  .96 in the first period
• BUT THESE INVESTORS WOULD BUY THE the
  restructured A-BANK LOANS as well, so the B
  banks would need to liquidate

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IGNORING SYSTEMIC RISKS

• More loans, and INTEREST RATES WILL RISE ABOVE
  1.95, CAUSING THEM TO BE INSOLVENT AS WELL,
  WHEREAS
• IF THE GOVERNMENT FACILITATED restructuring of
  loans by the more illiquid banks, at a Gross
  Interest Rate BELOW 1.4, they and its lucky
  borrowers together would need to buy .6.6.5of
  future restructured

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ARISING FROM SPILLOVERS

• LOAN PAYOFFS, .18 FROM UNLUCKY BANKS. THAT and
  .016 liquidity injection to B-BANKS, would be
  partially provided BY THE NON-LIQUIDATED (LUCKY)
  BORROWERS OF THE UNLUCKY A- BANKS, THUS REQUIRING
  POLICY MAKERS TO INJECT VERY LITTLE AS SUBSIDY
  TO THE UNLUCKY BANKS!

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HOW MUCH GOVERNMENT SUBSIDY WILL BE NEEDED?

• To preclude runs that would require them to
  restructure even their early-realised loans, A
  banks need to obtain liquidity injection of
  1-.4(1.28)- .6(0.4) 0.248 each, additional to
  cash they obtain from restructured loans.
• If they do so with ALL late loans, B-banks will
  not need to restructure any of their late loans
  lucky borrowers will fund them anew

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MAKING USE OF A PRIVATE CUM PUBLIC PARTNERSHIP

• A-BANKS HAVE 0.60.5 OF FUTURE PAYOFFS FROM THE
  RESTRUCTURED LOANS TO PUT UP AS COLLATERAL.
• FOR BUYING THESE RESTRUCTURED LOANS, THEIR LUCKY
  BORROWERS CAN PUT UP A TOTAL OF .24(.32) - .4
  .04 .061, AFTER ADDING LIQUIDITY TO FUND
  WITHDRAWAL AT B-BANKS

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WITH HIGH SOCIAL RETURN

• Thus the GOVERNMENT NEED ONLY PROVIDE (.6.248)
  - .061 .088, AND
• THEREBY ENSURE INTEREST RATES DO NOT RISE ABOVE
  .3/.248 1.21, OR 21 NET, SO THAT A-BANKS STAY
  SOLVENT,i.e., THEY CAN MEET THEIR
• DEPOSITORS EARLY WITHDRAWAL DEMANDS, OF UNITY AT
  EACH BANK

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INSOFAR AS GOVERNMENT

• LIQUIDITY INJECTION OF .088 EARNS THE RESPECTABLE
  RETURN OF 21 NET, AND ENDS UP PREVENTING THE
• ADDITIONAL RESTRUCTURING OF .6 .4 .24 OF
  EARLY-REALISED LOANS
• THIS GENERATES A SOCIAL SURPLUS OF AT LEAST .24
  (1.6 - 0.4 - 0.5).168 A SPECTACULAR POLICY
  SUCCESS!!

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WHAT THEY AND I DONT

• KNOW is, myopia as above aside, WHY FLIGHT TO
  QUALITY OF BANKS IN SUCH CIRCUMSTANCES IS SO
  MUCH!
• 64 BILLION QUESTION IS is it fear of adverse
  selection on the restructured loans?
• IT IS NOT EXPLAINABLE VIA BANKS ENSURING ADEQUATE
  CAPITAL per se

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EXCEPT HISTORICALLY

• WHEN even during the Great Depression in USA,
  aggregate volume of Bank Deposits in banks
  Subjected to Runs was around 5 of US Deposit
  Base, but banks as a whole
• Reduced their Loan-to Deposit ratios, from 85 or
  so to around 55 over five years!
• To need 30-35 in Reserves to Insure any Losses
  on 55 in Loans, seems Excessive!

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WHAT THEY SHOULDVE KNOWN, HOWEVER IS

• THAT, AT LEAST FACED WITH SUCH EXTREME FLIGHTS
  TO QUALITY BY
• (LUCKIER) BANKS, OPTIMAL POLICY
• SHOULD HAVE BEEN TARGETED NOT AUCTIONED
  LIQUIDITY INJECTIONS, SELECTIVELY TO THE LESS
  LUCKY BANKS WHO MUST RESTRUCTURE, BUT STILL FAIL
  W/O SUCH SUBSIDY

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Recent Banking Research on

• Loan Rollover and Credit Freezes
• Adverse Selection Impact Funding
• And Optimal Bank Bailout Policies

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Allen and Gale Rollover Risks

• Economy in One of Two States at Each of N Dates,
  then a Terminal Date at T1
• Terminal Asset Payoffs are Zero if state then is
  S1, and V gt 0 if it is S2. Earlier,
• Asset is Funded ONLY with Debt, which
• Is Short-term, Subject to Default Risks
• States Evolve as a Markov Process with

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Given Transition Probabilities

• P,1-P from S1 to S1, S2 and 1-Q,Q from S2
  to S1, S2 further, Q gt (1-P)
• Pessimistic Scenario Q 1, P is small
• If there is Default on Debt, leading to an Asset
  Sale, it realizes only a fraction f in 0,1) of
  its next period pledgeable value
• Examine Debt Capacity when N is large

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Maximum Debt Funding

• At date N, given the current state is S1, equals
  V(1-P) its promised payment V
• At date (N - 1), it becomes, based again on a
  promised repayment D2 V, B2 (1-P)V
  PfV(1-P) lt V(1 - P2), the expected value of
  Terminal asset Payoff
• Indeed, in the Limit as N goes to Infinity

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Holding Constant Credit Risk

• Or Probability of Default at the Terminal Date,
  at PP(N)(N1) the Initial Debt
• Funding Level BoV(1-P)/(1-fP), which
  Approaches 0 given flt1 P(N) tends to 1
• In Contrast, if the Markovian evolution is
  Optimistic, with Q in (0,1) and P 1, and the
  current state is S2, Maximal Debt at

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Depends on Current Mood

• Funding Level at the initial date equals Bo
  Q(N1)V, or EQUAL to Asset Value given
  expected terminal payoff!
• More generally, given BOTH P and Q in (0, 1) with
  Q gt (1-fP), following are true
• At any date, the Maximal Debt Funding level is
  Higher when the Economy is in

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Or, The State of the Economy

• State S2 than when its in State S1, and
• The sub-Sequence of Maximal Funding Levels in S2
  state are increasing across time as we approach
  the terminal date
• Whereas, the Opposite is True for the
  sub-Sequence of Maximal Debt funding levels in S1
  state A Crash vs a Bubble?

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The Credit Freeze Implication

• IS FRAGILE, if some Equity Capital is Available
  as well, especially in S1 state
• For example, in a Pessimistic Scenario with Q
  1, and P in (0,1), the borrowing
• Level in the final period would remain at B1
  V(1-P), on promised repayment V
• BUT, in the penultimate period, it would

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Need Not be Always Valid

• Be Optimal to issue only Safe Debt with Promised
  Repayment D2 B1 V(1-P), to maximize Overall
  Payoff Z2 (1-P) (V-D2)Pmax(B1- D2,0)
  Proceeds of Debt Issue given D2 debt value B2
  equals D2 only if its no higher than B1
• With three periods left, Safe Debt with a
  Promised Repayment D3 Z2 can then

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Funding Capacity Expands

• Leading to Overall Value equalling Z3
  (1-P)(V-Z2) Z2, and so on, so that as
• The number of sub-periods N goes to its limit of
  infinity, the maximal and safe debt funding level
  Bo would approach
• The Asset Value Ao V1 - P(N)(N1)
• Result related to Geanakoplos (2003).

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To Equal Full Asset Value

• As the number of periods until Maturity
  Increases, PROVIDED that sufficient equity
  capital is available, to Take Up Slack when the
  bad state S1 continues
• It is, of course, precisely such a lack of new
  equity capital injection, arising from past
  losses as A decreases, as well as Institutional
  Behavior, that needs study

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Implications for SPV Capital?

• In the funding sequence derived above, the
  sequences of debt, equity and total asset (A)
  values before maturity satisfy
• B1V(1-P) B2V(1-P) B3V(1-P2)
• E10 E2VP(1-P) E3VP2(1-P) ..
• A1V(1-P) A2V(1-P2) A3(1-P3) ..
• Limiting to the Initial Values at time 0 of

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With Infinite Debt Sequence of

• Ao V1-P(N)(N1) Bo V1-P(N)N Eo
  VP(N)N(1-P(N)), and in the limit
• As N tends to infinity, and P(N) to One, Credit
  Risk P 1-Ao/V P(N)(N1)
• Hence, to keep this chain of financing with
  Equity Injections and Riskfree Debt going until
  penultimate period, Expected

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Debt and Equity Injections

• Sum total of lost equity injections equals
• T VNP(N)(N1)1-P(N) which is the
  Minimum Equity needed per asset, given
  independent risks across many
• Since LN(P) Limit of (N1)LNP(N) and, as
  P(N) tends to 1 from below then LNP(N) P(N)
  - 1, hence we obtain

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Equity Commitment Required

• T VP- LN(P), where P(1 - Ao/V) measures
  the (initial) credit default risk,
• Relative to the Maximal Payoff of Asset
• When P is SMALL, say Ao/V .95 after a small
  regime shift from an Optimistic Scenario with Q
  1 and Ao V, Note
• T/V PLN(1/P) gtgt P same for T/Ao

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Can Far Exceed Magnitude of

• Long Run Default Risk of Funded Asset
• Note that Limit T(P) as P tends to zero is
  indeed zero, employing LHospitals Rule the
  more economically meaningful
• T(P)/Ao P-LN(P)/(1-P) always has a
  strictly positive derivative w.r.t. P
• Plus, P ltT(P)/Aolt1 for all P in (0, 1)

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Bolton, Santos, Scheinkman

• Build Model combining Liquidity Shocks with
  subsequent Adverse Selection due to private
  information accruing to owner of risky asset who
  seek interim liquidity
• Two groups of investors, less and more patient,
  with former having access to a technology having
  high expected return
• Coupled with above timing uncertainty

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Multiple (REE) Equilibrium

• Involving trading by the liquidity-seeking
  impatient asset owners at different time points
  pre- or post-resolution of private information
  about future asset returns
• Surprisingly, delayed trading equilibrium when it
  exists, is ex ante Pareto Better it leads to
  more investment by impatient agents in illiquid
  risky asset, less cash

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Inside vs Outside Liquidity

• In essence, greater recourse to Outside Liquidity
  in Delayed Trading equilibrium, leads to More
  Gains from Trade among patient and impatient
  agents, and hence greater ex ante expected social
  surplus, despite adverse selection in asset price
• HOWEVER, they ignore Problems such as Interim
  Runs, within Impatient Banks

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Bhattacharya and Nyborg

• Look at Optimal Bank Bailout Schemes which Seek
  to Remove Debt Overhang in Banks (in worse future
  states) that impede additional investments by
  them
• In the face of Private Information about
  Distribution of their Future Asset Values and,
  the Option Values of Their Equities
• While Minimizing Government Subsidy

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Asset Buyout vs New Capital

• If (size adjusted) Supports/Ranges, but Not
  Likelihoods of Future Returns Same across Banks,
  These Two Alternatives are Equivalent, and Either
  Measure can Recapitalize Banks with Subsidy Equal
  to their Outside (Equity) Option Values
• If NOT, and Worse Quality Banks also Have Lower
  Worst-case future returns

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MENUS Using Both Better

• We need to have Menu of Bailout Tools, and
  heterogeneous Banks self-selecting
• Ex1 Banks Future Payoffs 120. or 90, with
  Likelihoods 1/2, 1/2 and 2/3, 1/3 and Debt
  Due of 100. Either Buy 1/3 of Assets for 40 OR
  Take 1/3 Equity for 10
• Ex 2 (Menu) Bad Bank Payoffs 120, or 80 1/2
  Equity for 40/3, Assets for 110

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Proposal S. Bhattacharya, LSE

• Dynamic Credit Risk Transfer, and Financial
  Stability Collaborators
• Prof John Geanakoplos, Yale, USA
• Prof Kjell Nyborg, NHH, Norway

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Main Issues to be Addressed

• Impact of CRT on Monitoring Incentives of Loan
  Originators, in Varying Macro States
• Secondary Market Trading of CRT Assets
• Liquidity Shocks and Provision at Banks
• Adverse Selection Effects, and Cycles, in Trading
  Liquidity Sharing among Banks
• Resulting Shock Propagation Mechanisms

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A CRT Monitoring (Chiesa)

• Unlike most authors -- see the Duffie (2007)
  survey -- who judge CRT to be harmful for the
  originating banks monitoring incentives
• Chiesa (2007) considers a set up in which
  Monitoring is Unimportant in a Good state,
  leading to (say) zero proportion of defaults, but
  it Matters in Bad states, in which default is by
  say 2 with 5 without monitoring

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Violation of MLRP and CRT

• Hence, with agents having SYMMETRIC beliefs on
  underlying states, realisation of 2, rather than
  0, default is indicative of bank monitoring
  Rewarding Bank Insiders, as much as feasible,
  THEN is thus Optimal
• This is achieved by CRT, in the format of Selling
  the Most Toxic Tranch of payoff to arise from 0
  over 2 defaults, to Market

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But, What if Monitoring Matters

• Also in Good States, in which without it the
  default rate would be 2 instead of 0, so CRT is
  harmful for banks monitoring given good states,
  in which 0 default signals it?
• Further, suppose Bank Insiders who provide costly
  monitoring Effort obtain Asymmetric information
  regarding realised state a period in advance,
  before choosing CRT level offer

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Partial Transfers of Toxic Tails

• Would now be optimal, indeed None IF the bank
  insiders obtain Perfect Information on the
  realised local macro state Good vs Bad!
• In Dynamic contexts, with Markovian shifts across
  Good and Bad states, would Market Equilibrium
  Yield a Constrained Optimum?
• If Not, especially with higher size preferred,
  When would Sub-optimal monitoring arise?

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Giving Rise to Debt-Deflation

• Cycles even Without Irrational Exuberance?
• Arising from sub-optimal monitoring, hence
  third-best loss of bank capital in Good states
  making for Sub-optimal bank Capital levels, and
  THUS lending volume, in Bad states to follow
  inexorably, modulo serial correlation
• Is there a Role for Bank Capital Regulation,
  above level required for ex ante incentives?

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B. Liquidity Shocks and Adverse Selection in
Inter-Bank Markets

• Focus on ex ante inefficiencies in portfolio
  choices of banks, e.g., Bhattacharya Gale
  (1987), Bhattacharya, Goodhart, Sunirand,
  Tsomocos (Economic Theory, 2007), with
• Adverse Selection ex interim in Inter-Bank Loan
  cum Liquidity Provision Markets, and
• The impact of Securitization cum Tranching of
  bank-originated loans on these processes

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CRT as Diversification Versus

• Net Transfer of the overall Banking System Loan
  Default Risks to Other Market Agents
• Empirically Gross CRT position holdings of banks
  Dwarfs Net position, summed across them, by
  factor of seven to eight Duffie 07
• However, with Demandable Deposits access to net
  outside transfer of bank loan portfolio risks
  matters in low aggregate liquidity state

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Efficient Contingent Risk Transfers to Non-Bank
Players

• This channel is emphasised in the work of Diamond
  and Rajan (J of Finance, 2005) in which non-bank
  investors are banks Lucky borrowers themselves
  Bank Runs Imperil Their interim Ability to
  subsequently Invest
• Is CRT, Requiring Tranching to cope with adverse
  selection (Demarzo and Duffie), an
• efficient Mode of interbank Diversification?

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Non-Bank Investors and DPM

• Other Non-Bank Participants in CRT assets are
  Funds, very often managed by delegated Portfolio
  Managers with incentive contracts
• Can Processes of Herding, arising from say
  Reputational Concerns (Dasgupta and Prat,
• Theoretical Economics, 2006) contribute to
  explaining extent of liquidity withdrawal in

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Inter-bank CRT Markets when

• Liquidity Shocks may be Confounded with
  fundamental Solvency Shocks for a subset? Witness
  the massive lowering of their loan-deposit ratios
  by US Banks overall in 30s!
• Analogously, sharply differing flights to
  liquidity cum safety by banks, as opposed to
  security market participants, in ASEAN economies,
  during 1997-98 flow reversals