Banking crises

Question 1

Defenition of banking crisis

Answer 1

Bank runs that lead to closure of bank

Closure mind be inplicit: take-over by other bank

Question 2

Systemic banking ciris

Definition

Answer 2

When a large number of institutions is hit

example: US housemarket spread all over the world

Question 3

Systemic risk

Simultaneous faulure of several banks: problem

Answer 3

Risk complete meltdown financial system

Asset prices collapse: banks have to liquidate to obtain liquidity –> economic losses –> feedback to the banking system

Question 4

Source of systemic risk

3 sources

Answer 4

1. Failure of a large bank
2. Contagion
3. Correlated exposures

Question 5

Reasons for contagion banks (source of systemic risk)

4 reasons

Answer 5

1. Depositors at other banks panic
2. Direct losses trough credit exposure
3. Information contagion
4. Collapse in asset price

Question 6

Is bank deversification always good?

Answer 6

No, social and individual optimal is not the same. Banks neglect the effect if diversification on systemic risk.

Question 7

Proof that deversification reduces risk

Take 2 assets, random return, same variance and uncorrelated

Portfolio + variance

Answer 7

Minimal variance when r =0.5
Expected return of portfolio, than variance and minim

Question 8

Model of banking Wagner

Each bank has d deposit

Date 1 and date 2

Answer 8

Date 1: invest in everything, after returns are known. Date 2: look when they fall: x < d and y < d
Drawing

Question 9

Diversification at bank 2 in Wagner model

r is fraction of funds invested by B2 in asset X

How does it affect the outcome in period 2?

Answer 9

• Less failure when asset Y performes badly
• More faiure when asset X performes badly
• Less failure but more systemic crisis

Make drawing

Question 10

Definition liquidation cost

Answer 10

One bank fails: sell to other bank: loss = c
both banks fail: sell to outsider: loss = c x q (where q>1-

Question 11

Value of the banks: expected return

Answer 11

W = expected return on assets - liquidation costs

E(Vi) - Pi I x c - piS x c x q

Pi I: probability individual failure, pi s: prob. systemic failure

Question 12

Expected return on the bank when no diversification

Answer 12

Return on asset: v1 = x, v2 = y
Expected return on asset = mu
Expected return on bank= mu - c x (pi I + piS x q)

Question 13

Expected return on bank with diversification at bank 2

Answer 13

E(w2) = E(v2) - c (pi I 2 + pi s q)
V2 = r2 x + (1-r2)y

Both assets same expected return so E(v2) = mu, independent of r2

Question 14

What is the effect of r2?

r = fraction of funds invested by bank 2 in assets x

Answer 14

Higer r2, reduces pi I Z
Increases pi S

Question 15

Optimal r2 from bank perspective

Answer 15

R2 > 0: diversification
R2 < 0,5: less than full diversification becasue of higher costs of systemic risk (q>1)

Question 16

Externalities of diversification

Answer 16

Diversification at bank 2 increases pi S
pi s affects bank 1
for bank 1: pi I 1 + pi S does nog change but piS increases: larger fraction of bank 1 failutes during systemic risk
Diversification at bank 2 does not increase the probability of failure B1 but BA suffers higher expected liquidation costs because higher systemic risk

Drawing of puntje 2

Question 17

Diversification at both banks

Answer 17

choose rE1 = rE2 = rE > 0
Individual optimal diversificaton ratio: rE = 1 / 1 + wortel q
No extra cost of systemic risk (q = 1) –> RE = 0,5

Question 18

Social optimum

Bank optimizes only thinking about own return: write down total welfare

Answer 18

W1 + W2 = E(v1) + E(v2) - c(pi I1 + pi I 2 + 2pi S maal q)

Question 19

Value of social optimal diversification

Answer 19

rster = 1 / 1 + wortel (2q-1)
Lower than rE: because takes negetive externality into account

Question 20

Policy implication

Answer 20

Regulation should discourage diversification
More diversified banks should have higher capoital requirements

Enough motivation to diversify but negles effect dive on pi S