Applications of @Risk in Risk Financing Strategy
21 October 2010
Sydney
Andrew Kight
Why undertake risk analytics?
Total Cost of Insurable Risk Per $1,000 Revenue
25th
75th
Organisations that:
percentile
Median percentile
Use risk analytics
$3.19
$5.52
$12.12
Do not use risk analytics
$3.61
$7.59
$13.84
Difference
-27.3%
Source: Aon‟s 2009/10 Australasian Risk Management Benchmarking Survey
 Median TCOIR per $1,000 Revenue is 27.3% less for organisations that use
risk analytics
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Risk financing strategy
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Case Study A – Loss Modelling
Details
 Commercial Motor Vehicle Policy
 Large Motor Fleet – about 1,000 vehicles
 Use risk analytics to decide on most efficient retention level
Process
 Use historical loss data to forecast future losses at various retention levels
Benefits
 Retention optimisation
 Market negotiations
 Budgeting for expected losses
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Process






Summarise loss history
Incorporate changes to exposure and inflation
Select appropriate frequency and severity distributions
Set up model to analyse various retention levels
Run simulation and produce results
Use results to assist organisation with risk financing strategy
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Loss Summary
Year
2006
2007
2008
2009
2010
2011
No. of
Claims
241
245
254
255
224
Paid
Outstanding
813,441
1
539,611
1
936,089
0
1,150,796
4,604
838,294
239,310
Incurred
813,442
539,612
936,089
1,155,400
1,077,605
Pro-rata
1.0
1.0
1.0
1.0
1.2
Exposure
830
860
950
990
990
1,020
Inflation
1.19
1.15
1.11
1.07
1.04
1.00
Scaled
No. of
Claims
296
291
273
263
277
Revalued
Ultimate
1,187,273
734,420
1,114,333
1,275,199
1,378,942
Average
244
855,646
48,783
904,430
280
1,138,033
Std Dev
13
221,103
106,526
242,564
14
246,344
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Fit Distributions
Severity Distribution
Not a good fit
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Fit Distributions
Severity Distribution
 Attritional - Less than $500
– RiskLognorm(6650,2500)
 Losses - $500 to $10k
– RiskLognorm(2450,2150,RiskTruncate(500,10000))
 Large Losses – Greater than $10k
– RiskLognorm(21000,42000,RiskTruncate(10000,500000))
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Fit Distributions
Year
2006
2007
2008
2009
2010
2011
Less than
$500
Attritional
9,444
9,622
5,074
5,422
3,619
$500 to
Greater than
$10,000
$10,000
Frequency
Frequency
231
21
231
6
224
12
212
21
240
20
Average
6,636
228
16
Std Dev
2,730
10
7
Attritional
Large Losses (Greater than $10k)
RiskLognorm(6650,2500)
RiskPoisson(16)
Losses ($500 to $10k)
RiskPoisson(228)
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RiskCompound
Type
Banding
Distribution
p1
p2
lower
upper
Attritional
<$500
Lognormal
6,650
2,500
Frequency
$500-$10k
Poisson
228
Frequency
>$10k
Poisson
16
Severity
$500-$10k
Lognormal
2,450
2,150
500
10,000
Severity
>$10k
Lognormal
21,000
42,000
10,000
500,000
RiskCompound(FreqDist, SevDist, Attachment, Limit)
Gross Losses
RiskLognorm(6650,2500)
+ RiskCompound(RiskPoisson(228),RiskLognorm(2450,2150,RiskTruncate(500,10000)))
+ RiskCompound(RiskPoisson(16),RiskLognorm(21000,42000,RiskTruncate(10000,500000)))
= Gross Losses
Retained Losses
Eg. RiskCompound(FreqDist, SevDist, 0, 500)
Transferred Losses
Eg. RiskCompound(FreqDist, SevDist, 500)
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Results
Sample Value
1,324,261
139,651
Deductible
Mean
Std Dev
Gross
1,154,433
234,105
Retained Losses
500
2,000
5,000
128,654 401,974 601,984
8,235
26,636
44,643
Transferred Losses
500
2,000
5,000
1,025,779 752,459 552,449
231,778 226,137 217,690
Key Percentiles
Median
75th Percentile
90th Percentile
95th Percentile
99th Percentile
1,124,203
1,290,783
1,466,617
1,583,114
1,828,934
128,545
134,164
139,284
142,372
148,108
995,427 721,563 520,320
1,160,210 882,301 676,352
1,334,443 1,054,024 844,604
1,450,666 1,170,453 958,712
1,695,083 1,410,880 1,194,138
RiskMean(„Sample Value‟)
446,063
401,804
419,812
436,233
446,416
464,999
681,031
601,489
631,771
659,542
676,202
708,871
1,184,609
878,197
RiskPercentile(„Sample Value‟,0.75)
RiskStdDev(„Sample Value‟)
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643,230
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Pricing
Deductibles
Average Losses
Risk Margin
Expenses (10%)
Profit (10%)
Technical Pricing
500
1,025,779
134,430
128,912
143,236
1,432,358
2,000
752,459
129,841
98,033
108,926
1,089,260
5,000
552,449
123,903
75,150
83,500
835,002
 Technical Pricing has the following benefits:
– Can be used by brokers to negotiate competitive terms
– Can be used by organisations to test for reasonable market rates
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Deductible Optimisation
Option
(Underlying) Deductible
Aggregate Deductible
Option 1
$500
Option 2
$2,000
Option 3
$5,000
Option 4
$0
$1,350,000
Premium
Statutory charges
Total Premium
Claims handling fee
Average retained losses
Average Total Cost of Insurable Risk (TCOIR)
$1,350,000
$74,250
$1,424,250
$0
$128,654
$1,552,904
$1,100,000
$60,500
$1,160,500
$0
$401,974
$1,562,474
$900,000
$49,500
$949,500
$0
$601,984
$1,551,484
$300,000
$16,500
$316,500
$75,000
$1,122,080
$1,513,580
1 in 4 Year High TCOIR
1 in 10 Year High TCOIR
$1,558,414
$1,563,534
$1,580,312
$1,596,733
$1,581,271
$1,609,042
$1,682,283
$1,741,500
Option 4 has the lowest TCOIR on average,
but has a higher TCOIR in worse loss years.
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Results
TCOIR (Premium + Retained Losses) & Volatility
Millions
Total Cost of Insurable Risk Comparison
$2.0
Option 4 has the lowest TCOIR on
average, but has greater volatility.
$1.8
$1.6
$1.4
$1.2
$1.0
$0.8
$0.6
$0.4
$0.2
$0.0
Option 1
$500 e&e
Total Premium
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Option 2
$2k e&e
Claims handling fee
Average retained losses
Option 3
$5k e&e
1 in 4 Year High TCOIR
Option 4
$1.35m Agg
1 in 10 Year High TCOIR
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Results
Millions
Total Cost of Insurable Risk Comparison
Confidence Levels Chart
$1.8
$1.7
$1.6
$1.5
TCOIR
$1.4
Option 4 costs more in
worse loss years, however,
the total cost is capped,
allowing for a known
maximum cost.
$1.3
$1.2
Option 4 provides significant
savings in good loss years, thus
providing great incentive for
investment in risk management to
reduce claim costs.
$1.1
$1.0
$0.9
$0.8
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
Confidence Levels
Option 1
$500 e&e
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Option 2
$2k e&e
Option 3
$5k e&e
Option 4
$1.35m Agg
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95%
Budgeting
Option
Mean
Std Dev
Key Percentiles
Median
75th Percentile
90th Percentile
95th Percentile
99th Percentile
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TCOIR
Option 4
1,513,580
175,548
APRA‟s Prudential Standard GPS 310 states:
“… the valuation of insurance liabilities …
must include a risk margin over and above the
central estimate.”
75th Percentile: $1,682,283
1,515,703
1,682,283
1,741,500
1,741,500
1,741,500
Mean Plus 50% of Std Dev: $1,601,354
Irrespective of what amount is budgeted for,
this analysis provides information regarding
the unbudgeted risk that an organisation is
subject to (ie. how much more may be
required in bad loss years) and this amount
can be measured against an organisation‟s
risk appetite.
15
Other uses
 Long-tailed risk classes
– Public & Products Liability
– Medical Indemnity
– Professional Indemnity
– Workers Compensation
 Multi-class analysis
– Captive
– Internal Managed Fund
 It doesn‟t need to be an insurable risk!
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Risk financing strategy
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Case Study B – Limit Analysis
Source: US Coast Guard: 100421-G-XXXXL- Deepwater Horizon fire
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Case Study B – Limit Analysis
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Case Study B – Limit Analysis
BP believed its own safety
procedures had made such a
disaster impossible.
“The industry had drilled for 20
years in deep water without a
blow out”
As a result of this disaster, BP in
now “looking very closely across
the company at the low
probability, high impact risks”
Source: The Age – BP boss defends safety record
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Case Study B – Limit Analysis
Details
 Oil and gas exploration organisation
 Use risk analytics to decide on appropriate Public & Products Liability limit
Process
A deterministic approach to modelling:
 Identify worst case scenario
 Assess insurable impacts
 Quantify insurable loss
Key Benefits
 Set policy limits with confidence that underlying risks are better understood
 Demonstrate to the board and stakeholders a structured and auditable
process to selecting an appropriate limit of liability
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What is the „worst case‟ scenario?
Step 1 – Identify „worst case‟ scenario
 Well blowout resulting in oil spill
Step 2 – Assess insurable impacts
SCENARIO
IMPACTS
Clean Up Costs
Well blowout
resulting in oil
spill
Injury / death to
employees / contractors
Consequential Loss to
small businesses
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Parameters
SCENARIO
Well blowout
resulting in oil
spill
IMPACTS
PARAMETERS
Prod Volume
% Released
(t/day)
Clean up
cost (per
tonne)
Clean Up Costs
Spill in days
Injury / death to
employees / contractors
No. at risk
% Injured /
Dead
Consequential Loss to
small businesses
No. of
businesses
affected
Average
Time of
financial loss % successful
interruption
per business
claim
(days)
per day ($)
% Who
Claim
Average
Claim /
Person ($)
Step 3 – Quantify insurable loss
 Estimate parameters with triple point estimates
– ie. minimum, most likely, maximum
 What is the basis for parameter estimation?
– Industry knowledge
– Research
– Underwriting information
– Workshop the risk with key personnel within the organisation
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RiskPert
RiskPert(minimum, most likely, maximum)
 Why use the PERT distribution?
– It is an easily understandable distribution
– In the event of a skewed distribution, its smooth shape places less emphasis on the direction of the skew
 Issues with PERT distribution?
– It is bound on both sides, which may not be adequate for some modelling purposes where it is desired to
capture tail or extreme events.
PERT DISTRIBUTION CHARACTERISTICS
(Min = 0, Max = 20)
Pert(0, 10, 20)
Pert(0,
0, 20)
Pert(0,
15, 20)
Pert(0, 5, 20)
Pert(0, 10, 20)
0.10
0.12
0.12 0.30
0.30
0.10
0.10 0.25
0.25
0.08
0.08 0.20
0.20
0.06
0.06 0.15
0.15
0.04
0.04 0.10
0.10
0.02
0.02 0.05
0.05
0.00
0.00 0.00
0.00
0.10
0.09
0.09
0.08
0.08
0.07
0.07
0.06
0.06
0.05
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0
20
20
18
18
16
16
14
14
12
12
10
8
10
6
8
6
4
4
2
2
0
0
20
18
16
14
12
10
8
6
4
0
20
18
16
14
12
10
8
6
4
2
0
2
0.01
0.00
20.0000
0.0000
100.0%
100.0%
20
18
16
14
100.0%
12
10
8
6
4
0
100.0%
0.0000
2
0.00
20.0000
0.0000
0.0000
20.0000
20.0000
100.0%
0.0000
most likely = 5
most likely = 10
Pert(0, 5, 20)
20.0000
most likely = 0
Pert(0, 15, 20)
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0.12
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0.0000
RiskPertAlt
Scenario 1
Well blowout resulting in oil spill
Impact tables with triple point estimates
Total Impact
Impact 1
Clean Up Costs
Minimum
Most Likely
Maximum
Impact 2
Injury / death to employees /
contractors
Minimum
Most Likely
Maximum
Impact 3
Consequential Loss to small
businesses
Minimum
Most Likely
Maximum
A
B
Spill in days
60
90
120
90
A
B
No. at risk
20
30
50
32
A
No. of
businesses
affected
50
75
100
75
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Prod Volume
(t/day)
1,000
1,000
1,000
1,000
Parameter
C
% Released
1%
10%
20%
12%
Parameter
C
Time of
interruption
(days)
180
360
360
330
RiskPertAlt
D
Clean up cost
(per tonne)
10,000
30,000
100,000
55,571
Allows distribution to pick up a tail at either end
607,958,577
Impact 1A
RiskPertAlt(10%,60,”m. likely”,90,90%,120)
D
% Injured /
Average Claim
Dead
% Who Claim
/ Person ($)
50%
100%
400,000
75%
100%
600,000
100%
100%
800,000
75%
100%
600,000
B
653,914,827
Parameter
C
D
Average
financial loss
per business % successful
per day ($)
claim
1,000
70%
1,500
85%
2,000
100%
1,500
85%
Impact 1C
RiskPertAlt(“min”,1%,”m. likely”,10%,90%,20%)
14,400,000
Impact 3A
Round(RiskPertAlt(10%,50,”m. likely”,75,90%,100),0)
31,556,250
25
Correlation
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Correlation
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Correlation
Scenario 1
Well blowout resulting in oil spill
Impact tables with triple point estimates
Total Impact
Impact 1
A
B
Parameter
C
654,556,494
Spill in days % Released
in $B$17
in $D$17
D
@RISK Correlations
Clean Up Costs
Minimum
Most Likely
Maximum
Impact 2
Injury / death to employees /
contractors
Minimum
Most Likely
Maximum
Impact 3
Consequential Loss to small
businesses
Minimum
Most Likely
Maximum
Spill in days
60
90
120
90
A
B
No. at risk
20
30
50
32
A
No. of
businesses
affected
50
75
100
75
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Prod Volume
(t/day)
1,000
1,000
1,000
1,000
% Released
1%
10%
20%
12%
Parameter
C
Clean up cost
(per tonne)
10,000
30,000
100,000
55,571
Spill in days in $B$17
D
1.00
% Released in $D$17
0.00
1.00
Clean up cost (per tonne) in $E$17
-0.50
-0.50
1.00
Time of interruption (days) in $C$33
0.75
0.00
0.00
1.00
For example:
15,041,667
Parameter
C
D
Average
financial loss
per business % successful
per day ($)
claim
1,000
70%
1,500
85%
2,000
100%
1,500
85%
31,556,250
Time of
interruption
(days)
180
360
360
330
Time of
interruption
(days) in
$C$33
607,958,577
% Injured /
Average Claim
Dead
% Who Claim
/ Person ($)
50%
100%
400,000
75%
100%
600,000
100%
100%
1,000,000
75%
100%
633,333
B
Clean up
cost (per
tonne) in
$E$17
Impact 1A
RiskPertAlt(10%,60,”m. likely”,90,90%,120,
RiskCorrmat(NewMatrix1,1))
28
Results
Limit
Level of
Sufficiency
$500m
51%
$600m
66%
$700m
78%
$800m
86%
$900m
91%
$1.0b
94%
$1.2b
98%
40%
$1.5b
99.5%
30%
$2.0b
99.9%
Scenario 1 - Well blowout resulting in oil spill
Loss Estimate Chart
100%
90%
80%
Level of Sufficiency
70%
Current limit of
$800m is at the
86% level of
sufficiency
60%
50%
20%
10%
RiskTarget(„Sample Value‟,800000000)
0%
0
200
400
600
800
1,000
Loss Estimate ($)
Loss Estimate
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1,200
1,400
Millions
Current Limit
29
Conclusions
Time to make a decision
 When making a decision on an appropriate limit, an organisation should consider
finding the right balance between risk and reward. There are three key factors need
to be considered:
– The level of sufficiency of particular limit in a „worst case‟ scenario
– Additional cost or potential savings of purchasing higher or lower limits
– The organisation‟s risk appetite
Key Benefits
 Set policy limits with confidence that underlying risks are better understood
 Base decisions on understanding your own risks, rather than using benchmarking or
industry claims, which are based on the risks of others
 Demonstrate to the board and stakeholders a structured and auditable process to
selecting an appropriate limit of liability
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Other Uses
 Other Liability risk classes
– Professional Indemnity
– Medical Indemnity
 It doesn‟t have to be a liability risk
– Internal Fraud / Crime
– Accidental Contamination / Malicious Product Tamper
 Uninsurable risk – measure total financial consequence
 Sensitivity analysis
– Use for decision-making around control strategies
– Assess the impact certain controls will have on the loss
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Questions
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