composite indicators

1

Enter Presentation Title Here

Composite Indicators

&

Senior Management ReportingLondon

January 17th & 18th, 2006

Charles Taylor

Director, Operational Risk

2

Agenda

Basic Concepts

Transforming Individual KRIs

Creating a Composite Indicator

Senior Management Reporting

3

Agenda

Basic Concepts




4

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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L1 L0 E H0 H1


L0L1 H1H0E

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L1 L0 E H0 H1


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




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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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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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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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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




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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


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




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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