Banking and Bank Runs

1
Banking and Bank Runs

• We are going to learn a bit about what a bank
  does and why it leads to the possibility of bank
  runs.
• We will start out today with a couple of movie
  clips.
• Then discuss a theoretical model of a bank.

2
Mary Poppins

• Two things to notice.
• Bank Run was caused by panic w/o financial
  reasons. The bank was fully solvent.
• The bank closed its doors stopped payment.

3
Its a Wonderful Life

• It was a systemic panic.
• There may have been a justification for the bank
  run.
• A bank takes money and invests it in long-term
  assets (mortgages).
• The bank cant easily liquidate these assets.
• The bank did not fully suspend payments. Doing so
  would hurt depositors.
• There was a degree of negotiation on who gets
  what.

4
Diamond Dybvig Model (1983)

• Captures elements of what a bank does.
• Shows that there is a basic problem of bank runs.
• The model consists of two parties.
• Depositors
• Banks
• The model has three time periods yesterday,
  today and tomorrow.

5
Depositors

• Depositors placed money (say 1000) in a bank
  (yesterday) before learning when they need the
  money.
• Depositors either need their money today
  (impatient) or tomorrow (patient). There is a 50
  chance of being either type.
• The ones that need their money tomorrow can
  always take the money today and hold onto it.
• The ones that need money today get relatively
  very little utility for the money tomorrow.

6
Banks

• Banks have both a short term and a long term
  investment opportunity for the money.
• The short term investment (reserves) is locking
  the money in the vault. This investment returns
  the exact amount invested.
• The long term investment returns an amount R
  tomorrow. It is illiquid and returns only Llt1
  today.

7
Deposit Contract

• The depositors invested 1000 yesterday have a
  contract with the bank.
• The depositors can withdraw their money today and
  receive 1000 or wait until tomorrow and receive
  R1000.

8
Banks decision

• How can the bank meet this contract?
• The bank can divide into two parts.
• Take half and keep it as reserves.
• Take the other half and put it in the long term
  investment.
• Say there are 10 depositors 5 patient and 5
  impatient. The bank puts 5000 in the vault and
  invests 5000.
• Demands today are 51000, and 5R1000. The bank
  has 5000 and R5000 tomorrow.
• Thus, a bank makes zero profit.

9
Danger!

• The bank can not always remain solvent.
• If too many depositors try to withdraw today, it
  wont be able to meet the contract tomorrow.
• For instance if 7 depositors withdraw today, then
  the bank can pay 5000 out of reserves. It then
  must sell its illiquid asset to meet the rest of
  the needs, 2000.
• How much must it sell to meet the needs? How much
  is left?
• How much does those withdrawing tomorrow receive?
• On average, how much does those withdrawing today
  receive?
• At what value of L does is the bank unable to
  meet demands today for those 7 depositors?

10
Multiple equilibria

• This leads to multiple (Nash) equilibria.
• It is inherent in banking.
• Here is an example with 2 patient depositors (and
  2 impatient depositors).
• This forms a 2x2 game between the patient
  depositors.
• R1.5 and L.5

11
Game between patient depositors
Depositor 1
Tomorrow
Today


0
3/4
Today
3/4
1
Depositor 2
1
3/2
Tomorrow
0
3/2
R1.5, L.5
12
Experiment

• We then went to the lab and had 3 treatments with
  9 patient and 9 impatient.
• Credit Crunch R1.1, L.11
• Normal Conditions R2, L.7
• Credit Crunch with 90 deposit insurance.
• How many other patient depositors need to
  withdraw today for you to want to withdraw today?

13
Normal Conditions
Credit crunch w/ 90 deposit ins.
Credit crunch
14
Hidden assumption

• Depositors withdraw sequentially a bank cannot
  count the number of people wanting to withdraw
  today and then decide how much to pay them.
• Otherwise, they can just pay them 5000/N where N
  is the number withdrawing early (for the 10
  depositor case). This would make suspension less
  painful.

15
What is not captured in the model

• Uncertainty in depositors preferences.
• Too many actually need the money today.
• Riskiness in technology.
• Riskiness in R Perhaps there really isnt enough
  to meet demand tomorrow.
• Implication it will be worthwhile to withdraw
  money independent of what others do. Sometimes a
  bank run will be the unique equilibrium.
• Riskiness in L Perhaps one cant really get L.
  Particularly if it is a systemic risk.
• With LTCM, prices went down on any asset that
  LTCM owned! Dual listed stocks arbitraged by
  LTCM diverged

16
Early Solutions to Bank Runs

• Put money in the windows
• Slow up payments.

17
Solutions.

• Make sure R L are not risky. Difficult
  doesnt stop multi. Equilibria.
• Pay early withdrawers less than 1 or pay late
  withdrawers less than R (and keep more
  reserves/Narrow Banking)
• Problems not best contract.
• Suspend payments/ Partial Suspension.
• Problem when number needing money today is
  uncertain.
• Creditor Coordination.
• Long Term Capital Management ran into trouble in
  1998.
• The NY FED organized a bailout with creditors.
• Lender of last resorts.
• Central bank will stop in and loan the bank money
  to replace deposits.
• This should work with depositors in the case of a
  problem with liquidity
• In 1975,
• April 14th, Credit Suisse announced lost some
  money in one of its branches. It didnt mention
  details.
• April 25th, The Swiss Central Bank announced it
  was willing to lend money.
• This had the opposite result causing share price
  to tumble 20.
• Combination Bailout.
• 1907 Banking panic (JP Morgan and US treasury).
• Deposit Insurance.
• This works well. Risk-Sharing between banks.

18
Insurance Problem Moral hazard

• Todd buys theft insurance for his laptop.
• Because he buys the insurance, he is more likely
  to leave the laptop in his car.
• Ideally, he would like to commit to not leaving
  the computer in his car.
• Sometimes, we can contract on it.
• Other times, we cant.
• Do we have a moral hazard problem with deposit
  insurance?

19
Answer Yes.

• Marc is the manager of a Springfield SL.
• Marc pays higher interest than a bigger and safer
  bank claiming his small size helps him cut costs.
• Springfield has deposit insurance (100).
• Todd puts money in Springfield.
• Springfield lends money to a dodgy lecturer at
  Springfield State University at a higher rate.
• When there is no default, everyone wins.
• When there is a default, Todd still gets paid.
• Without insurance, Todd wouldnt invest if he
  sees Springfields risky behavior.

20
Model of Moral Hazard.

• The bank can choose any investment x, where
  3gtxgt1.
• Any investment costs .95 and is either
  successful and pays of x or unsuccessful and pays
  0.
• The probability of the investment being
  successful is
• P(X)(3-x)/2.
• Choosing x1 is safe, choosing x close to 3 is
  unsafe.
• Todd is close to risk neutral and wants to earn
  at least as much as 1 (in expectation) which the
  other banks are offering as a risk free
  investment. He wants R where RP(x)1.
• Without insurance, the bank maximizes
• P(X)(X-R) where R1/P(x)
• With insurance, Todd only needs R1. So the bank
  maximizes
• P(X)(X-R) where R1

21
Savings and Loans scandal

• In the 1980s about 1000 SLs went bankrupt.
• They originally lent money out at fixed rates of
  6 and paid deposits 3.
• With inflation, they had to pay deposits 14 and
  lost money.
• Took gambles to catch up, went to Vegas.
• They were able to take high risk due to the
  deposit insurance.
• This cost US taxpayers 120 billion.

22
Solution to Moral Hazard

• One solution is for insurance to not be 100
  (co-pay as in the UK).
• However, this requires the depositors to be savvy
  and this still keeps the multiple equilibrium
  problem.
• In the US, in 2006 Bush signed a law allowing the
  FDIC to charge premiums based upon risk.