Week 2: Banking and Financial Intermediation Flashcards
(40 cards)
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
