Asset correlation and network fragility: How should we intervene? - PowerPoint Presentation

Slide1

Asset correlation and network fragility: How should we intervene?

Teruyoshi KobayashiKobe University, Japan

2014/9/3

1

Slide2

Observation

1. Banks form networks, but they do not take into account the whole network structure.

- which creates externality. - Need for regulation.

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Slide3

Idea

2. Regulator’s intervention should internalize the externalities that would prevail in the financial network.

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Layer 1

:

i

nterbank market

Layer 2

：

Asset correlation

１

２

４

５

３

１

２

３

Financial network

Slide5

Question

How to internalize the externality

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Slide6

On-site and off-site monitoring

Capital requirements Leverage ratio Liquidity coverage ratio

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Micro

-prudential policies

Slide7

Macro-prudential policies

Countercyclical capital buffer adjusted in accordance with the Credit-to-GDP ratio.

G-SIBs and G-SIFIs selected based on some indicator of “systemic importance”.

(e.g., size,

interconnectedness

,

complexity

, etc.).

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Slide8

Interconnectedness? (definition by BIS, 2013)

(i) intra-financial

system assets

(ii

)

intra-financial

system liabilities

(iii) securities outstanding.

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Complexity? (definition by BIS, 2013)

(i) notional amount of over-the-counter (OTC)

derivatives(ii) Level 3

assets

(iii) trading and available-for-sale

securities

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Slide10

Current approach to “Macro-prudence” is heuristic. - It is not clear why this is OK.

Externalities depend on the network

topology

(

c.f. Acemoglu et al., 2013).

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Slide11

“Meso-prudential” policies

take into account the structure of multilayer network seriously (e.g., asset correlation and interbank market).

try to internalize the network-dependent externalities.

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1. Revisit Beale et al.’s (2011) model

2. Identifying systemically important banks2014/9/3

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Two examples of “meso-prudential” policies

Slide13

Example 1:

Revisit Beale et al. (2011, PNAS)2014/9/3

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“Fundamental default”

- Defaults due to the loss of external assets only.“Contagious default” - Defaults that would not occur without the loss of

interbank assets.

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Two types of defaults

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Diversity

Diversification

Kobayashi (2013, EPJB)

Slide16

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16The eight patterns of interbank networks

Kobayashi (2013, EPJB)

Slide17

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17Visualization

of contagion likelihood: The number of dots in the

-th element indicates the expected number of defaults of bank

per 1000-time single defaults of bank

.

 

20 dots…

Bank 1 causes bank 5 to fail with prob. 20/1000.

Infectivity

susceptibility

Slide18

Question:

How does the optimal macro-portfolio structure look like? Conjecture: More

infective banks should hold relatively less risky (more diversified) portfolio.

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safe

risky

Slide19

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19The

optimal allocation of correlated external assets. Assets 1 and 2 are negatively correlated while 3 and 4 have a positive correlation. Asset 5 is independent of any other assets, and 6 is the diversified asset.

 

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Single default 　

Multiple defaults 　Relative importance depends on the network

topology.

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　　　⇒　

low

costs

, yet

high probability

　

⇒

　

high costs

, yet low probability

　

Slide21

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21Decomposing the contribution of simultaneous fundamental defaults to the expected costs. There are 31 possible combinations in total. The numbers in parentheses indicate the combination of failed banks.

super-spreader!

Slide22

1. The desirable portfolio does not always reflect bank size or infectivity.

The most infective banks need not always be the safest.

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Summary

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2. The

whole network structure needs to be taken into account in optimizing individual banks’ asset holdings. This is because externalities are dependent on the network topology.

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Summary

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Example 2:

Identifying systemically important banks in the network

Slide25

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25Efficient immunization strategies

Who should be vaccinated first?

RIBI Image Library

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Blue solid

:

random

Purple solid

:

Red dashed

:

(dynamical importance)

 

Restrepo et al

.

(

2008,

Phys.Rev.Lett

)

An example of

i

mmunization strategies

n

ode removal

Slide27

Immunization in financial network

Additional capital requirement- Capital surcharge in Basel III

Uniform immunization – Think of a common low-risk asset as a vaccine

(e.g., Kobayashi and Hasui 2014, Sci. Rep.).

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Question:

What if immunization is not one-by-one basis?

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In practice, tens of systemically important nodes are likely to be chosen

at one time

rather than

one-by-one

.

Slide29

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29Question:

What if immunization is not one-by-one basis?

If

,

then

 

 

One-by-one selection is OK if the following axiom (addition axiom) holds true

.

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Systemic importance

Ａ

Ｂ

（Ａ，Ｂ）

（Ａ，Ｃ）

Ｃ

（Ｂ，Ｃ）

Node(s)

Individual rank

Pairwise rank

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B

A

D

E

C

F

Threshold = 1/2

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B

A

D

E

C

F

Default of node B

 

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B

A

D

E

C

F

Default of node A

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B

A

D

E

C

F

Default of node A

 

 

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B

A

D

E

C

F

Default of nodes B and C

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B

A

D

E

C

F

Default of nodes B and C

 

 

 

 

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Immunization with the

“pairwise dynamical importance”

(work in progress)

　

One-by-one Immunization

Pairwise Immunization

Slide38

We need to identify systemically important banks from a

combinatorial optimization problem.

However, the greedy algorithm (i.e., one-by-one basis) will work if the objective function takes a form of a submodular function

.

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Summary

Slide39

In multilayer or modular networks, the indicator should be modified (c.f., Masuda, 2009 New J. Phys.)

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S

ummary

Slide40

Identifying influential nodes in a linear threshold model

Kempe, Kleinberg and Tardos (2003) show that the greedy algorithm gurantees the lower-bound of accuracy.

,

where

is the optimal combination.

Many

financial network models are a version of the linear threshold

model!! (

e.g.,

Gai

-Kapadia

).

 

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However, the threshold value, needs to be uniformly distributed (not constant) to ensure submodularity.

- Not realistic for financial networks.

 

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Identifying

influential nodes in a linear threshold model

Slide42

Distribution of threshold,

, in financial networks

 

is the threshold of contagious default.

It depends on the amount of interbank asset AND the

distribution of the external assets’ return

.

 

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Distribution of threshold,

, in financial networks

 

(

+

) / (

)

(

)/

It follows that

the distribution of

depends on the distribution of

.

(c.f., Kobayashi, 2014,

Econ. Lett.)

 

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Concluding remarks

The network-dependent externalities need to be internalized by regulators. - The idea of

“meso-prudential policy”.

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Concluding remarks

For instance, the desirable asset-holding regulation heavily depends on the network structure.

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Slide46

Concluding remarks

Identification of influential nodes should be addressed as a combinatory optimization problem, because addition axiom does not hold.

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Issues for future research

Need to find a combinatorial optimization method to identify influential banks in a multi-layer network.

How to prevent regulatory arbitrage.

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Issues for future research

Meso-prudential regulation requires comprehensive cross-border data. Need

for a worldwide research collaboration.

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