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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
3
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
4
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
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
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
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.
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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
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
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
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
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
14
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
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
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
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
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
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
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
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
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
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
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
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
27
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) .
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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
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
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
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
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
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?
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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
2π
)σkσlM(ρkl)
M(ρ) =
[12π + arcsin (ρ)
]ρ+
√1− ρ2 − 1
π − 1
40
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
2π
)σkσlM(ρkl)
M(ρ) =
[12π + arcsin (ρ)
]ρ+
√1− ρ2 − 1
π − 1
41
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
2π
)σkσlM(ρkl)
M(ρ) =
[12π + arcsin (ρ)
]ρ+
√1− ρ2 − 1
π − 1
42
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
2π
)σkσlM(ρkl)
M(ρ) =
[12π + arcsin (ρ)
]ρ+
√1− ρ2 − 1
π − 1
43
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Noncrowded trades
security/
risk factor 1n1n2
n3
n4
security/
risk factor 2
45
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
2π
1111
, var(E ) =1
2π
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
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
2π
1111
, var(E ) =1
2π
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
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
2π
1111
, var(E ) =1
2π
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Crowded trades
security/
risk factor 1n1n2
n3n4
security/
risk factor 2
49
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
2π
1111
, var(E ) =1
2π
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
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
2π
1111
, var(E ) =1
2π
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
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
2π
1111
, var(E ) =1
2π
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
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.
58
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
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
2π
)σlM(ρkl)
2. Therefore,
Margin(A) =∑j
√1
2πσj︸ ︷︷ ︸
Member-specific
part (old)
+ ασj∑l
1
std(A)
(π − 1
2π
)σlM(ρkl)︸ ︷︷ ︸
Crowded-trade part (new)
61
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
2π
)σlM(ρkl)
2. Therefore,
Margin(A) =∑j
√1
2πσj︸ ︷︷ ︸
Member-specific
part (old)
+ ασj∑l
1
std(A)
(π − 1
2π
)σlM(ρkl)︸ ︷︷ ︸
Crowded-trade part (new)
62
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
2π
σf
σjBjj
1.2∂
∂σfstd(A) =
(π − 1
4π
)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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
65
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
72
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
82
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
84
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
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
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
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
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
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
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
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
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
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Outline
Motivation
Objective
Measure+Allocation
Illustration
Conclusion
Appendix
95
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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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Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
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.
99
Motivation Objective Measure+Allocation Illustration Conclusion Appendix References
Acharya, Viral V. 2009. “A Theory of Systemic Risk and Design ofPrudential Bank Regulation.” Journal of Financial Stability 5:224–255.
Acharya, Viral V. and Alberto Bisin. 2011. “Counterparty RiskExternality: Centralized versus Over-the-Counter Markets.”Manuscript, NYU.
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