Banks as Liquidity providers

Question 1

What is the structure of the Diamond-Dybvig Model?

Answer 1

• Three period
• One homogenous good consumed either in first or second period: c_1,c_2
• Individuals → initial endowment of unit 1 in T = 0
• Individuals can either store endowment or invest in project characterized by long-term production technology

Question 2

How is the production technology defined?

Answer 2

Production technology requires investment in T = 0

• Yields R > 1 in T = 2 for each unit invested

Or

• Returns liquidation value equal to initial investment when production aborted in T = 1

Intuition: LT investments irreversible and liquidating early may result in losses

Question 3

What are the two types of individuals?

Answer 3

Individuals identical in T = 0 but in T = 1 learn in private whether type 1 or type 2

• Type 1: early consumers and only car about c_1
• Type 2: patient and care about c_2

Intuition: Individuals face private and stochastically independent risk of sudden liquidity needs

Question 4

What is the intuition behind the First Best assumption?

Answer 4

Individuals share risk of being early consumer optimally

• Exante: individuals smooth consumption across states
• Expost: type 1/2 is better/worse off than under autarky

Question 5

What happens under optimal risk sharing when it cannot be achieved via financial markets?

Answer 5

• Claims only contingent on publicly available and verifiable information
• But optimal risk sharing require claims contingent on type-membership which = private information

→ Contingent claims allowing for optimal risk sharing are unavailable in financial markets

Question 6

What happens under optimal risk sharing when it cannot be achieved using self-selection of types?

Answer 6

Financial intermediary offer contract based on self.seletion of types that achieves optimal risk sharing

Question 7

What is the sequential service constraint?

Answer 7

Depositors willing to withdraw = served in sequential order they appear at bank’s desk

Question 8

How is it possible that the demand deposit contract achieves optimal risk sharing ?

Answer 8

• Risk t of being of type 1 = stochastically independent
• According to law of large numbers the share of early withdrawers bank faces very close to t

→ bank can stay solvent while engaging in maturity transformation

Question 9

What happens if the bank invest the rest in illiquid assets ?

Answer 9

It renders bank illiquid = cannot serve more than expected t early without liquidating assets.

→ equilibrium relies entirely on type 2 not withdrawing early
→banks inherently fragile and prone to liquidity risk

Question 10

What happens when some type 2 lose confidence and withdraw early ?

Answer 10

• Bank pays them c_1* in sequential order (liquidation value smaller than actual payout so bank = insolvent)

→ All individuals run and try to withdraw as early as possible since latecomers get nothing
→ Great economic damage: all investments liquidated = output lower than under autarky

Question 11

What is the intuition behind bank run equilibrium?

Answer 11

Type 2 face coordination problem:

• Either none withdraws early = efficient equilibrium with optimal risk sharing
• All withdraw early = inefficient equilibrium with bank run

→ Even weak signals can cause loss of confidence and switch from efficient to inefficient equilibrium
→ Bank run may spread easily throughout whole banking system

Question 12

What is narrow banking ?

Answer 12

Requires bank to hold enough liquidity to withstand bank run

→ Runs never occur
→ Drawback: Benefits from maturity transformation eliminated and optimal risk sharing no longer possible

Question 13

What are the various techniques to avoid bank runs?

Answer 13

• Suspension of convertibility
• Deposit insurance
• Lending of last resort

Question 14

What is suspension of convertibility?

Answer 14

Bank pay out at most tc_1* in T = 1

• Only first t depositors can withdraw early
• Bank can surely meet obligations in T = 2

→ removes incentive of type 2 to run
→ drawback: It random, some type 1 may not be able to withdraw

Question 15

What is deposit insurance?

Answer 15

Guarantees promised return to all who withdraw even if bank fails

• Removes sequential service constraint as payouts independent of depositors’ place in line
→ type 2 no incentive to run

• government natural provider of deposit insurance due to ability to tax

Question 16

What is the lending of last resort?

Answer 16

Central bank provides unlimited liquidity against good collateral

• Banks can obtain emergency loans from CB using illiquid assets as collateral
→ Prevents liquidation of assets

• Depositors know CB provides sufficient liquidity when needed
→ Type 2 no incentive to run

Question 17

What are the drawbacks of safety nets ?

Answer 17

• Full insurance = depositors indifferent about banks’ risk
→ market discipline breaks down

• Banks incentive to take higher risks
→ Privatize profits, socialize losses

Question 18

What is the repo ?

Answer 18

• Major source of ST finance
o Sale of securities with agreement ot purchase back at later date for predefined repurchasing price
o Repurchasing price higher than initial selling price implying an interest rate = repo rate

• Traded security = collateral to mitigate credit risk
• Securities’ quality defines haircut

Question 19

What does the DD model not explain ?

Answer 19

• Standard loan contract and banks’ role as loan providers
→ focus on banks’ liabilities

• Coexistence of banks and markets
→ Introduction of financial market destroys risk sharing contract offered by banks