Bank runs

Question 1

Maturity mismatch

Answer 1

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While liabilities (deposits) are short-term and liquid liabilities (can be withdrawn overnight) 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

Question 2

banks face cost of liquidation because

Answer 2

they will unlikely get the full face value of a loan if they try to recall it or sell it to another bank

Question 3

Fundamental issue in the Diamond-Dybvig model

Answer 3

1. Banks invest in illiquid assets with long-run return R and high cost of liquidation
2. Banks take deposits that offer a lower return and low cost of liquidation

Question 4

Diamond-Dybvig model

pt.1 Utility of depositors

Answer 4

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

Question 5

Why is there an inherent instability of the banking system

Answer 5

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

Question 6

liquidity transformation

Answer 6

one of the most important functions of banks

banks offering deposits that are more liquid than the underlying assets

Question 7

Diamond-Dybvig model

pt.2 Bank liquidity creation

Answer 7

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!

Question 8

r1 increases in

and decreases in

Answer 8

r1 increases in R, and decreases in p

Question 9

r2 depends on

Answer 9

the number of people that actually withdraw in T=1

Question 10

The only think keeping late consumers from withdrawing in T=1 is

Answer 10

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

Question 11

2 equilibria of the DD model

Answer 11

1. Good - both types trust that only p fraction of depositors will withdraw in T=1, so late consumers keep their deposits in the bank
2. Bank run - Late types believe that more than p fraction will withdraw at T=1, so all consumers will withdraw at T = 1

Question 12

What happens in a bank run

Answer 12

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

Question 13

The only thing determining whether you stay in the good equilibrium or end up in the bad is

Answer 13

your beliefs about other depositors beliefs about other depositors beliefs

Question 14

The conclusion of DD model

Answer 14

Banks that offer liquidity transformation through maturity transformation are inherently unstable

Question 15

Remedies to Bank runs

Answer 15

1. Suspension of Convertibility
2. Lender of last resort
3. Bank holiday
4. Deposit Insurance

Question 16

Suspension of Convertibility

Answer 16

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

Question 17

Lender of Last Resort

Answer 17

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

Question 18

Bank holidays

Answer 18

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.

Question 19

Deposit insurance

Answer 19

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

Question 20

Deposit insurance in US

Answer 20

The Federal Deposit Insurance Corporation FDIC started in 1933

Question 21

Deposit insurance in EU

Answer 21

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.

Question 22

Iyer and Puri findings

Answer 22

• 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

Question 23

Deposit Insurance in NL

Answer 23

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