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.

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.

It’s 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 can’t 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.

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.

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.

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 L<1 today.

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 R*£1000.

Bank’s 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 5*1000, and 5*R*1000. The bank has 5000 and R*5000 tomorrow.

• Thus, a bank makes zero profit.

Danger!

• The bank can not always remain solvent.• If too many depositors try to withdraw today, it won’t 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?

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.

• R=1.5 and L=.5

Game between patient depositorsDepositor 1

Depositor 2

Today

Today

Tomorrow

Tomorrow

3/2

3/2

R=1.5, L=.5

0

0

1

13/4

3/4

Experimental results (Exeter, UK)Number withdrawing early

0

5

10

15

20

0 10 20

Round

Nu

mb

er Both types

Type B's

SuspensionNormal conditions

credit crunch

Haifa results.

Early Solutions to Bank Runs

• Put money in the windows

• Slow up payments.

Solutions.• Make sure R & L are not risky. Difficult & doesn’t stop multi. Equilibria.• Pay early withdrawers less than 1 or pay late withdrawers less than R (and keep

more reserves)– 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 didn’t 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.

What is not captured in the model

• Uncertainty in depositor’s preferences.– Too many actually need the money today.

• Riskiness in technology.– Perhaps there really isn’t 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.

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).

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 can’t. • Do we have a moral hazard problem with

deposit insurance?

Answer: Yes.

• Marc is the manager of a Springfield S&L. • 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 wouldn’t invest if he sees

Springfield’s risky behavior.

Model of Moral Hazard.• The bank can choose any investment x, where 3>x=>1. • 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 x=1 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 R*P(x)=1.

• Without insurance, the bank maximizes – P(X)*(X-R) where R=1/P(x)

• With insurance, Todd only needs R=1. So the bank maximizes– P(X)*(X-R) where R=1

Savings and Loans scandal

• In the 1980s about 1000 S&L’s went bankrupt.

• They originally lent money out at fixed rates of 6% and paid deposits 3%.

• With inflation, they 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.

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.

Lender of Last Resorts: commitment

• Gambling Jim has a rich uncle. • Jim’s uncle loves him very much.• Jim blows his money in a poker game. His rich uncle

bails him out.• His uncle says that is the last time.• Jim gambles again and loses. His rich uncle can’t bear to

see Jim’s legs broken.• The problem is that Jim knows his uncle will always be

there for him.• The uncle can either find some way to commit not to

help Jim afterwards, or sacrifice Jim to stop his other nephews from gambling.

Northern Rock and the Subprime crisis.

Subprime mortgages• Miriam, a divorced mother, was offered a mortgage on a 2-

28 deal: 2 years of a teaser rate of a mortgage and the rest floating.

• Finally, the dream of owning a home is a reality.• Miriam did not have to verify income or assets. She got a

piggyback loan to cover the down payment. • She was told that she can refinance after two years and with

the prices the way they are going get some money out as well.

• She took some extra credit cards and agreed.• The bank took her mortgage packaged it up with others. The

rating agency (paid by the bank) rates the package high. It is sold to various institutions: other banks, hedge funds.

• The bank now only collects the money.

Sub-prime continued

• Unfortunately, rates went up and she couldn’t make the payments.

• Housing prices didn’t go up and she has no equity.• The local bank doesn’t want to work out a deal so

forecloses (actually collects extra fees doing so).• These packages drop faster than one would have

thought. • It wasn’t clear that the low liquidation price was

because of actual expected future payments or illiquidity.

Highly leveraged institutions• Some institutions that bought these packaged

loans were highly leveraged. The price of these securities drop more than they should given the state of the economy, interest rate, etc.

• People loaning the institutions want to take their money out. Forcing them to sell more. This further suppresses the price.

• They started to go broke.• Banks also had these on their books. It isn’t clear

who owns what. • Banks don’t want to lend to each other for two

reasons:– Afraid of the financial state of other banks.– Want to keep extra reserves in case they can’t borrow.

Northern Rock

• Had mortgages not necessarily subprime.• To provide funding for these mortgages, it had

deposits and borrowed from other banks.• The other banks were in essence another

depositor. • When the credit dried up, the other banks

needed the money (became impatient). • Northern Rock couldn’t continue to borrow. • They had to borrow from the lender of last

resorts.

Analogy

• There are a limited number of homes around a lake.• The owners of the homes only sometimes go there for a

few days. They only know if they can go last minute.• When they don’t go, they rent them out. Say that they

stay there only 1/5 the time and there is 3 non-owners for every owner during a summer.

• The owners are indifferent to staying at their home or someone else’s home.

• Thus, the owners are not too worried about renting out their home since they can always rent someone else’s home.

Lake Analogy

• Suddenly, a rumour spreads that it will be hard to rent.

• The owners want to stay very much when they are free and take their homes off the market.

• Since all the owners do so, there is no rental market and it is self-fulfilling.

Northern Rock Bank Run

• Depositors now started to run.

• Was it rational for shareholders to run as well?

• Not enough deposit insurance.

• It also wasn’t clear how much lending was to Northern Rock.

• It isn’t clear how good their loans are.

What should governments do?

What Should Governments do?

Questions:• Is there a risk of contagion.• Is it a solvency problem or a liquidity problem?• Would it cost tax-payers?• Does this set a bad example?Short-term Actions: Cut Rate, Lend, Organize a

bailout (LTCM), Buy assets, Nationalize (partial or full), Allow failure.

Future:• Rewrite the deposit insurance. Other regulation.

Narrow banking.

Northern Rock

• Feb 18, 2008. The British government decided to nationalize Northern Rock. (Which I thought was the best option at the time.)

• Before, the Bank of England was lending it $100 billion and perhaps would need to increase this to $200 billion.

• This had the taxpayers bear the risk w/o the rewards.

Bear Stearns.

• It is an investment bank founded in 1923 with 14,000 employees.

• Focuses on stock investments, hedge funds, brokerage (historical division of banks). Services firms/professionals.

• Market cap was at 20 billion last year ($170 per share)• Two hedge funds lost billions last year. • Early March 2008, there was a “bank run”. • Money was withdrawn from accounts.• They couldn’t sell assets instantly to cover demand.

Needed to borrow $30 billion.

Bail out of Bear Sterns.

• On Friday, March 14th, Fed guaranteed a loan of 30 billion from JP Morgan to Bear Sterns.

• On Sunday, March 16th, it was announced that JP Morgan will buy the company for $2 a share (200 million total).

• This is less than the value of their building on Wall Street (worth more than 1 billion dollars).

Was this a good outcome?• Bear Stearns shareholders were screwed (though

eventually paid $10/share). • JP Morgan was rewarded.• Not really a bailout. Bad behaviour was punished.• Rewarded a firm that was more conservative and

played it correctly.• One problem is those most at fault, Hedge fund

managers, already have their bonuses.• Others claim that this solution created a bigger

moral hazard problem. Know the government will help out.

Incentive Problem

• Some of my best friends are Hedge fund managers. • They take something like 25% of profits but do not pay

losses. • Bad incentives.• Hedge funds in principle should never lose money: they

hedge!• They should be supervised so that they aren’t taking risk.• Problem is that it is a bit complicated and many firms

don’t know how to value it.• Easy way is just to look at value at end of day and

measure standard deviation.• This doesn’t work!

E-trade bank run

Iceland Bank Run

• Iceland has a GDP of about 20 billion pounds.• Iceland banks had deposits of 120 billion (in foreign

currencies).• They lent the money to groups that bought assets.• There was a run on Iceland and the country had to

nationalize the three main banks.• Suspended payments to a half million depositors:

including many UK city councils (almost 1 billion pounds worth) and U. of Exeter (5 million pounds).

• The government was only responsible for the first 15,000 pounds.

Incentive compensation problem

• Take a manufacturing plant that doesn’t take fire insurance, flood insurance, Kassam insurance. For the most part, returns would be steady.

• The returns would be higher than a similar (smarter) plant that does take out the insurance.

• The smarter (more honest?) hedge fund managers are paid less.

• One only sees the difference in unlikely events.• Big moral hazard problem.

Costly mistakes• [(New York) Bank of the United States] had a bank run Dec.

10, 1930. (It is a private bank with a catchy name.) The New York Federal Reserve Banking did not arrange financing to keep it open and it closed its doors forever on Dec. 11. Ultimately it was able to pay depositors upwards of 80 cents on the dollar. This indicates that the bank was solvent at the time.

• Friedman claims that the demise of this bank was one of the downward turning points towards the Great Depression (and also claims that the depression's cause was a credit crunch that was caused by the FED's inaction).

• Sept. 14, 2008. After 150+ years, Lehman Brothers announced it was going bankrupt. Paulson decided not to bail it out. This caused problems for AIG who insured Lehman’s debt. Is Lehman brothers the new Bank of the United States?

Other applications

• Farepak.– People saved during the year and got

coupons at end worth their savings.– Company used next year’s money to pay for

this year’s coupons.

• Defined-Benefit Pension schemes/Social Security.– Young pay for old.– Usually mandatory to stop runs.

What we learned

• Theoretical Model of Bank Runs.

• That these may actually happen (experiment).

• Possible solutions to the problem.

• The Moral Hazard problem.

• A bit about the current credit crisis.

Homework.

• Take the DD model with L=.5 and R=2. Let us say that deposits are insured up to fraction f. For what values of f is there only one equilibrium and what values are there two equilibria? (Early withdrawers are guaranteed to get 1*f and late get 2*f.)

• In each of the treatments of our classroom experiment, were there two equilibria? In each, how many would have to withdraw for you to have the dominant strategy to withdraw as well (always want to withdraw)? Under what parameters do you think we will get a bank run? Why?