Property & Casualty Reserving IASA 2019 Southern California - - PowerPoint PPT Presentation

December 12, 2019

Jing Liu, FCAS, MAAA Chris Cortner, ACAS, MAAA, CPCU

Property & Casualty Reserving

IASA 2019 Southern California

1

About Today’s Presenters

• Jing Liu, FCAS, MAAA
• Consulting Actuary
• San Ramon, CA
• Chris Cortner, ACAS, MAAA, CPCU
• Consulting Actuary
• San Ramon, CA

2

• IBNR: Covering the losses . . . All of them
• Projecting Ultimate Losses: Basic Reserving Methodologies
• But what if…
• Just to be safe (Confidence levels)
• Actual vs. Expected Development
• Industry State and Trends

Outline of Presentation

3

• Paid Loss: Indemnity + Expenses - Recoveries

– A hard auditable amount

• Case Reserves: Adjuster estimates of value of individual

claims

– A hard auditable amount

• IBNR Reserves: a financial reserve estimated by actuary; re-

estimated periodically

– A soft, fungible amount calculated in bulk – A moving target

Components of Losses

4

• Property/Casualty insurance business is characterized by lags

(which give rise to need for IBNR)

Necessity of IBNR: Lags

Date of Occurrence Injuries Manifest Report Date

Adjusting, Investigation, Healthcare Providers, Employers, Body Shops, Attorneys, Depositions, Negotiations, Trial, Settlement

Closed Date

5

• IBNR => Incurred but not reported
• Sources of IBNR:

– Pure IBNR

• Late reported claims

– IBNER (Incurred but not enough reported)

• Case reserve development
• Reopened cases
• Claims in transit: pipeline claims

IBNR Components

6

• Accrual accounting requires posting of liability for all events

that have occurred and are reasonably determinable

• How many claims have occurred?
• What is the ultimate value of such claims?
• Estimate IBNR using a variety of means
• IBNR is “real” & “significant”

Why is IBNR Important?

7

• Losses develop (change) over time

– Depending on line, view (gross/net of recoveries), point in time and case reserving practices, losses can develop upward or downward – Periodic snapshots allow us to view a pattern to use in estimating

• Homogeneity and Credibility

– Grouping of losses by development behavior – Coverage trigger – Mix of business – Credibility

Projecting Ultimate Losses

8

• Things change

– Underlying business – Loss prevention/safety – Legal environment – Claims handling – Self-insurance/funding program

• How to react to changes

– A Track & Field Example

Projecting Ultimate Losses

9

• Runner has a long-run history of running this distance at 4:00

minutes

• In current competition, split time after first 375 meters is 1:15
• What is your estimate of final time?

– 4:00 ignore all intermediate information – 5:00 projected value is 4X first lap time – 4:15 add “expected” time from long-run history to intermediate information – Other?

1,500 Meter Race

10

• Time after 750 meters is 2:15
• Now, what is your estimate of final time?

– 4:00

ignore all intermediate information

– 4:30

projected value is 2X first lap time

– 4:15

add “expected” time from long-run history to intermediate information

– 3:30

reflects “trend” in improved time for each lap

– Other?

• How would this information change your estimates?

1,500 Meter Race

11

• What if the first point were 375 meters in a marathon?

– Partial information of time after 375 meters represents less than 0.1% of final race time – Outdoor conditions may have considerable impact (temperature, precipitation, etc.) – Uncertainty in forecasting much greater early in the life of the “event”

Projecting Ultimate Losses

12

Reporting Patterns

Basic reserving methodology

5,000 10,000 15,000 20,000 25,000 12 24 36 48 60 72 84 96 108 120

Months of Maturity

Reported Losses (Cumulative Payments + Case Reserves) for Policy Period 2008

Cumulative Paid Losses Case Reserves

13

Reported Loss Triangle

Basic reserving methodology

Reported Losses By Policy Period At Annual Evaluations

Policy Period 12 24 36 48 60 72 84 96 108 120 2008 10,000 15,000 17,550 19,305 20,463 20,873 20,873 20,873 20,873 20,974 2009 11,500 17,020 19,403 20,955 22,003 22,223 22,667 22,894 23,123 2010 16,200 24,138 28,000 30,240 31,450 32,079 32,399 32,723 2011 17,500 26,775 30,256 32,071 33,995 33,995 33,995 2012 16,000 24,000 28,080 29,765 31,253 31,566 2013 14,000 20,860 23,989 25,668 26,952 2014 14,500 21,895 24,960 26,708 2015 14,500 22,040 25,566 2016 15,000 22,200 2017 15,500

14

5000 10000 15000 20000 25000 12 24 36 48 60 72 84 96 108 120

Months of Maturity

Reported Losses (Cumulative Payments + Case Reserves) for Policy Period 2008

Cumulative Paid Losses Case Reserves

Reporting Patterns

x 1.17 x 1.10 x 1.06 x 1.02 x 1.00 x 1.00 x 1.00 x 1.00 x 1.50

15

Reported Losses By Policy Period At Annual Evaluations Policy Period 12 24 36

2008 10,000 15,000 17,550 2009 11,500 17,020 19,403 2010 16,200 24,138 28,000 2011 17,500 26,775 30,256 2012 16,000 24,000 28,080 2013 14,000 20,860 23,989 2014 14,500 21,895 24,960 2015 14,500 22,040 25,566 2016 15,000 22,200 2017 15,500

Reported Loss Age-to-Age Factors

Reported Loss Age-to-Age Factors By Policy Period Policy Period 12 - 24 24 - 36 36-48

2008 1.50 1.17 1.10 2009 1.48 1.14 1.08 2010 1.49 1.16 1.08 2011 1.53 1.13 1.06 2012 1.50 1.17 1.06 2013 1.49 1.15 1.07 2014 1.51 1.14 1.07 2015 1.52 1.16 2016 1.48

16

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 2011 1.53 1.13 1.06 1.06 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 2013 1.49 1.15 1.07 1.05 2014 1.51 1.14 1.07 2015 1.52 1.16 2016 1.48

Reported Loss Age-to-Age Triangle

17

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 2011 1.53 1.13 1.06 1.06 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 2013 1.49 1.15 1.07 1.05 2014 1.51 1.14 1.07 2015 1.52 1.16 2016 1.48 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00

Reported Loss Age-to-Age Triangle

18

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00

Reported Loss Age-to-Age Triangle

19

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Age to Ultimate Factor 1.00 1.00

Reported Loss Age-to-Ultimate Factors

20

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Age to Ultimate Factor 1.00 1.00 1.00

Reported Loss Age-to-Ultimate Factors

21

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Age to Ultimate Factor 1.01 1.00 1.00 1.00

Reported Loss Age-to-Ultimate Factors

22

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Age to Ultimate Factor 1.02 1.01 1.00 1.00 1.00

Reported Loss Age-to-Ultimate Factors

23

Reported Loss Age-to-Age Factors By Policy Period

Policy Period 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120+ 2008 1.50 1.17 1.10 1.06 1.02 1.00 1.00 1.00 1.00 1.00 2009 1.48 1.14 1.08 1.05 1.01 1.02 1.01 1.01 1.00 1.00 2010 1.49 1.16 1.08 1.04 1.02 1.01 1.01 1.00 1.00 1.00 2011 1.53 1.13 1.06 1.06 1.00 1.00 1.01 1.00 1.00 1.00 2012 1.50 1.17 1.06 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2013 1.49 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2014 1.51 1.14 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2015 1.52 1.16 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 2016 1.48 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Selected 1.50 1.15 1.07 1.05 1.01 1.01 1.01 1.00 1.00 1.00 Age to Ultimate Factor 2.00 1.33 1.16 1.08 1.03 1.02 1.01 1.00 1.00 1.00

Reported Loss Age-to-Ultimate Factors

24

Age to Ultimate Factors By Policy Period Policy Period Maturity @ 12/31/17 % of Ultimate Paid % of Ultimate Reported 2008 120 100% 100% 2009 108 99% 100% 2010 96 98% 100% 2011 84 95% 99% 2012 72 93% 98% 2013 60 88% 97% 2014 48 82% 92% 2015 36 75% 86% 2016 24 50% 75% 2017 12 25% 50%

Payment Pattern vs. Reporting Pattern

0% 20% 40% 60% 80% 100% 120% 12 24 36 48 60 72 84 96 108 120

% of Ultimate Loss Maturity

Development Patterns

Payment Pattern Reporting Pattern

25

• Runner has a long-run history of running this distance at 4:00

minutes

• In current competition, split time after first 375 meters is 1:15
• What is your estimate of final time?

– Expected Loss Method

• 4:00

ignore all intermediate information

– Loss Development Method

• 5:00

projected value is 4X first lap time

– Bornhuetter-Ferguson (BF) Method

• 4:15

add “expected” time from long-run history to intermediate information

Estimating Ultimate Loss – Methods

26

• Ultimate loss =

– (Reported loss to date) x (Reported age to ultimate factor) – (Paid loss to date) x (Paid age to ultimate factor)

• Assumptions

– Claims will develop similarly to past experience

• Considerations

– Relies fully on claims experience to date – Requires reliable development patterns – Can be distorted by changing claims environment – Sensitive to loss experience for immature policy periods

Loss Development Method

27

Loss Development Method

Policy Period Maturity @ 12/31/17 % of Ultimate Reported Age to Ultimate Factor Reported Loss to Date Development Method Estimate 2008 120 100% 1.00 20,974 20,974 2009 108 100% 1.00 23,123 23,123 2010 96 100% 1.00 32,723 32,723 2011 84 99% 1.01 33,995 34,335 2012 72 98% 1.02 31,566 32,197 2013 60 97% 1.03 26,952 27,761 2014 48 92% 1.08 26,708 28,845 2015 36 86% 1.16 25,566 29,657 2016 24 75% 1.33 22,200 29,526 2017 12 50% 2.00 20,000 40,000

Equal to reported loss to date when age to ultimate factor is 1.00 Sensitive to loss experience in most recent policy periods.

28

• Initial estimate of ultimate loss
• Considerations

– May be more reliable for immature policy periods – Can be used to reflect changing claims environment – Does not reflect claims experience to date

Expected Loss Method

29

Commonly based on historical experience adjusted for trend and/or other changes

Initial Expected Loss Estimate

Calculation of Initial Expected Loss Estimate Policy Period Prior Ultimate Loss Exposure Loss Cost Trend Factor Trended Loss Cost 2008 21,000 42,000 500 1.30 652 2009 23,000 42,000 548 1.27 694 2010 33,000 42,000 786 1.23 966 2011 34,000 42,000 810 1.19 967 2012 35,000 42,000 833 1.16 966 2013 28,000 42,000 667 1.13 750 2014 22,000 42,000 524 1.09 572 2015 21,000 42,000 500 1.06 530 2016 20,500 42,000 488 1.03 503 Recent data suggests improved loss costs More mature experience suggests a higher expected loss cost 2017 Initial Expected Losses = 2016 Initial Expected Loss Cost x 2017 Exposure

30

Expected Loss Method

Policy Period Maturity @ 12/31/17 % of Ultimate Reported Age to Ultimate Factor Reported Loss to Date Development Method Estimate Initial Expected Loss 2008 120 100% 1.00 20,974 20,974 30.000 2009 108 100% 1.00 23,123 23,123 30,000 2010 96 100% 1.00 32,723 32,723 30,000 2011 84 99% 1.01 33,995 34,335 30,000 2012 72 98% 1.02 31,566 32,197 30,000 2013 60 97% 1.03 26,952 27,761 30,000 2014 48 92% 1.08 26,708 28,845 30,000 2015 36 86% 1.16 25,566 29,657 29,000 2016 24 75% 1.33 22,200 29,526 29,000 2017 12 50% 2.00 20,000 40,000 28,000

Does not reflect claims experience to date. May be more reliable for immature policy periods.

31

• Ultimate loss =

– A mix of development and expected loss methods

• Assumptions

– Use development patterns to determine % of ultimate loss unreported – Unreported ultimate loss (IBNR) will develop based on initial expected loss

• Considerations

– Provides stability while still responding to claims experience

BF Method

32

Selecting Ultimate Loss

Policy Period Maturity @ 12/31/17 Age to Ultimate Factor % of Ultimate Reported Reported Loss to Date Development Method Estimate Expected Loss Method Estimate BF Method Estimate Selected Ultimate Loss 2008 120 1.00 100% 20,974 20,974 30.000 20,974 20,974 2009 108 1.00 100% 23,123 23,123 30,000 23,123 23,123 2010 96 1.00 100% 32,723 32,723 30,000 32,723 32,723 2011 84 1.01 99% 33,995 34,335 30,000 34,295 34,300 2012 72 1.02 98% 31,566 32,197 30,000 32,166 32,175 2013 60 1.03 97% 26,952 27,761 30,000 27,852 27,800 2014 48 1.08 92% 26,708 28,845 30,000 29,108 29,000 2015 36 1.16 86% 25,566 29,657 29,000 29,626 29,650 2016 24 1.33 75% 22,200 29,526 29,000 29,450 29,500 2017 12 2.00 50% 20,000 40,000 28,000 34,000 34,000

33

• Thin Data

– Industry benchmarks

• Change in reserving/claims handling

– Case reserve adequacy

• Berquist-Sherman method adjusts average case reserves
• Reconstruct triangle using the new normal

– Speed of closure

• Berquist-Sherman method with adjusted disposal rates and

modeled severities

But what if …

34

• Actuarial Central Estimate - “best” estimate of future claim

liabilities and defined as “an estimate that represents an expected value over the range of reasonably possible

• utcomes”

Just to be safe

Likelihood Unpaid Loss and Expense Liabilities $

Possible Outcomes

Actuarial Central Estimate

35

• A confidence level of x% means there is a x% chance that

losses will ultimately be less than the estimate of unpaid losses at that level

• Scenarios can include assumptions that represent favorable or

adverse outcomes of future events

Just to be safe

Likelihood Unpaid Loss and Expense Liabilities $

Possible Outcomes

Actuarial Central Estimate 75% Confidence Level

36

Actual v. Expected

• Reported in next year = 1 – (% expected unreported / % unreported)
• 2016 Expected % of IBNR in next year: 1 – (14% / 25%) = 44%

Corresponds to IBNR

Policy Period % of Ultimate Reported % of Ultimate Unreported IBNR

Expected IBNR Emergence in the Next Year @ 12/31/17 Expected @ 12/31/18

% $ 2008 100% 0% 0% 0% 2009 100% 0% 0% 0% 2010 100% 0% 0% 0% 2011 99% 1% 0% 305 100% 305 2012 98% 2% 1% 609 50% 305 2013 97% 3% 2% 848 33% 283 2014 92% 8% 3% 2,292 62% 1,433 2015 86% 14% 8% 4,084 43% 1,750 2016 75% 25% 14% 7,300 44% 3,212 2017 50% 50% 25% 14,000 50% 7,000

37

Actual v. Expected

@ 12/31/17 @ 12/31/18

Policy Period % of Ultimate Reported

Reported Loss to Date

Selected Ultimate Loss IBNR Expected Change Actual Change Actual - Expected 2008 100% 20,974 20,974 2009 100% 23,123 23,123 2010 100% 32,723 32,723 2011 99% 33,995 34,300 305 305 296

• 9

2012 98% 31,566 32,175 609 305 283

• 21

2013 97% 26,952 27,800 848 283 249

• 34

2014 92% 26,708 29,000 2,292 1,433 1,604 172 2015 86% 25,566 29,650 4,084 1,750 1,733

• 18

2016 75% 22,200 29,500 7,300 3,212 3,219 7 2017 50% 20,000 34,000 14,000 7,000 6,780

• 220

Total 263,807 293,245 29,438 14,288 14,164

• 123

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• Paid comparison

– Reported → Paid – Unreported (IBNR) → Unpaid (Ultimate – Paid) – Reported comparison may be spot on while paid is off

• Considerations

– Volatility – Interim comparison

• Interpolation is needed
• Linear in practice but in reality may not be the expectation (earlier

periods)

Actual v. Expected

39

• Linearity

– More/less may be expected in first half of period – Period dependent

Actual v. Expected

0% 20% 40% 60% 80% 100% 120% 12 24 36 48 60 72 84 96 108 120

% of Ultimate Loss Maturity

Development Patterns

Payment Pattern Reporting Pattern

40

Industry 1 Year Development (Millions) vs. Net Income/Surplus

• 0.15
• 0.10
• 0.05

0.00 0.05 0.10 0.15

• 25,000
• 20,000
• 15,000
• 10,000
• 5,000

5,000 10,000 15,000 20,000 25,000 1 Year Dev Net Income / Surplus

41

Industry 1 Year Development (Millions) vs. Underwriting Gain/Loss

• 0.20
• 0.15
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20

• 25,000
• 20,000
• 15,000
• 10,000
• 5,000

5,000 10,000 15,000 20,000 25,000

Underwriting Gain / (Loss)

1 Year Dev UW Gain/(Loss) to EP

42

Total Industry by Accident Year Change in Initial vs. Mature Incurred Loss Development (000s)

• Initial incurred is an initial value of held incurred loss, including IBNR, values as of 12/31/xx (12 months old)
• Mature valuation is from a Schedule P several years more mature (limited to 10 years maturity)

(40,000,000) (30,000,000) (20,000,000) (10,000,000) 10,000,000 20,000,000 30,000,000 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Adverse industry development coincides with high loss ratios in underwriting cycle 2002 and 2003 is where the number

• f companies showing reserve

development > 0 or < 0 are closest Immature Development

43

Commercial Auto by Accident Year Change in Initial vs. Mature Incurred Loss Development (000s)

• Initial incurred is an initial value of held incurred loss, including IBNR, values as of 12/31/xx (12 months old)
• Mature valuation is from a Schedule P several years more mature (limited to 10 years maturity)

(1,500,000) (1,000,000) (500,000) 500,000 1,000,000 1,500,000 2,000,000 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Change in Initial vs. Mature Incurred Loss Development (000s)

Immature Development

44

CY_2018 – 1-Year Reserve Development - Top 30

• 800,000
• 600,000
• 400,000
• 200,000

200,000 400,000 600,000 800,000 1,000,000 1,200,000

HO/FO PPAL CAL WC CMP MPL-OCC MPL-CM SL OL-OCC OL-CM Spec Prop APD Fidelity Other International Re A Re B Re C PL-OCC PL-CM Warranty Line of Business 1 Year Development (in 000s)

45

Observations Related to Commercial Auto Liability

60% 65% 70% 75% 80% 85%

• 1000
• 500

500 1000 1500 2000 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

CAL Industry 1 Yr Dev (Millions) vs. Net AY Loss & LAE Ratio

CAL 1 Yr Dev CAL Net AY Loss & LAE Ratio

Increase in held ultimate loss ratio precedes reserve deterioration

46

Commercial Automobile - AM Best

85 90 95 100 105 110 115 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Combined Ratio

Combined Ratio Trend

Commercial Auto Liability P/C Industry Commercial Lines

47

Frequency Trends

• 20

40 60 80 100 120

• 50

100 150 200 250 300 350 400 450 500 2009 2010 2011 2012 2013 2014 2015 2016

Buses (in thousands) Large Trucks (in thousands)

Total Crashes by Vehicle Type Federal Motor Carrier Safety Administration

Lg Trucks Buses

Commitment Beyond Numbers 48

Thank You for Your Time and Attention

Jing Liu, FCAS, MAAA

Jliu@pinnacleactuaries.com

(415) 692-0937

Chris Cortner, ACAS, MAAA

ccortner@pinnacleactuaries.com

(415) 692-0262