Introduction to the handbook on cyclical composite indicators
Composite indicators
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Enter Presentation Title Here
Composite Indicators
&
Senior Management ReportingLondon
January 17th & 18th, 2006
Charles Taylor
Director, Operational Risk
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Agenda
Basic Concepts
Transforming Individual KRIs
Creating a Composite Indicator
Senior Management Reporting
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Agenda
Basic Concepts
Transforming Individual KRIs
Creating a Composite Indicator
Senior Management Reporting
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The Basic Problem
Combining apples and oranges
Combining things in a way that will highlight what senior management needs to focus on
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KRIs & Management LevelsBasic Concepts
Location KRI Type Management Level
Local Individual Lower/Mid-Level
Organization Composite Mid-Level/Senior
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KRIs & Management LevelsBasic Concepts
Location KRI Type Management Level
Local Individual Lower/Mid-Level Transformation – apples to apples
Aggregation – flagging what should be flagged
Organization Composite Mid-Level/Senior
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Individual KRI ThresholdsBasic Concepts
Junior management is managing the risk; no mid-level attention required
Junior management is managing the risk; mid-level management should monitor the indicator
Management should escalate from junior to mid-level management
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Composite KRI ThresholdsBasic Concepts
Mid-level (or junior) management is managing the risk; no senior attention required
Mid-level management is managing the risk; senior management should monitor the indicator
Management should escalate from mid-level to senior management
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Ranges of Individual KRIsBasic Concepts
Low Low Exected High HighUnderlying KRIs Red Yellow /Target Yellow Red
L1 L0 E H0 H1
Staff Turnover (%) 1 3 8 14 20Staff Training Days (days/year) 4 8 15 na na
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Ranges of Individual KRIsBasic Concepts
Low Low Exected High HighUnderlying KRIs Red Yellow /Target Yellow Red
L1 L0 E H0 H1
Staff Turnover (%) 1 3 8 14 20Staff Training Days (days/year) 4 8 15 na na
L0L1 H1H0E
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Ranges of Individual KRIsBasic Concepts
Low Low Exected High HighUnderlying KRIs Red Yellow /Target Yellow Red
L1 L0 E H0 H1
Staff Turnover (%) 1 3 8 14 20Staff Training Days (days/year) 4 8 15 na na
L0L1 H1H0E
Typically, KRIs go: red-yellow-green-yellow-red or red-yellow-green or green-yellow-red
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Basic Concepts
Individual KRIs
Staff Turnover
0
5
10
15
20
25
1 5 9 13 17 21 25 29 33 37 41 45
Months
Perc
ent
Training
02468
10121416
1 5 9 13 17 21 25 29 33 37 41 45
Months
Ave
rage
day
s in
last
12
mos
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Basic Concepts
Individual KRIs
Staff Turnover
0
5
10
15
20
25
1 5 9 13 17 21 25 29 33 37 41 45
Months
Perc
ent
Training
02468
10121416
1 5 9 13 17 21 25 29 33 37 41 45
Months
Ave
rage
day
s in
last
12
mos
The ranges and measures are very different before we transform the KRIs
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Basic Concepts
Individual KRIs
Staff Turnover
0
5
10
15
20
25
1 5 9 13 17 21 25 29 33 37 41 45
Months
Perc
ent
Training
02468
10121416
1 5 9 13 17 21 25 29 33 37 41 45
Months
Ave
rage
day
s in
last
12
mos
The thresholds are very different too
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Agenda
Basic Concepts
Transforming Individual KRIs
Creating a Composite Indicator
Senior Management Reporting
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Transformation to T-ValueTransforming Individual KRIs
T-V
alue
KRI L0L1 H1H0
1
2
The graphic presentation of the transformation
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Transformation to T-ValueTransforming Individual KRIs
T-V
alue
KRI L0L1
1
2
The graphic presentation of the transformation for a red-yellow-green KRI
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Transformation to T-ValuesTransforming Individual KRIs
T = 1 when L0< KRI < H0
T = (KRI + L1 – 2*L0 )/ (L1 – L0) when KRI < L0
T = (KRI + H1 – 2*H0)/(H1 – H0) when KRI > H0.
The algebraic presentation of the transformation
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Individual KRIs: T-ValuesTransforming Individual KRIs
Staff Turnover T-value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Training T-Value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9
13 17 21 25 29 33 37 41 45
Months
T-Va
lue
The transformed ranges and measures are now the same
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Individual KRIs: T-ValuesTransforming Individual KRIs
Staff Turnover T-value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Training T-Value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9
13 17 21 25 29 33 37 41 45
Months
T-Va
lue
And so are the thresholds
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Individual KRIs: T-ValuesTransforming Individual KRIs
Staff Turnover T-value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Training T-Value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9
13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Does this work really? Three ranges of months are red in the two graphs …
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Individual KRIsTransforming Individual KRIs
Staff Turnover
0
5
10
15
20
25
1 5 9 13 17 21 25 29 33 37 41 45
Months
Perc
ent
Training
02468
10121416
1 5 9 13 17 21 25 29 33 37 41 45
Months
Ave
rage
day
s in
last
12
mos
… exactly as they were for the untransformed KRIs. So it does work!
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Individual KRIs: T-ValuesTransforming Individual KRIs
Staff Turnover T-value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Training T-Value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9
13 17 21 25 29 33 37 41 45
Months
T-Va
lue
So, now we can combine “apples” to “apples.”
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Agenda
Basic Concepts
Transforming Individual KRIs
Creating a Composite Indicator
Senior Management Reporting
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Senior Management Focus
Are many small things going slightly wrong in (one or related) area(s)? Are any things going gravely wrong in any (unrelated but similar) areas?
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Basic DistinctionsCreating a Composite Indicator
Related indicators reflect factors that compound one another in their influence on a common underlying risk
Eg: staff turnover and training
Unrelated indicators reflect factors that do not impact one another
Eg: staff turnover in London and staff turnover in Sydney
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Basic PrinciplesCreating a Composite Indicator
Related T-Values indicators we combine by “multiplying” them:
NB: green x green = green, because 1 x 1 = 1. yellow x yellow can equal yellow or red, because yellows on average between 1 and square root 2 multiply to less than 2, and yellows on average above square root 2 multiply to more than 2
Unrelated T-Values we combine by taking the “maximum”:
NB: then the combined indicators tells us if anything really serious is happening in any of the covered areas
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RefinementsCreating a Composite Indicator
We should be able to:
Weight the influence of different individual KRIs differently
adjustable weights for each T-Value
Adjust the overall composite indicator to reflect how closely and how soon senior management wants to be alerted to issues – their appetite for risk. (We want “red” to be “higher” for senior management than for middle management: how much higher?)
scaling parameters that affect the thresholds up and down and the sensitivity of the composite to changes in the weighted underlying T-Values
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Individual KRIs: T-ValuesCreating a Composite Indicator
Staff Turnover T-value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
Training T-Value
0.0
0.5
1.0
1.5
2.0
2.5
1 5 9
13 17 21 25 29 33 37 41 45
Months
T-Va
lue
The two component individual KRIs …
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Aggregation FormulaeCreating a Composite Indicator
Related I = max [1, a * [T(1)w(1) * T(2)w(2)]b]
Unrelated I = max [1, a * max [T(1)w(1), T(2)w(2)]b]
where I = composite indicatorT(i) = the ith individual KRIw(i) = the ith KRI weight, Σw(i) = 1, i = 1,2a and b = “appetite” parameters
It is straightforward to generalize to more than 2 indicators
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Staff Quality IndexCreating a Composite Indicator
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Months
T-Va
lues Turnover
Training
SQI
a = 0.2b = 1.2w(1) = 2w(2) = 2
... And the Composite Staff Quality Index (SQI)
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Adjusting Appetite and WeightsCreating a Composite Indicator
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue a = 0.2
b = 1.2w(1) = 2w(2) = 2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue a = 0.2
b = 0.9w(1) = 2w(2) = 2
6 – 8, 19, 23 - 24 6 - 8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1 5 9 13 17 21 25 29 33 37 41 45
Months
T-Va
lue
a = 0.2b = 0.6
w(1) = 5w(2) = 1
7 - 10
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Agenda
Basic Concepts
Transforming Individual KRIs
Creating a Composite Indicator
Senior Management Reporting
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The One-Page SummarySenior Management Reporting
Staff Quality Index ___ Audit Issue Management Index ___
Business Continuity Index ___ Failed Customer Interactions Index ___
Information Security Index ___ Information Technology Index ___
Operational Losses ___Process Breaks Index ___
Profitability Index ___Policy Exceptions Index ___
Regulatory Index ___Change Management Index ___
EuropeNorth AmericaAsia
Trading and Sales Payments and Settlement Retail BankingBrokerage
Maybe the trading and sales business in North America is growing too fast? Drill down and see…
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Enter Presentation Title Here
Composite Indicators
&
Senior Management ReportingLondon
January 17th & 18th, 2006
Charles Taylor
Director, Operational Risk