Systemic risk and contagion

Question 1

What is systemic risk ?

Answer 1

Refers to risk affecting the banking system (or the

financial system) as a whole.

Question 2

How can systemic risk develop ?

Answer 2

• Common shock
• Contagion
• Combination of both

Question 3

What is an individual risk ?

Answer 3

Imperfect measure of systemic risk

Question 4

What are the characteristics of a bank ?

Answer 4

• their capital C
• their level/quality of risk management M
• their asset risk σ(M)

Question 5

How do the characteristics of a bank determine its probability of survival ?

Answer 5

P[C/σ(M)]

Question 6

What are the two component of a bank’s asset risk ?

Answer 6

Systematic and an idiosyncratic
component:
σ^2 = σ^2(S) + σ^2(I)

Question 7

What defines idiosyncratic and systematic risk ?

Answer 7

• The systematic risk component may represent the probability
of a common shock affecting all banks

• The systematic component is perfectly correlated across banks

• The idiosyncratic component is uncorrelated across banks
• Better risk management M reduces the idiosyncratic, but not the systematic component

Question 8

How do better risk management influence banks ?

Answer 8

Better risk management increases banks’ individual survival probabilities, but leads to higher correlation of risks

→ banking system with individually stable banks following similar business models may still be affected by systemic risk

→ Bank failures in such a system rare but tend to occur clustered during systemic crises

Question 9

What are the policy implications of correlated behavior and herding ?

Answer 9

1. Regulation + supervision only focussing on individual institutions may not prevent systemic crises
   → Stability individual level not necessarily imply stability system-wide level
   → Macroprudential policy may be necessary
2. regulation appropriate on system-wide level may be perceived as excessive from individual bank’s perspective

Question 10

What are the three types of contagion ?

Answer 10

• Contagion through direct exposure
• Contagion through asset prices
• Contagion through information

Question 11

What are the interbank market characteristics given Allen and Gale (2000) ?

Answer 11

• Model contagion through interbank market linkages
• Interbank mkt enables efficient use of liquidity and mitigates liquidity shocks at individual banks
• Not enough liquidity in aggregate = contagion through interbank linkages may lead to disaster
• Higher liquidity buffers + complete interbank mkt lower risk of disastrous liquidity crisis

→ Trade-off between efficiency (no liquidity buffers) and stability (high liquidity buffers)

Question 12

What is Allen & Gale’s model structure ?

Answer 12

• 4 banks offering standard demand deposit contract to depositors
• T = 0 : banks either store deposits or invest in long-run project with higher returns
• Early liquidation of long-run project in T =1 costly
• Banks can trade deposits with each other on interbank market in T = 0
• T = 1 : each bank confronts high t(H) or low t(L) share of early withdrawers with equal probabilities
• In both state, avg share of early withdrawers = t
• Banks face individual liquidity risks : t(i) low or high

→ Achieving first best (c(1), c(2)) requires that each bank stors tc*(1) and invests rest in long-run project

→ But without ability to trade deposits on interbank market, stable banks would need to hold liquidity buffer > tc*(1) → cannot achieve first best

Question 13

How does the interbank market look like at T = 0 ?

Answer 13

Each bank :

• Offers demand deposit contract providing c(1) or c(2) in exchange for 1 unit of deposits

• Stores tc*(1) to serve expected number or early withdrawers and invests the rest
→ no liquidity buffers

• Trades claims on interbank mkt to insure against state where it faces t(H) withdrawers

Question 14

How does the interbank mkt look like at T = 1 ?

Answer 14

• Each bank faces either t(L) or t(H) early withdrawers
• Banks facing t(L) withdrawers have excess liquidity

• Banks facing t(H) withdrawers need liquidity
o Liquidate interbank claims

• Efficient reallocation of liquidity equalizes supply & demand
• No costly liquidation of investments

→ High output in T = 2 → all projects finished

→ Optimal risk sharing + offer (c(1),c(2)) despite random individual liquidity shocks

→ Liquidity only reallocated but no new liquidity created

Question 15

What does the interbank mkt allow ?

Answer 15

• Share individual liquidity risks efficiently

* Hold lower liquidity buffers

Question 16

What is the drawback of liquidity buffers ?

Answer 16

Holding liquidity buffers = opportunity cost since liquid assets cannot be used for investments in more profitable long run projects
→ Optimal risk sharing via interbank mkt allow banks to avoid opportunity costs of holding large individual liquidity buffers

Question 17

What is if one of the bank faces t + ε early withdrawers with ε > 0 whereas the others face t ?

Answer 17

• If all banks store tc*(1) in T = 0 → not enough aggregate liquidity to serve all early withdrawers
• Some long run projects need to be liquidated early in T =1

Question 18

Explain the concept of contagion where bank A faces t+ε and the three other banks face t early withdrawers.

Answer 18

• Bank B, C and D hold just enough liquidity whereas A needs additional liquidity

• A liquidates its claim on B
o B cannot serve early withdrawers and pay out A
o Needs additional liquidity and liquidates claims on C

• Same story for B and C

• When D liquidates claims on A, bank A’s liquidity crisis aggravates
o A starts liquidating long run projects as cannot pay out depositors and D
o A becomes insolvent and faces bank run
o Finally, all banks stat liquidating long run projects, get insolvent and go bankrupt.

• Reason : not enough aggregate liquidity in first place to serve all early withdrawers without liquidating some project → great damage to real economy as all projects = liquidated.

Question 19

Why do contagion happen ?

Answer 19

• Bank hold insufficiently low liquidity buffers in aggregate
• Interbank mkt incomplete ⇒ bank only trades with few other banks

→ Unexpected local liquidity shock may trigger liquidity crisis propagating via interbank mkt through whole banking system

Question 20

What happens if the interbank mkt is complete and each banks holds small liquidity buffer between ε/4 and ε ?

Answer 20

• Individual liquidity buffers < than liquidity shock ε
• But enough liquidity in aggregate

• Bank affected by liquidity shock liquidates its interbank mkt claims on all other banks.
o Each bank pay out only ε/4 to affected bank and stay liquid
o Complete interbank mkt with diversified cross-holdings more resilient against individual liquidity shocks.

Question 21

How can the mkt structure affect the risks of contagion ?

Answer 21

Depending on architecture, interbank mkt mixed effects on banking system’s resilience vs liquidity shocks

• Risks of contagion dominates in incomplete interbank mkt, especially with low liquidity buffers
• Well diversified cross-holdings in complete interbank mkt can absorb unexpected liquidity shocks exceeding individual bank’s liquidity buffer

Question 22

What happens if there is a severe liquidity crisis ?

Answer 22

• Interbank mkt may dry up as banks lose trust in each other
• Banks start hoarding liquidity once fear contagion and refuse to lend to most affected institutes
• Interbank mkt’s liquidity evaporates when it is needed most.

Question 23

What is the contagion through asset prices ?

Answer 23

Levered banks in distress may be forced to sell assets even at heavily discounted prices to meet capital requirements

• Fire sales depress asset prices further
• Fall in asset prices puts solvency of otherwise stable banks under pressure and forces to sell assets too

Question 24

What are the results of a contagion through asset prices ?

Answer 24

In highly levered banking system even relatively small losses may trigger fire sales that result in self-reinforcing loss spiral

• High leverage causes fire sale externalities
→ justification for capital requirements limiting leverage

• In loss spiral capital requirements are procyclical
→ In normal times, regulators should require banks to maintain capital ratios exceeding hard requirements

Question 25

What is contagion through information ?

Answer 25

Problems of one bank → interpreted as signal other banks similar problems

Interpretation may be either :
• Correct leading to “efficient” bank runs
• Incorrect resulting in “inefficient” bank runs

→ Information-based contagion may affect banks not connected via direct exposures or via similar asset holdings