Week 2: Banking and Financial Intermediation Flashcards
What is maturity transformation
Maturity transformation is the process by which financial institutions borrow short-term (e.g., through deposits) and lend or invest long-term, bridging the liquidity preferences of depositors with the funding needs of borrowers.
Role of bank in maturity transformation
- Bank deposits held by savers, offering interest payment and access to funds on demand (banks borrow short)
- Banks use deposists to fund loans to firms with longer-term investment project (banks lend long)
Deposits are more liquid asset for savers than dirrect equity –> maturity transformation has a social value
What are the assumptions for the Diamond Dybving Model
- Large N of household who save but dont know when they will access their ssavings
3 Time Periodss: 0,1 and 2. All housesholds starts with 1 unit of wealth or income in period 0
Some are early types (1st period consume), others are late types (2nd period consumer)
P(Early) = t. P(Latet) = 1-t
Households learn types in period 2 but private
C1 (early type consumption), C2 (late type consumption)
What is the risk level of householdds in the Diamd Dybving Model
Individuals prefer to consume a sure amount (c1=c2) than same expected amount c(e) = tc1 + (1-t)c2
How do you represent the preferences of households in the diamond dybving model
- X,y acis (c1,c2)
- 45 degree line (c1 = c2)
- Uncertainty increases as distance from 45 degree line becomes larger
- Households indifference curves are convex to origin
- On 45 degrees line, indifference curves are tangent to a line where expected consumption c(e) is constant
What is the equation of the expected consumption line
c(e) = tc1 + (1-t)c2
with gradient (-t/1-t)
Why on the 45 degrees line, are the indifference curves tangent to the constant c(e) line
Because for a risk averse household:
any c1 not equal to c2 with the same c(e) is worse for a risk-averse household
Best point when at 45 degrees line and with same c(e)
What are the two types of investments, wealth can be used in the Diamond Dybving Model
Short-term liquid investment: 0 rate of return
- Avaliable between periods 0 and 1, and periods 1 and 2
Long-term illiquid investment: positive return over long horizon
- each unit in investment in period 0 gives 1+R payoff in period 2
- if abandoned in p1, only initial funds recovered
In an economy with no banks, how would investments operate
Long-term investment strictly better than short-term
In period 1:
Early types only gain from selling if p > 1
Late types only gain from buying if p < 1 as they can only buy from stored wealth or abandoning investmetns
Thus equilibrium is p=1; no gains from trade, market does not help
What are the qualities of bank deposits
Baank pay interest on deposits:
r betwen p0 and p1
r’ between p1 and p2
Right to withdraw in eitherr periodsd
How do bank units grow given interest rates r and r’
Bank creates N units of deposits
Period 1: d1 = 1 + r by
Period 2: d2 = (1 + r)(1 + r’)
No other bank liabilities, so total assets = N
In period 0, what portfolio of assets does the bank invest in
Fraction x in liquid short term
- payoff of xN in period 1
Fraction 1-x in illiquid long-term investment
- Payoff of (1+R)(1-x)N if held until period 2
- Payoff of only (1-x)N if abandoned in period 1
How do banks anticipate withdrawl of deposits
Early: tN depositors
Late: (1-t)N depositors
Due to LLN, e(t) is close to reality
Why are late types willing to wait until period 2
As r=>0 requiring d2>=d1
as if d2< there is no desire to wait for a less sum
How do bank have enough liquid and illiquid asssets for early and late types in period 1 and 2
Bank chooses x such that there is enough liquid assets if only early types withdraw in period 1:
pick x such that td1 < x
same applies for late types:
(1-t)Nd2 <= (1+R)(1-x)N
How do you derive the zero profit condition for deposit contraccts
No profit is asset payoffs = cover withdrawals
td1=x and (1-t)d2 = (1+R)(1-x)
sub x=td1 and dividing by 1+R
td1 + (1-t)d2/1+R = 1
What are feasible deposit contracts
Those on or below the 0 profit line and above 45 degrees line (d2 > d1)
0 Profit line: td1 + (1-t)d2/1+R = 1
On the d1,d2 graph what is line for the outcome with no banks, and the outcome where d1 = d2
What is maturity transformation
Turn long-term assets into short-term liabilities
whaat do bankn liabilitites do in the sr
offer better return (r>0) in short term than assets
no baank scenario has r=o and r’=R
where do depositts have beter short term returns then bank assets
To the right of point N (no banks) where d1>1 (minimum bank offers) so r>0 andd r’< R
up to maximum at L ( popint where d1=d2)
Where is the equilibrium deposit contract
assuming comeptiton among banks with free entry
Competiton –> 0 profits amongst banks
Equilibrium deposit contract (d1 * , d2 * ) at tangency of depositors’ indifference curves and zero-profit lilne (point E)
What determines if E (the equilibrium deposit contract) lies to the right of point N
How sufficiently risk averse households are (curvatre of indiff curve)
Won’t go down to L as no profit line is steeper than c(e) line
What is the value of financial intermediation with banks and sufficiently risk averse households
Householdsd reach higher indiff curve at E rather than N
–> d * 1 > and d * 2< 1+R at E
Why do households need to be risk averse for financial intermediation to have valuue
People prefer certainity rather than expected
so willing to take trade off that late types do not get the full investment return
Essentially providing insurance to those neednng early access by paying some potion of the illiquid long-term asset return
What crucial difference is there between normal insurance policies and bank
Normal insurance policies pay out when obj. verifiable event occurs
Unverifiable nature of ‘early type’ event enails banks runs
What do we call a bank run?
When someone who does not need funds in period 1 requesets withdrawal at that date
What is the maximum recoverable assets in period 1 during a bank run where all but one late types will attempt to withdraw in period 1
xN + (1-x)N = N
as holds xN of depositors funds in liquid and (1-x)N in long-term investments
Can the Bank recover enough from investments from all withdrawal requests?
In the case where there is requests from all late types in period 1 except 1
Bank faces N-1 requests to withdraw d1 > 1 each in period 1
For large N, (N-1)/N = 1 so (N-1)d1>N as d1>1
so cannot recover enough from investment for all withdrawal requests
Is a bank run self-fuffilling
If all otherss withdrawing, nothing left for creditors in period 2
Best to join quue and participate and then waiting
What are the multiple equilibria in the Diamon Dybvig Model
Good Equilibrium: Only early types request withdrawal in period 1; bank survives and facilitating risk sharing
Bad Equilibrium: All depositors request wiithdrawal in period 1 (bank run), bank fails
both indv.. rational
can also happen in financial markets
What are possible policy interventions to precent bank runs
- Deposit insurance
- Lender of last resort
- Capital Requiremenets
- Reserve requirementss
more radical; 100% reserve req. , CBDCs
How does deposit insurance prevent bank runs
Gov guarantees it will compensate depositors for losses from bank failures
Late types never req withdrawal; guaranteed to recieve d2 > d1
No runs occurs, and absent any other problem, no banks fail
What are problems with the deposit insurance;
Creates morral hazard –> banks take too much risk
Create bank failures owing to losses –> could create an insolvency problem
Deposit insuirance solves illiquidity but encourages insolvency
How does being a lender of last resort prevent bank runs
- CB borrowing facility provides liquidity to commercial banks by illiquid assets pledged at collateral
Still moral hazard as difficult to distinguish illiquidity from insolvency in a crisi
What is bank capital and equity
Bank capital = bank equity
Funds provided by shareholders and retained profits not paid out as dividends
How do capital requirements help avoid bank runs and reduce the risk of bank insolvency
Cap. req. specify min ratio of bank equity to bank assets
capital absors bank losses without jeopardising ability to repay depositors
needs to be large enough to cover losses
How do reserve requirements reduce bank runs
Banks forced to hold min deposit fraction as a reserve
Only reduces severity of bank runs
Min. liquidity coverage ratio also used; required to hold high quality liquid assets sufficient to meet a given period of elevated withdrawal
How does 100% reserve requirements help reduce bank runs
Banks always able to satisfy requests for withdrawals
Banks cannot make loans; no maturity transformation
How does CBDC reduce bank runs
Cannot have a run on CB; fiat money not redeembable for anything else
similar problem of how to fund commercial bank lending
