Bank runs Flashcards
Maturity mismatch
Money is in long-term illiquid assets like mortgages, business loans, etc. While liabilities (deposits) are short-term and liquid liabilities (can be withdrawn overnight)
Hence, the maturities of the assets (long-term) and liabilities (short-term) don’t match
banks face cost of liquidation because
they will unlikely get the full face value of a loan if they try to recall it or sell it to another bank
Fundamental issue in the Diamond-Dybvig model
- Banks invest in illiquid assets with long-run return R and high cost of liquidation
- Banks take deposits that offer a lower return and low cost of liquidation
Diamond-Dybvig model
pt.1 Utility of depositors
2 depositor types, 2 periods (T=0; 1; 2)
1) Type 1: Early consumers will need cash at T=1
2) Type 2: Late consumers - will need cash at T=2
At T=0 the depositors don’t know their type, only the probability p of being type 1
EU = pU(r1) + (1-p)U(r2)
To simplify, assume U (c) = 1-1/c
Why is there an inherent instability of the banking system
For every bank there is a healthy and a bank run equilibrium and it is impossible to predict which equilibrium will materialize, hence no matter how healthy the bank is there is always a risk of bank run
liquidity transformation
one of the most important functions of banks
banks offering deposits that are more liquid than the underlying assets
Diamond-Dybvig model
pt.2 Bank liquidity creation
Bank takes 100 depositors ($1 each), and invests in illiquid assets with return of R (r1=1, r2 = R = 2)
The bank promises depositors r1 = 1.28 for T=1 : p= 0.25 so 25 withdraw at t = 1 1.28*25 = $32
This leaves 100-32=$68 for T=2 -> 68*2 = $136 for T=2
And since there will be 75 late consumers they get r2 = 136/75 = 1.813 for T=2
Hence, liquidity transformation!
r1 increases in
and decreases in
r1 increases in R, and decreases in p
r2 depends on
the number of people that actually withdraw in T=1
The only think keeping late consumers from withdrawing in T=1 is
their belief that there will be enough money left in T = 2 r2>r1
Hence, if they believe there’ll be a lot of withdrawals in T=1, they will withdraw as well
2 equilibria of the DD model
- Good - both types trust that only p fraction of depositors will withdraw in T=1, so late consumers keep their deposits in the bank
- Bank run - Late types believe that more than p fraction will withdraw at T=1, so all consumers will withdraw at T = 1
What happens in a bank run
The bank should allow its customers to withdraw r1>1, but even if the bank liquidates all its assets, there will only be r1 = 1 available. Thus, customers are only able to withdraw a fraction of the money they were promised or only the first that come to the bank will get their money and the rest get nothing
The only thing determining whether you stay in the good equilibrium or end up in the bad is
your beliefs about other depositors beliefs about other depositors beliefs
The conclusion of DD model
Banks that offer liquidity transformation through maturity transformation are inherently unstable
Remedies to Bank runs
- Suspension of Convertibility
- Lender of last resort
- Bank holiday
- Deposit Insurance
Suspension of Convertibility
If bank commits to not allow more than p deposits withdrawals in T=1, type 2 consumers always know they will get r2, so a run shouldn’t start, but the announcement of SoC itself can trigger a panic about the health of the banking system and might result in a self-fulfilling prophecy
Lender of Last Resort
When bank is not insolvent yet, only illiquid, a LLR can extend liquidity at face value of the assets (R), if the bank can cover its liabilities without liquidating its assets, it is expected that in T=2 the return will be high enough to repay the loan.
-> usually LLR is the central bank, but sometimes it can be an individual bank
Bank holidays
Closing down all the banks, allowing panic to subside, while banks have time to prove they are not insolvent, shore up finances, but again it can cause panics.
Deposit insurance
Insuring deposits to a certain amount in case of bank failure.
It can be financed by a small tax banks pay during good times in order to fill up an insurance fund, or by forcing all banks to guarantee losses at other banks in case of failure.
Runs could still happen if:
- > Insurance is only partial, and lots of depositors are over the limit
- > Depositors don’t trust the insurance guarantee
- > The insurance takes a long time to pay our and depositors have a demand for immediacy
Deposit insurance in US
The Federal Deposit Insurance Corporation FDIC started in 1933
Deposit insurance in EU
Member states have to cover at least 90% up to ECU 20,000 of deposits
-> During the crisis it was raised to 50 000
And then to 100 000 euro.
Iyer and Puri findings
• Deposit insurance is only partially effective: even
customers with balances below the insurance limit
withdraw, although the larger the balance the more
likely a withdrawal (knowledge?).
• Long-term customers are less likely to withdraw.
• Customers that also have a loan with the bank are less likely to withdraw.
• This is now taken into account for bank stress tests.
• Social networks play an important role:
• The more people in your social network have run, the more
likely you are to run.
• Long-run effects: For only 10% of customers that
ran, balances returned to baseline within 6
months
Deposit Insurance in NL
up to 100 000 Eur per BANK for individual consumers and small firms only!!
• Deposits at banks licensed in other EU member
states (+Norway, Iceland, Lichtenstein) are
insured by the foreign deposit insurance.
• Covers almost all current and (long-term) savings
accounts (up to 1 year).
• If you have loans with the bank (e.g., a mortgage),
these are discounted from your account total
• Depositors should receive their insured amounts within
20 days after contacting DNB (which has to happen
within 3 months).
• The financing used to be ex-post: other banks had to
pay for the deposit insurance payouts after a default
event), but from July 1st 2015, will switch to financing
ex-ante: A deposit guarantee fund will be raised from
contributions from the bank. When this fund proves to
be insufficient, the remainder will be collected from
surviving banks
