Eric S. Rosengren

English

Research Papers in Economics

Capital Allocation for Operational Risk
Implementation Challenges for Bank Supervisors
Eric Rosengren
Senior Vice President
Federal Reserve Bank of Boston
Joint Operational Risk Conference
November 15, 20012
Goals of Bank Supervisors
• Allocate capital according to a risk-focused approach to the
quantification of operational risk
• Provide incentives for banks to measure and manage operational risks
– Promote sound internal policies / controls / procedures
– Motivate investment in operational risk infrastructure to reduce
operational risk
• Ensure appropriate consideration of stress testing / systemic risk
– Consideration of systemic implications of operational risk decisions made
by individual firms3
Role for OpRisk Quantification
• Enables measurement of capital based on historical experience of firm
– Most accurate measure of idiosyncratic risk of individual firms
– Rewards firms that can reduce operational risk
• Improves bank decision making
– Provides framework for explicitly measuring gains from reducing risk
• Provides a mechanism for better understanding “tail events,” those
that may be outside a bank’s historical experience
• Provides method for measuring the effect of risk mitigation tools4
FRB Boston Operational Loss Data Initiative
• Several institutions, of varying size and product mixes, provided us
with operational loss data
• Data is considered strictly confidential
– Bank-specific information is used solely for supervisory purposes
• We have detailed discussions with banks regarding data collection
issues and quantification methods
• General observations about quantification methods:
– AMA methods are within the reach of most large institutions
• main cost is data collection
• with data, loss distributions can be calculated relatively easily5
Data Discussion
• To maintain the confidentiality of bank-specific data, all empirical
examples provided in this presentation are based on a “constructed”
database, not actual bank-level data.  The database was constructed in
a manner so that it would be impossible to uncover bank-specific
information, but still provide empirical results that mirror our general
findings from actual data.
• The constructed database:
– omitted several banks that supplied us with data
– combined business lines from several banks
– contains no bank in its entirety
– transformed data that was used
• Thus, the axes on each of the graphs in this presentation are not
relevant and not reflective of any bank.6
Overview of Quantification Techniques
Generally, the estimation of operational loss distribution involve 3 steps:
1. Estimating a frequency distribution
2. Estimating a severity distribution
3. Running a statistical simulation to produce a loss distribution
Severity Distribution
$ Value of a Loss Event
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Frequency Distribution
N umber of Loss Events per Year
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Overview of Quantification Techniques
• The estimated operational loss distribution would take the
form of something similar to:
Severity of Loss
Probability of Loss
Expected Loss -
Expense / Provision
Unexpected Loss –
Reserves / Insurance / Capital
Catastrophic Loss -
Insurance ?
.108
Quantification: Distributional Assumptions
• Selection of distributional assumptions are important
– Parametric vs. Non-Parametric
– Appropriate distributional assumption likely differs
• by business lines
• by institution
• Supervisors must be concerned about incentives banks have to
choose a specific methodology9
Distributional Assumptions Matter
Non-Parametric Parametric
Frequency of Operational Loss Events: BL1
Non-Parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
960 1,080 1,200 1,320 1,440 1,560 1,680 1,800 1,920 2,040 2,160 2,280 2,400
Number of Occurrences in One Year
D
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Median = 1,440
99.0% = 1,920
99.5% = 1,970
99.9% = 2,120
Frequency of Operational Loss Events: BL1
Parametric Technique
0.00
0.05
0.10
0.15
0.20
0.25
Bin 1,330 1,370 1,410 1,450 1,490 1,530 1,570
Number of Occurrences in One Year
D
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Median = 1,449
99.0% = 1,540
99.5% = 1,550
99.9% = 1,564
Operational Loss Distribution: 1 Year Time Horizon, BL1
Non-parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99
Total Loss Amount in One Year (millions $)
F
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Median = $56M
99.0% = $78M
99.5% = $80M
99.9% = $85M
Operational Loss Distribution: 1 Year Time Horizon, BL1
Parametric Technique
0.00
0.05
0.10
0.15
0.20
0.25
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
Total Loss Amount in One Year (millions $)
F
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c
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Median = $56.5M
99.0% = $61.5M
99.5% = $62.1M
99.9% = $62.8M10
Quantification: Scaling of Data
• Why scale data?
– Level and mix of business activity changed so that historic data are
not reflective of current loss rates
• impact on frequency distribution - more/less frequent events
• impact on severity distribution -  exposure increases/decreases
– Thus, blindly using historical operational loss data can be misleading
• Conceptually, scaling is straightforward
• In practice, implementing is quite difficult
– What variable / methodology  should be used to scale?
– The return of the exposure indicator?11
Scaling Matters
Non-Parametric, No Scaling of Data Non-Parametric, Scaling of Frequency Data
Frequency of Operational Loss Events: BL1
Non-Parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
960 1,080 1,200 1,320 1,440 1,560 1,680 1,800 1,920 2,040 2,160 2,280 2,400
Number of Occurrences in One Year
D
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Median = 1,440
99.0% = 1,920
99.5% = 1,970
99.9% = 2,120
Operational Loss Distribution: 1 Year Time Horizon, BL1
Non-parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99
Total Loss Amount in One Year (millions $)
F
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Median = $56M
99.0% = $78M
99.5% = $80M
99.9% = $85M
Frequency of Operational Loss Events: BL1
Scaled Frequency Data
Non-Parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600
Number of Occurrences in One Year
D
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Median = 1,673
99.0% = 2,224
99.5% = 2,280
99.9% = 2,431
Operational Loss Distribution: 1 Year Time Horizon, BL1
Scaled Frequency Data
Non-parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
36 42 48 54 60 66 72 78 84 90 96 102 108
Total Loss Amount in One Year (millions $)
F
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Median = $65M
99.0% = $90M
99.5% = $93M
99.9% = $100M12
Scaling Matters
Non-Parametric, Scaling of Frequency and
Severity Data Impact of Scaling
• Required capital at the 99.9%
confidence level, no scaling of
data: = 85M
• If scale frequency data:
= 100M (18% increase)
• If scale both frequency and
severity data:
= 111M (30% increase)
Frequency of Operational Loss Events: BL1
Scaled Frequency Data
Non-P arametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600
Number of Occurrences in One Year
D
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Median = 1,673
99.0% = 2,224
99.5% = 2,280
99.9% = 2,431
Operational Loss Distribution: 1 Year Time Horizon, BL1
Scaled Frequency and Severity Data
Non-parametric Technique
0.00
0.02
0.04
0.06
0.08
0.10
0.12
39 45 51 57 63 69 75 81 87 93 99 105 111 117
Total Loss Amount in One Year (millions $)
F
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Median = $72M
99.0% = $100M
99.5% = $103M
99.9% = $111M13
Implementation Details are Important
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NonPar, Scaled Freq/Sev
NonPar, Scaled Freq
NonPar, No Scaling
Par, No Scaling
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Total Loss Amount in One Year (millions $)
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Sensitivity of Loss Distribution to Modeling Assumptions
Note: Same Underlying Data
99.9% Confidence:
Par, No Scaling:                       63M
NonPar, No Scaling:              85M
NonPar, Scaling Freq:          100M
NonPar, Scaling Freq/Sev:  111M14
Quantification: How to Handle “Tail Events”
• How does a bank with no experience with high-severity events incorporate
the possibility that such an event could occur at their institution?
– External data?
– Scenario analysis?
• How does a bank that experienced a high-severity event deal with that
event in their quantification analysis?
– Loss distributions are sensitive to the inclusion of extreme events
– How long should the bank retain the extreme event in their database?
– If problem is corrected / controls enhanced, should event remain in
database?15
Quantification: Risk Mitigation Techniques
• Insurance: outstanding issues regarding conversion of
operational risk to credit / legal risk
• Insurance as capital offset:
– Using information about deductibles/limits, “event policies” can
be thought of as altering the severity  distribution
• Incorporating this mitigation technique into the quantification
analysis can significantly affect the tail of the operational loss
distribution
• Quantification techniques discussed above provide firms with
the framework to determine appropriate insurance coverage16
Benefits of Quantifying OpRisk
• Allows banks to identify operational loss outcomes that they have
exposure to, but have yet to experience.
– example: bad cluster of high frequency, low impact events
• Provides a framework for modeling extreme events.
– “Scenario Analyses” of low frequency, high impact events
– example: business interruption
• Large potential payoff to banks :
– Help incorporate the quantification of “risk reduction” into the decision
making process of whether to make a particular technological
investment or not.
– Banks that measure and manage operational risk can significantly
reduce costs
– Banks that measure and manage operational risk are likely
to be less susceptible to systemic problems17
Significant Challenges for Bank Supervisors
• What modeling assumptions are reasonable?
• Many different types of models will be employed by banks
– models idiosyncratic to firm
– models idiosyncratic to business line
– models idiosyncratic to controls
• Attaining flexible firm-specific modeling and consistency of
treatment across organizations will be difficult
• Supervisory staff will need to understand modeling issues as well as
the nature of operational risk for different business lines.

Capital allocation for operational risk: implementation challenges for bank supervisors

http://www.bostonfed.org/bankinfo/conevent/oprisk/rosen.pdf

Capital allocation for operational risk: implementation challenges for bank supervisors

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Research Papers in Economics