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Page 1: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
Page 2: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
Page 3: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Crowded Risk as a Systemic Concern for CentralClearing Counterparties

Albert J. Menkveld

VU University Amsterdam, Tinbergen Institute, Duisenberg school of finance

July 3, 2014

3

Page 4: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

4

Page 5: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. BIS and IOSCO cooperated over the last decade to write two reportson central clearing counterparty (CCP) risk management:

1.1 BIS-IOSCO (2004)“Recommendations for Central Counterparties.”

1.2 BIS-IOSCO (2012)“Principles for Financial Market Infrastructures.”

5

Page 6: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. BIS and IOSCO cooperated over the last decade to write two reportson central clearing counterparty (CCP) risk management:

1.1 BIS-IOSCO (2004)“Recommendations for Central Counterparties.”

1.2 BIS-IOSCO (2012)“Principles for Financial Market Infrastructures.”

6

Page 7: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. BIS and IOSCO cooperated over the last decade to write two reportson central clearing counterparty (CCP) risk management:

1.1 BIS-IOSCO (2004)“Recommendations for Central Counterparties.”

1.2 BIS-IOSCO (2012)“Principles for Financial Market Infrastructures.”

7

Page 8: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

ESRB annual report 2012, p. 16:

Structural reforms being promoted across the globe have pavedthe way for improved risk management throughout the financialsystem. In particular, the mandatory move to clearingstandardised over-the-counter (OTC) derivatives trades viaCCPs will help to reduce counterparty risk between financialinstitutions, . . .

However, the more prominent role of CCPs will also introducenew systemic risks. Mandatory clearing will turn CCPs intosystemic nodes in the financial system, with unknown, butpossibly far-reaching, consequences.

8

Page 9: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

ESRB annual report 2012, p. 16:

Structural reforms being promoted across the globe have pavedthe way for improved risk management throughout the financialsystem. In particular, the mandatory move to clearingstandardised over-the-counter (OTC) derivatives trades viaCCPs will help to reduce counterparty risk between financialinstitutions, . . .

However, the more prominent role of CCPs will also introducenew systemic risks. Mandatory clearing will turn CCPs intosystemic nodes in the financial system, with unknown, butpossibly far-reaching, consequences.

9

Page 10: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Exhibit 1: CPSS-IOSCO Technical Committee

Recommendations for Central Counterparties (CCPs)

1. Legal risk A CCP should have a well founded, transparent and enforceable legal framework for each aspect of its activities in all relevant jurisdictions.

2. Participation requirements A CCP should require participants to have sufficient financial resources and robust operational capacity to meet obligations arising from participation in the CCP. A CCP should have procedures in place to monitor that participation requirements are met on an ongoing basis. A CCP’s participation requirements should be objective, publicly disclosed, and permit fair and open access.

3. Measurement and management of credit exposures A CCP should measure its credit exposures to its participants at least once a day. Through margin requirements, other risk control mechanisms or a combination of both, a CCP should limit its exposures to potential losses from defaults by its participants in normal market conditions so that the operations of the CCP would not be disrupted and non-defaulting participants would not be exposed to losses that they cannot anticipate or control.

4. Margin requirements If a CCP relies on margin requirements to limit its credit exposures to participants, those requirements should be sufficient to cover potential exposures in normal market conditions. The models and parameters used in setting margin requirements should be risk-based and reviewed regularly.

5. Financial resources A CCP should maintain sufficient financial resources to withstand, at a minimum, a default by the participant to which it has the largest exposure in extreme but plausible market conditions.

6. Default procedures A CCP’s default procedures should be clearly stated, and they should ensure that the CCP can take timely action to contain losses and liquidity pressures and to continue meeting its obligations. Key aspects of the default procedures should be publicly available.

7. Custody and investment risks A CCP should hold assets in a manner whereby risk of loss or of delay in its access to them is minimised. Assets invested by a CCP should be held in instruments with minimal credit, market and liquidity risks.

8. Operational risk A CCP should identify sources of operational risk and minimise them through the development of appropriate systems, controls and procedures. Systems should be reliable and secure, and have adequate, scalable capacity. Business continuity plans should allow for timely recovery of operations and fulfilment of a CCP’s obligations.

4 Recommendations for Central Counterparties

Page 11: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. Standard margin methodologies are typically imposed on a memberby member basis.

2. They scale with a member’s yet-to-clear trade portfolio timesvolatility.

3. For example, 54 exchanges and clearing houses use SPAN developedby Chicago Mercantile Exchange (CME).

11

Page 12: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. Standard margin methodologies are typically imposed on a memberby member basis.

2. They scale with a member’s yet-to-clear trade portfolio timesvolatility.

3. For example, 54 exchanges and clearing houses use SPAN developedby Chicago Mercantile Exchange (CME).

12

Page 13: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Motivation

1. Standard margin methodologies are typically imposed on a memberby member basis.

2. They scale with a member’s yet-to-clear trade portfolio timesvolatility.

3. For example, 54 exchanges and clearing houses use SPAN developedby Chicago Mercantile Exchange (CME).

13

Page 14: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

14

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Objective

1. Do crowded trades constitute a hidden risk to a CCP?

Yes!

2. If so, can one come up with a reasonable measure of crowding?

Yes!

3. And, is there an alternative way to calculate margins so that(systemic) CCP risk is allocated appropriately across members?

Yes!

15

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Objective

1. Do crowded trades constitute a hidden risk to a CCP?

Yes!

2. If so, can one come up with a reasonable measure of crowding?

Yes!

3. And, is there an alternative way to calculate margins so that(systemic) CCP risk is allocated appropriately across members?

Yes!

16

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Objective

1. Do crowded trades constitute a hidden risk to a CCP?

Yes!

2. If so, can one come up with a reasonable measure of crowding?

Yes!

3. And, is there an alternative way to calculate margins so that(systemic) CCP risk is allocated appropriately across members?

Yes!

17

Page 18: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Objective

1. Do crowded trades constitute a hidden risk to a CCP? Yes!

2. If so, can one come up with a reasonable measure of crowding? Yes!

3. And, is there an alternative way to calculate margins so that(systemic) CCP risk is allocated appropriately across members? Yes!

18

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

19

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).

1.2 Homeogeneity of degree one yields a decomposition of CCP riskacross members.

1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

20

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.

1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

21

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

22

Page 23: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

23

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

24

Page 25: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Findings

1. CCP risk is measured by the aggregate loss in clearing members’portfolios. The approach has the following appealing properties:

1.1 It uses the “aggregate exposure” measure of Duffie and Zhu (2011).1.2 Homeogeneity of degree one yields a decomposition of CCP risk

across members.1.3 Sensitivity to any security/risk factor is based on an analytic result.

2. Crowded trades raise CCP tail risk without changing individualmember portfolio (tail) risk.

3. To account for crowded-trade risk the paper proposes the following:

3.1 A crowding index, CrowdIx, to measure the size of crowded-traderisk.

3.2 A new margin methodology, Margin(A), to appropriately accountcrowded-trade risk.

25

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Literature

1. CCP vs. OTCDuffie and Zhu (2011), Koeppl, Monnet, and Temzelides (2012),Menkveld, Pagnotta, and Zoican (2013).

2. Counterparty risk monitoringBiais, Heider, and Hoerova (2011), Acharya and Bisin (2011),Koeppl (2013).

3. Systemic risk in tradesBasak and Shapiro (2001), Acharya (2009), Farhi and Tirole (2012).

4. CCP risk managementCruz Lopez et al. (2014), Hedegaard (2012), Jones and Perignon(2013), Menkveld (2013).

5. Crowded tradesKhandani and Lo (2007), Khandani and Lo (2011), Pojarliev andLevich (2011).

6. Systemic risk allocationBrunnermeier and Cheridito (2014), . . .

26

Page 27: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

27

Page 28: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. CCP risk measure is based on Duffie and Zhu (2011).

2. Consider I securities with normally distributed returns

R ∼ N(0,Ω).

3. nj is the vector of yet-to-settle trade portfolio of member j .

4. Let Xj = nj′R be the P&L on member j ’s trade portfolio, then

X ∼ N(0,Σ), Σ = N ′ΩN, N = [n1, · · · , nJ ] .

5. CCP aggregate exposure to trade portfolios of all members isdefined as

A =∑j

Ej with Ej = −min (Xj , 0) .

28

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. CCP risk measure is based on Duffie and Zhu (2011).

2. Consider I securities with normally distributed returns

R ∼ N(0,Ω).

3. nj is the vector of yet-to-settle trade portfolio of member j .

4. Let Xj = nj′R be the P&L on member j ’s trade portfolio, then

X ∼ N(0,Σ), Σ = N ′ΩN, N = [n1, · · · , nJ ] .

5. CCP aggregate exposure to trade portfolios of all members isdefined as

A =∑j

Ej with Ej = −min (Xj , 0) .

29

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. CCP risk measure is based on Duffie and Zhu (2011).

2. Consider I securities with normally distributed returns

R ∼ N(0,Ω).

3. nj is the vector of yet-to-settle trade portfolio of member j .

4. Let Xj = nj′R be the P&L on member j ’s trade portfolio, then

X ∼ N(0,Σ), Σ = N ′ΩN, N = [n1, · · · , nJ ] .

5. CCP aggregate exposure to trade portfolios of all members isdefined as

A =∑j

Ej with Ej = −min (Xj , 0) .

30

Page 31: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. CCP risk measure is based on Duffie and Zhu (2011).

2. Consider I securities with normally distributed returns

R ∼ N(0,Ω).

3. nj is the vector of yet-to-settle trade portfolio of member j .

4. Let Xj = nj′R be the P&L on member j ’s trade portfolio, then

X ∼ N(0,Σ), Σ = N ′ΩN, N = [n1, · · · , nJ ] .

5. CCP aggregate exposure to trade portfolios of all members isdefined as

A =∑j

Ej with Ej = −min (Xj , 0) .

31

Page 32: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. CCP risk measure is based on Duffie and Zhu (2011).

2. Consider I securities with normally distributed returns

R ∼ N(0,Ω).

3. nj is the vector of yet-to-settle trade portfolio of member j .

4. Let Xj = nj′R be the P&L on member j ’s trade portfolio, then

X ∼ N(0,Σ), Σ = N ′ΩN, N = [n1, · · · , nJ ] .

5. CCP aggregate exposure to trade portfolios of all members isdefined as

A =∑j

Ej with Ej = −min (Xj , 0) .

32

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Duffie and Zhu (2011, p. 78): “For given collateralization standards,the risk of loss caused by a counterparty default is typicallyincreasing in average expected exposure.”

2. Can the standard deviation of exposure also be derived analytically?

33

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Duffie and Zhu (2011, p. 78): “For given collateralization standards,the risk of loss caused by a counterparty default is typicallyincreasing in average expected exposure.”

2. Can the standard deviation of exposure also be derived analytically?

34

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Page 36: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
Page 37: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
Page 38: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
Page 39: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,
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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Results for the folded and truncated normal distribution are used tocalculcate the mean and standard deviation of A (Nabeya, 1951;Rosenbaum, 1961):

2.

mean(A) =∑j

√1

2πσj (Duffie and Zhu, 2011)

3.

std(A) =

√√√√∑k,l

(π − 1

)σkσlM(ρkl)

M(ρ) =

[12π + arcsin (ρ)

]ρ+

√1− ρ2 − 1

π − 1

40

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Results for the folded and truncated normal distribution are used tocalculcate the mean and standard deviation of A (Nabeya, 1951;Rosenbaum, 1961):

2.

mean(A) =∑j

√1

2πσj (Duffie and Zhu, 2011)

3.

std(A) =

√√√√∑k,l

(π − 1

)σkσlM(ρkl)

M(ρ) =

[12π + arcsin (ρ)

]ρ+

√1− ρ2 − 1

π − 1

41

Page 42: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Results for the folded and truncated normal distribution are used tocalculcate the mean and standard deviation of A (Nabeya, 1951;Rosenbaum, 1961):

2.

mean(A) =∑j

√1

2πσj (Duffie and Zhu, 2011)

3.

std(A) =

√√√√∑k,l

(π − 1

)σkσlM(ρkl)

M(ρ) =

[12π + arcsin (ρ)

]ρ+

√1− ρ2 − 1

π − 1

42

Page 43: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1. Results for the folded and truncated normal distribution are used tocalculcate the mean and standard deviation of A (Nabeya, 1951;Rosenbaum, 1961):

2.

mean(A) =∑j

√1

2πσj (Duffie and Zhu, 2011)

3.

std(A) =

√√√√∑k,l

(π − 1

)σkσlM(ρkl)

M(ρ) =

[12π + arcsin (ρ)

]ρ+

√1− ρ2 − 1

π − 1

43

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Measure

1.0 0.5 0.0 0.5 1.00.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

M(.)

44

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Noncrowded trades

security/

risk factor 1n1n2

n3

n4

security/

risk factor 2

45

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Simple example noncrowded trades

1.

N =

(1 −1 0 00 0 1 −1

), Σ =

1 −1 0 0−1 1 0 0

0 0 1 −10 0 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 0 0−1 π − 1 0 0

0 0 π − 1 −10 0 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

2π≈ 0.85

46

Page 47: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Simple example noncrowded trades

1.

N =

(1 −1 0 00 0 1 −1

), Σ =

1 −1 0 0−1 1 0 0

0 0 1 −10 0 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 0 0−1 π − 1 0 0

0 0 π − 1 −10 0 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

2π≈ 0.85

47

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Simple example noncrowded trades

1.

N =

(1 −1 0 00 0 1 −1

), Σ =

1 −1 0 0−1 1 0 0

0 0 1 −10 0 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 0 0−1 π − 1 0 0

0 0 π − 1 −10 0 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

2π≈ 0.85

48

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Crowded trades

security/

risk factor 1n1n2

n3n4

security/

risk factor 2

49

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Simple example crowded trades

1.

N =

(1 −1 1 −10 0 0 0

), Σ = N ′ΩN =

1 −1 1 −1−1 1 −1 1

1 −1 1 −1−1 1 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

π≈ 1.21

50

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Simple example crowded trades

1.

N =

(1 −1 1 −10 0 0 0

), Σ = N ′ΩN =

1 −1 1 −1−1 1 −1 1

1 −1 1 −1−1 1 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

π≈ 1.21

51

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Simple example crowded trades

1.

N =

(1 −1 1 −10 0 0 0

), Σ = N ′ΩN =

1 −1 1 −1−1 1 −1 1

1 −1 1 −1−1 1 −1 1

2.

E (E ) =

√1

1111

, var(E ) =1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

π − 1 −1 π − 1 −1−1 π − 1 −1 π − 1

3.

E (A) = 4

√1

2π≈ 1.60 and std(A) = 2

√π − 2

π≈ 1.21

52

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Histogram aggregate exposure for four members (N=4)

0 1 2 3 4 5 6 7 8 9Aggregate exposure

0.0

0.1

0.2

0.3

0.4

0.5Pro

babili

ty d

ensi

ty

crowded tradesnoncrowded trades

53

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A crowded-trade risk thermometer?

Is there a natural “thermometer” for crowded-trade risk?

Definition

CrowdIx for Σ is defined as

CrowdIx = std(A)/std(A)

where A is CCP aggregate exposure when all members’ trades arere-allocated to a single risk factor to the maximum extent possible.1

Lemma

CrowdIx ≥√

1

J/2where J = 2 bJ/2c J

1A feasible approach to this NP hard problem is to convert it to a standardbin-packing problem which can be “solved” heuristically (see Appendix A of the slides).

54

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A crowded-trade risk thermometer?

Is there a natural “thermometer” for crowded-trade risk?

Definition

CrowdIx for Σ is defined as

CrowdIx = std(A)/std(A)

where A is CCP aggregate exposure when all members’ trades arere-allocated to a single risk factor to the maximum extent possible.1

Lemma

CrowdIx ≥√

1

J/2where J = 2 bJ/2c J

1A feasible approach to this NP hard problem is to convert it to a standardbin-packing problem which can be “solved” heuristically (see Appendix A of the slides).

55

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A crowded-trade risk thermometer?

Is there a natural “thermometer” for crowded-trade risk?

Definition

CrowdIx for Σ is defined as

CrowdIx = std(A)/std(A)

where A is CCP aggregate exposure when all members’ trades arere-allocated to a single risk factor to the maximum extent possible.1

Lemma

CrowdIx ≥√

1

J/2where J = 2 bJ/2c J

1A feasible approach to this NP hard problem is to convert it to a standardbin-packing problem which can be “solved” heuristically (see Appendix A of the slides).

56

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A crowded-trade risk thermometer?

1. CrowdIx in the simple example is√1/2 = 0.71 in the noncrowded case.

1 in the crowded case.

57

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An alternative margin methodology?

Prelude: Standard (member by member) margin methodologies basemargins on the tail risk in a trade portfolio.

1. A standard tail risk measure is value-at-risk (VaR).

2. VaR is often calculated by the “delta-normal method” (Jorion, 2007,p. 260).

Definition

Let Margin(A) be the total margin a CCP should collect to protectagainst tail risk:

Margin(A) := E (A) + α std (A) .

Claim: Margin(A) is the “aggregate” approach extrapolated from existingmember by member approaches.

58

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

An alternative margin methodology?

Prelude: Standard (member by member) margin methodologies basemargins on the tail risk in a trade portfolio.

1. A standard tail risk measure is value-at-risk (VaR).

2. VaR is often calculated by the “delta-normal method” (Jorion, 2007,p. 260).

Definition

Let Margin(A) be the total margin a CCP should collect to protectagainst tail risk:

Margin(A) := E (A) + α std (A) .

Claim: Margin(A) is the “aggregate” approach extrapolated from existingmember by member approaches.

59

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

An alternative margin methodology?

Prelude: Standard (member by member) margin methodologies basemargins on the tail risk in a trade portfolio.

1. A standard tail risk measure is value-at-risk (VaR).

2. VaR is often calculated by the “delta-normal method” (Jorion, 2007,p. 260).

Definition

Let Margin(A) be the total margin a CCP should collect to protectagainst tail risk:

Margin(A) := E (A) + α std (A) .

Claim: Margin(A) is the “aggregate” approach extrapolated from existingmember by member approaches.

60

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An alternative margin methodology?

1. Homogeneity of degree one of mean(A) and std(A) implies thatMargin(A) naturally decomposes across members (Euler’shomogeneous function theorem).1.1

mean(A) =∑j

√1

2πσj

1.2

std(A) =∑k

σk∂std(A)

∂σk=∑k

σk

∑l

1

std(A)

(π − 1

)σlM(ρkl)

2. Therefore,

Margin(A) =∑j

√1

2πσj︸ ︷︷ ︸

Member-specific

part (old)

+ ασj∑l

1

std(A)

(π − 1

)σlM(ρkl)︸ ︷︷ ︸

Crowded-trade part (new)

61

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An alternative margin methodology?

1. Homogeneity of degree one of mean(A) and std(A) implies thatMargin(A) naturally decomposes across members (Euler’shomogeneous function theorem).1.1

mean(A) =∑j

√1

2πσj

1.2

std(A) =∑k

σk∂std(A)

∂σk=∑k

σk

∑l

1

std(A)

(π − 1

)σlM(ρkl)

2. Therefore,

Margin(A) =∑j

√1

2πσj︸ ︷︷ ︸

Member-specific

part (old)

+ ασj∑l

1

std(A)

(π − 1

)σlM(ρkl)︸ ︷︷ ︸

Crowded-trade part (new)

62

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An alternative margin methodology?

1. To identify risk factor(s) on which members’ trades crowd, thefollowing results are useful:

1.1∂

∂σfE(A) =

∑j

√1

σf

σjBjj

1.2∂

∂σfstd(A) =

(π − 1

)σf

σA

∑k,l

[M ′(ρkl)Bkl+

+ρ2kl

π − 1

(1 − 2

√1 − ρ2

kl

)(σl

σkBkk +

σk

σlBll

)]with

Bkl := nk′ββ′nl and β = cov(R, r f )/var(r f )

63

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An alternative margin methodology?

1. The sensitivity of Margin(A) to a particular risk factor is naturallydescribed by the following elasticity:

eMargin(A)σf

=σf

Margin(A)

(∂

∂σfE(A) + α

∂σfstd(A)

).

64

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Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

65

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Data

1. A European Multilateral Clearing Facility (EMCF) sample of “tradereports” filed by its (anonymized) members.

2. It contains all trades in stocks listed in Denmark, Finland, andSweden.

3. The period is Oct 19, 2009 through Sep 10, 2010.

4. It spans almost all exchanges: NASDAQ-OMX, Chi-X, Bats,Burgundy, and Quote MTF (Turquoise not included).

5. Sample consists of 1.4 million trades by 57 clearing members in 242securities across 228 days.

66

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Data

1. A European Multilateral Clearing Facility (EMCF) sample of “tradereports” filed by its (anonymized) members.

2. It contains all trades in stocks listed in Denmark, Finland, andSweden.

3. The period is Oct 19, 2009 through Sep 10, 2010.

4. It spans almost all exchanges: NASDAQ-OMX, Chi-X, Bats,Burgundy, and Quote MTF (Turquoise not included).

5. Sample consists of 1.4 million trades by 57 clearing members in 242securities across 228 days.

67

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Data

1. A European Multilateral Clearing Facility (EMCF) sample of “tradereports” filed by its (anonymized) members.

2. It contains all trades in stocks listed in Denmark, Finland, andSweden.

3. The period is Oct 19, 2009 through Sep 10, 2010.

4. It spans almost all exchanges: NASDAQ-OMX, Chi-X, Bats,Burgundy, and Quote MTF (Turquoise not included).

5. Sample consists of 1.4 million trades by 57 clearing members in 242securities across 228 days.

68

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Data

1. A European Multilateral Clearing Facility (EMCF) sample of “tradereports” filed by its (anonymized) members.

2. It contains all trades in stocks listed in Denmark, Finland, andSweden.

3. The period is Oct 19, 2009 through Sep 10, 2010.

4. It spans almost all exchanges: NASDAQ-OMX, Chi-X, Bats,Burgundy, and Quote MTF (Turquoise not included).

5. Sample consists of 1.4 million trades by 57 clearing members in 242securities across 228 days.

69

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Data

1. A European Multilateral Clearing Facility (EMCF) sample of “tradereports” filed by its (anonymized) members.

2. It contains all trades in stocks listed in Denmark, Finland, andSweden.

3. The period is Oct 19, 2009 through Sep 10, 2010.

4. It spans almost all exchanges: NASDAQ-OMX, Chi-X, Bats,Burgundy, and Quote MTF (Turquoise not included).

5. Sample consists of 1.4 million trades by 57 clearing members in 242securities across 228 days.

70

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Clearing membersC Clearing members EMCF (December 2010)ABN AMRO Clearing Bank N.V. Numis Securities LtdBNP Paribas Securities Services S.A. UBS LtdBank of America Merrill Lynch Barclays Capital Securities Ltd.Citibank Global Markets and Citibank International Alandsbanken AbpJPMorgan Securities Ltd. Alandsbanken Sverige ABGoldman Sachs International Amagarbanken A/SSkandinaviska Enskilda Banken Arbejdernes Landsbank A/SKAS BANK N.V. Avanza Bank ABParel S.A. Carnegie Bank A/SDeutsche Bank AG Dexia Securities FranceCitigroup E-Trade BankMF Global UK Ltd Eik Bank A/SCACEIS Bank Deutschland EQ Bank Ltd.Danske Bank Evli Bank PlcABG Sundal Coller Norge FIM Bank Ltd.DnB NOR Bank GETCO Ltd.Deutsche Bank (London Branch) HandelsbankenHSBC Trinkaus & Burkhardt Je↵eries International Ltd.Istituto Centrale delle Banche Popolari Italiane SpA Knight Capital MarketsInteractive Brokers Lan & Spar Bank A/SKBC Bank N.V. Nordnet Bank ABNordea Nomura International PlcSwedbank Nykredit A/SCredit Agricole Cheuvreux Pohjola BankCredit Suisse Securities (europe) Ltd RBC Capital MarketsMorgan Stanley International Plc Saxo Bank A/SRBS Bank N.V. Spar Nord Bank A/SInstinet europe Ltd. Sparekassen Kronjylland A/SMorgan Stanley Securities Ltd.

Source: Zhu (2011)

ReferencesAdrian, Tobias and Markus K. Brunnermeier. 2011. “CoVaR.” Manuscript, Princeton.

Bisias, Dimitrios, Mark Flood, Andrew W. Lo, and Stavros Valavanis. 2012. “A Survey of SystemicRisk Analytics.” Manuscript, MIT.

Brunnermeier, Markus K. and Martin Oehmke. 2013. “Bubbles, Financial Crises, and Systemic

27

71

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Summary statistics

Table 1: Summary statistics, overall and cross-sectional

This table presents summary statistics based on 1,434,946 Nordic ‘trade’ reports sent to the clear-ing house by 55 clearing members. The sample covers 242 stocks listed in Denmark, Finland, orSweden. Each report contains a time stamp to the second, an anonymized clearing member ID,the symbol of a stock, price, a buy or sell indicator, and the size of the transaction in terms ofshares. The sample period consists of 228 trading days. It starts on October 19, 2010 and ends atSeptember 9, 2010. The sum of signed volume is zero for each stock.

Mean Std Min Median Max

Panel A: Overall summary statisticsDaily number of reports 6,293.6 699.0 1,135.0 6,426.5 7,663.0Daily volume (in mln shares) 160.9 42.1 8.1 155.5 342.4Daily volume (in mln euro) 1,809.8 475.1 272.4 1,762.3 3,649.6Volume per report (in 1000 shares) 25.6 114.1 0.0 2.6 18,631.8Volume per report (in 1000 euro) 287.6 1,067.6 0.0 36.1 142,271.3

Panel B: Cross-sectional summary statistics, based on clearing-member averagesDaily number of reports 114.4 143.7 0.0 64.9 736.4Daily volume (in mln shares) 2.9 4.2 0.0 0.7 20.8Daily volume (in mln euro) 32.9 46.9 0.0 7.8 222.4

Panel C: Cross-sectional summary statistics, based on stock averagesDaily number of reports 26.0 21.9 0.0 20.6 84.2Daily volume (in mln shares) 0.7 1.6 0.0 0.1 14.2Daily volume (in mln euro) 7.5 14.6 0.0 0.9 124.0

29

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Aggregate daily margin: actual margin and Margin(A)

Nov 2

009

Dec

2009

Jan 2

010

Feb 2

010

Mar

2010

Apr

2010

May 2

010

Jun 2

010

Jul 2010

Aug 2

010

Sep 2

010

0

100

200

300

400

500

600

700

800m

illio

n e

uro

Apr 22:Nokia

publishesQ1 results

May 2:Eurozoneand IMF agree tobailout Greece

Margin(A)MarginCCP

73

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Aggregate daily margin: actual margin and Margin(A)

Apr

21 2

010

Apr

24 2

010

Apr

27 2

010

Apr

30 2

010

May 0

3 2

010

May 0

6 2

010

May 0

9 2

010

May 1

2 2

010

0

200

400

600

800

1000m

illio

n e

uro

Margin(A)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

May 2: Eurozone and IMF agree to bailout Greece

Apr 22: Nokia publishes Q1 results

CrowdIx (right)

74

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Aggregate exposure distribution ‘Greek Bailout’

0 100 200 300 400 500 600 700 800Aggregate exposure (million euro)

0.000

0.002

0.004

0.006

0.008

0.010

0.012Pro

babili

ty d

ensi

ty

Greek bailoutMedian CrowdIx day benchmarkMin CrowdIx day benchmark

75

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Aggregate exposure distribution ‘Greek Bailout’

Figure 5: CCP aggregate exposure distribution

This figure plots the simulated probability density function of CCP aggregate exposure for May10, 2010. On this day the CCP collected most margin of all days in the sample. It was the periodright after the first Greek bailout. The crowding index was particularly high on that day, i.e.,CrowdIx=0.62. The aggregate exposure distribution is based on 100,000 simulations of securityreturns that are each assumed to be normally distributed. To illustrate the enhanced right-tail riskdue to crowding, the plot also contains the distributions for the median- and minimum-CrowdIxdays as a benchmark. The aggregate exposure for the benchmark days was multiplied by the ratioof aggregate CCP margin on the ‘Greek-bailout’ day and the benchmark day in order to make themcomparable in terms of the shape of the distribution. The exhibit below the graph reports the 90%,99%, and the 99.9% quantile for each distribution.

Date CrowdIxQ(0.90)(million

euro)

Q(0.99)(million

euro)

Q(0.999)(million

euro)

Greek bailout May 10, 2010 0.62 267 405 510Median CrowdIx day benchmark Jul 29, 2010 0.46 196 289 360Min CrowdIx day benchmark Nov 12, 2009 0.31 175 233 277

38

76

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Actual margin versus Margin(A)

0 5 10 15 20Member margin actually posted (million euro)

0

5

10

15

20M

arg

in(A

), m

odel-

implie

d m

em

ber

marg

in (

mill

ion e

uro

)CrowdIx=0.46

77

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Actual margin versus Margin(A)

Figure 6: Scatter plot of actual margin vs. model-implied margin

This figure contains three scatterplots of the margin that members actually posted versus the model-implied margin, Margin(A). The plots correspond to three days in the sample: the median-CrowdIxday and the two days for which the CCP charged highest aggregate margin. The exhibit below thescatterplots contains the ten largest positions in the trade portfolio of a member in the top-leftcorner and a member in the bottom-right corner.

Panel A: A representative day, i.e., CrowdIx at median level (July 29, 2010)

Clearing member 41

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

ER 23.1 23.1 13.7SHBA 14.5 14.5 8.6NOVNB -11.0 11.0 6.5NBH 10.1 10.1 6.0HMB 8.9 8.9 5.3FSPAA -7.2 7.2 4.3SAND 6.5 6.5 3.8VOLB 5.6 5.6 3.3BOLI 5.3 5.3 3.2ASSAB -4.5 4.5 2.7

Clearing member 6

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

FSPAA 17.1 17.1 8.3ASSAB -12.7 12.7 6.2SEBA 12.4 12.4 6.1NBH 10.6 10.6 5.2VWS 10.4 10.4 5.1SSABA -7.5 7.5 3.6MEO1V -6.4 6.4 3.1FUM1V 6.2 6.2 3.0SAND -5.6 5.6 2.7STERV -5.3 5.3 2.6

39

78

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Actual margin versus Margin(A)

0 50 100 150 200 250 300Member margin actually posted (million euro)

0

50

100

150

200

250

300M

arg

in(A

), m

odel-

implie

d m

em

ber

marg

in (

mill

ion e

uro

)CrowdIx=0.62

79

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Actual margin versus Margin(A)

Panel B: Greek bailout (May 10, 2010)

Clearing member 41

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

ER -99.9 99.9 13.5NOKI -65.7 65.7 8.9HMB -48.3 48.3 6.5NBH -35.6 35.6 4.8ATCOA -31.7 31.7 4.3SAND -29.4 29.4 4.0TLS1V -28.8 28.8 3.9FSPAA -28.3 28.3 3.8SHBA -22.7 22.7 3.1ZEN -20.6 20.6 2.8

Clearing member 12

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

SKFB 22.7 22.7 5.4NOKI 20.7 20.7 4.9NOVNB 18.7 18.7 4.5NBH 18.3 18.3 4.4SHBA 15.5 15.5 3.7GETIN 15.4 15.4 3.7ER 15.4 15.4 3.7ABBN -14.7 14.7 3.5ZEN -14.1 14.1 3.4SAND 13.8 13.8 3.3

40

80

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Actual margin versus Margin(A)

0 20 40 60 80 100Member margin actually posted (million euro)

0

20

40

60

80

100M

arg

in(A

), m

odel-

implie

d m

em

ber

marg

in (

mill

ion e

uro

)CrowdIx=0.72

81

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Actual margin versus Margin(A)

Panel C: Nokia reports Q1 (April 26, 2010)

Clearing member 41

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

NOKI -84.7 84.7 20.7ER 64.8 64.8 15.8FUM1V -39.2 39.2 9.6NDA1V -31.7 31.7 7.7VOLB 16.2 16.2 4.0HMB 15.5 15.5 3.8STERV 15.3 15.3 3.7TLS1V 9.8 9.8 2.4OUT1V -8.9 8.9 2.2SEN -8.3 8.3 2.0

Clearing member 12

StockNetPos(mln e)

AbsNetPos(mln e)

AbsNetPos(%)

VOLB 35.7 35.7 12.6TLS1V -17.4 17.4 6.2MAERS -15.2 15.2 5.4ABBN -13.2 13.2 4.7ALFA -9.7 9.7 3.4VWS -9.2 9.2 3.2TRELB -9.0 9.0 3.2TEL2B -8.7 8.7 3.1ASSAB 6.8 6.8 2.4BOLI 6.3 6.3 2.2

41

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Margin(A) sensitivity

Table 2: CCP risk sensitivity to security/risk factor

This table shows how sensitive CCP risk is to a particular security or risk factor. CCP risk ismeasured by the aggregate margin that it would collect when accounting for crowded risk, i.e.,Margin(A). Sensitivity could be used to identify securities or risk factors that members crowdedon. Sensitivity is reported in two ways. The table shows what the change in Margin(A) is whenone percentage point is added to the daily volatility of a particular risk factor. The further reportsthe elasticity of Margin(A) to change in the risk in the risk factor. Three days were picked from thesample: the median-CrowdIx day and the two days for which the CCP charged highest aggregatemargin. The risk factors considered are the market return (based on the STOXXNordic30), theNokia stock return, and the telecom sector return (based on STOXXTelecom).

Date CrowdIx Riskfactor

Margin(A)(million

euro)

Margin(A)on

f=0.01(million

euro)

Elasticity

Median CrowdIx day Jul 29, 2010 0.46 Market 128 81 0.91Nokia 128 11 0.15Telecom 128 46 0.46

Greek bailout May 10, 2010 0.62 Market 747 307 0.98Nokia 747 27 0.14Telecom 747 298 0.83

Nokia reports Q1 Apr 26, 2010 0.72 Market 644 116 0.19Nokia 644 147 1.05Telecom 644 -2 -0.00

32

83

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

84

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

85

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

86

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

87

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.

3.2 It allocates such risk appropriately across members, i.e., the more amember joins crowded-trades the more margin he has to contribute.

3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

88

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.

3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

89

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.

3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

90

Page 91: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.

3.5 It extrapolates standard practice which should make introductioneasier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

91

Page 92: Motivation Objective Measure+Allocation Illustration ...€¦ · Motivation Objective Measure+Allocation Illustration Conclusion AppendixReferences Motivation ESRB annual report 2012,

Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

92

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Conclusion

1. Crowded trades constitute a hidden risk to a CCP.

2. CrowdIx developed as a “thermometer” for crowded-trade risk.

3. Margin(A) is proposed as an alternative margin methodology. Itsmain benefits are

3.1 It accounts for crowded risk.3.2 It allocates such risk appropriately across members, i.e., the more a

member joins crowded-trades the more margin he has to contribute.3.3 It is easily computed.3.4 An analytic result helps identifying crowded-trade securities.3.5 It extrapolates standard practice which should make introduction

easier.

4. The implementation on real data shows that it matters, in particularwhen the market gets turbulent.

93

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Crowded Risk as a Systemic Concern for CentralClearing Counterparties

Albert J. Menkveld

VU University Amsterdam, Tinbergen Institute, Duisenberg school of finance

July 3, 2014

94

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Outline

Motivation

Objective

Measure+Allocation

Illustration

Conclusion

Appendix

95

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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References

Appendix A: Max crowding benchmark, A

1. If all members would trade the same risk factor, then ∃n ∈ RI s.t.∀j :

Xj = νj × (n′X ) , νj ∈ R.

2. Then,Σ = n′Ωn

1×1×(νjν′j

)J×J

.

3. Without loss of generality, let n′Ωn = 1.

4. For member by member portfolio risks to remain unchanged, oneneeds ∀j :

ν2j = σ2

j ⇒ νj = ±√σ2j . (1)

5. In addition, the aggregate (signed) trade is zero:∑j

νj = 0. (2)

96

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Appendix A: Max crowding benchmark, A

1. The member trade reallocation that yields the maximum crowdingbenchmark is

argmaxν1,ν2,...,νJ

min

∑j

ν+j ,∑j

ν−j

subject to (1), (3)

where

ν+j := max (νj , 0) and ν−j := max (−νj , 0) .

2. If∑

j ν+j =

∑j ν

+j then trade reallocation is perfect. No portfolio

risk is left unallocated.

97

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Appendix A: Max crowding benchmark, A

1. The trade reallocation is a combinatorial problem that is NP hard.

2. It maps into a one-dimensional bin packing problem (Coffman,Garey, and Johnson, 1996). Can all items be packed into two bins ofsize (1/2)

∑j σj? If not, how much can be packed into two such

bins? The minimum of the two bins can be matched, i.e., buyersbuy this amount from sellers.

3. First fit descending (FFD) algorithm solves the offline bin packingproblem in O(J log J) time (brute force requires 2J).

4. Why FFD instead of alternative approaches?

4.1 Average-case analysis: If item size is drawn from U[0, 1/2] forone-unit bins then Coffman, Garey, and Johnson (1996, p. 39) claim“FFD is typically optimal.”

4.2 Worst-case analysis: If all items are smaller than 1/2 then FFD doesas well its closest contender MFFD (modified first fit descending)(Coffman, Garey, and Johnson, 1996, p. 16-19).

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Appendix B: Q&A

1. Is it reasonable to assume equity returns are normal? In theimplementation the return distribution is assumed to beconditionally normal. Time-varying volatility is accounted for bycalculating the covariance matrix as an exponentially weightedaverage of the outer product of historical daily returns.2

2. Why not divide total risk by the number of members and usethat as base for a crowding index? Such alternative approachdoes not recognize that individual member portfolio risk isaccounted for in existing member by member approaches. Considerthe case that only member one and member two engaged in a trade.Dividing total portfolio risk by J > 2 suggests that there werecrowded trades not accounted for. This is not the case here.

2EWMA(0.94) which is the RiskMetrics standard for daily equity returns.

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