atlanta, georgia september 11, 2006 anita sathe, acas, asa – deloitte consulting llp christopher...

Atlanta, GeorgiaSeptember 11, 2006

Anita Sathe, ACAS, ASA – Deloitte Consulting LLPChristopher Bozman, FCAS, MAAA – Towers Perrin TillinghastMichael Angelina, ACAS, MAAA – Endurance Specialty Holdings

Introduction To Reinsurance Reserving

22006 CASUALTY LOSS RESERVE SEMINAR An Introduction to Reinsurance Reserving

Agenda

• Reinsurance Contract Types

• Data Grouping Dimensions

• Differences Between Reinsurance and Primary that affect Loss Reserving

• Other Considerations & Development Methods

• Other Reserving Methods


Agenda







Reinsurance Contract Types

• Type of policies

• Mechanics of cession


Reinsurance Contract Types – Type of Policies• Treaty Reinsurance

– Covers a book or class of business – Automatic reinsurance– Insured/policies are unknown at inception but become known

subsequently– Typical Uses:

• Provide stability• Increase aggregate capacity

• Facultative Reinsurance– Covers a specific individual risk– The reinsurer retains the right to accept or reject each risk– The one insured/policy is known to the reinsurer at inception– Typical uses:

• Unique exposures• Hazardous exposures• Provide line capacity


Reinsurance Contract Types – Type of Policies• Finite Reinsurance

– Non-traditional treaty reinsurance– Transfers a limited amount of risk – Involves profit sharing elements– Typical uses

• Surplus relief• “Smoothing” results


Reinsurance Contract Types – Mechanics of cession• Two mechanics of cession:

– Pro Rata reinsurance• Proportional sharing of premiums and losses

– Excess of loss reinsurance• Losses in excess of a given dollar retention are covered

• Applicable to both treaty and facultative reinsurance


Reinsurance Contract Types – Mechanics of cession• Pro Rata reinsurance

– Quota Share• Fixed percentage of premium & losses shared• Dollar amount ceded varies by size of risk• E.g. QS Reinsurance with 25% retention.

Total Premiums = $1,000,000Total Losses = $700,000

25% 75%Total Retained Ceded

Premiums 1,000,000 250,000 750,000

Losses 700,000 175,000 525,000

Loss Ratio 70% 70% 70%


Reinsurance Contract Types – Mechanics of cession• Pro Rata reinsurance

– Surplus Share• Fixed amount (line) of losses ceded• Percentage shared varies by size of risk• E.g. Surplus share $200,000 xs of $150,000

% Sharing of Risk Share of Losses

Size of % % LossPolicy Risk Retained Ceded Amount Retained Ceded

A 100,000 100% 0% 100,000 100,000 0

B 200,000 75% 25% 200,000 150,000 50,000

C 500,000 60% 40% 400,000 240,000 160,000


Reinsurance Contract Types – Mechanics of cession• Excess Reinsurance

– Per risk• Applies to property risks• Limit applies separately to each risk (e.g. building)

– Per occurrence• Typically applies to liability covers• Limit applies to total loss for an occurrence regardless of

number of risks or policies involved

– Aggregate excess• Can apply to both property and liability covers• Limits and retentions stated in terms of loss ratio bands

– Reinsurer’s relative participation is NOT pre-determined, but depends on the size of the loss or loss ratio


Reinsurance Contract Types – Mechanics of cession• Excess Reinsurance

– E.g. XOL $3,000,000 xs of $400,000

LossPolicy Amount Retained Ceded

PER RISK

X 500,000 400,000 100,000

Y 1,200,000 400,000 800,000

Z 400,000 400,000 -

Total 2,100,000 1,200,000 900,000

PER OCCURRENCE

A 2,100,000 400,000 1,700,000


Agenda







Data Grouping Dimensions

• Accident Year vs. Underwriting Year– or “Losses Occurring” vs. “Risks Attaching”

• Casualty vs. Property

• Treaty vs. Facultative

• Excess of Loss vs. Proportional

• Broker vs. Direct


Data Grouping Dimensions• Accident Year vs. Underwriting Year

– AY allows for easiest application of standard techniques• Premium fixed as of December 31• Population of claims fixed at December 31 as well, though many

may be unknown• May not always be an option for reinsurance

– Underwriting year includes experience on all treaties written during the year

– Underwriting Year is often used in reinsurance, especially for proportional contracts

– UY can cover two policy years and three calendar years for losses. Current UY as of 12 months is “incomplete”


“Incomplete Underwriting Year”

• UY 2001 includes all treaties written by the reinsurer in 2001– “Risks Attaching” and/or “Policies Incepting”– UY 2001 can span two years and three accident years

• At 12/31/2001, UY 2001 is “incomplete”– Standard development methods derived from the past UYs

will overstate the development of UY 2001.– Historical development after 12 months includes exposures

yet to be earned– Provision for these losses should not be included in reserves

at the 12/31/2001 accounting date.


“Incomplete Underwriting Year”

1/1/2001 1/1/2002 1/1/2003 1/1/2004

Sample Time Line

Underwriting Year 2001 Covers

Policies Incepting During

this PeriodAccident Year 2002

Accident Year 2003

Accident Year 2001

Underwriting Year 2001 Covers Losses

Occurring During this Period



• Casualty vs. Property– Casualty business generally has a longer development tail

– Line of business (LOB) detail is often not available to the reinsurer, but if it is you might want to further subdivide by LOB as different LOBs may develop differently



• Treaty vs. Facultative– These display different development patterns, all else equal



• Excess of Loss vs. Proportional– Can be more important to split than line of business– Different development patterns– Possible reserve adequacy mix

• Excess of Loss - Case reserves generally reviewed by reinsurer claim dept and “ACRs” established

• Proportional - Case reserves booked as reported by ceding company without reinsurer review

– Split Excess by layer - low, high, catastrophe



• Broker vs. Direct– Reinsurers obtain business either directly from cedant or

through broker (or both)

– Data flowing through broker may create additional reporting lag and result in different development patterns


Agenda







Differences Between Primary and Reinsurance

• Reporting Lag/Development Lag

• Data

• Increased Variability

• Tailor-Made or Atypical Contracts or Features

• “Accumulation of Issues”


• Reporting Lag/Development Lag– Primary losses develop faster than reinsurance losses due to

time lag for data to reach reinsurer

– Proportional business: Accounts not due to reinsurer until 30-90 days after quarter close

• It is possible that losses booked by ceding company in calendar year “X” will be realized and booked by reinsurer in calendar year “X+1”

– Excess business: Reporting lag compounds with development lag

• Reinsurer not notified immediately of the loss• The losses do not “hit” the reinsurer’s data until they exceed

the threshold established in the Excess reinsurance contract



• Reporting Lag/Development Lag– Excess business: Reporting lag compounds with

development lag• Example:

– $400,000 excess of $100,000 per risk cover– Loss occurs in Year 1, reserved for $25,000– Year 3 - reserve increased to $50,000, reinsurer verbally notified

that loss MAY eventually reach their contract– Year 5, reserve increased to $150,000, reinsurer incurs loss 4

years after the primary company



Primary vs. Reinsurer

Historical Loss DevelopmentWorkers Compensation

0%10%20%30%40%50%60%70%80%90%

100%

1 2 3 4 5 6 7 8 9 10

Report Period (Year)

Perc

enta

ge o

f Ulti

mat

e

PrimaryReinsurer

Reproduction of RAA 2001 Historical Loss Development Study GraphPrimary Company Data Source: A.M. Best Company


• Reporting Lag/Development Lag

– Premium Estimates• Needed in reinsurance more than for primary insurance• Reserves must be set against premium earned as of the

accounting date• Reporting lag can cause large earned premium amounts to be

unreported to the reinsurer as of the accounting date• Creates a need to estimate premium and losses associated

with this premium



• Data– Quantity

• The “infinite” detail of primary company data is often lost when reported to reinsurers as data gets “collapsed” along several dimensions

– Accident dates not reported– Lines of business not reported

• Industry benchmarks by line of business or accident year can thus be difficult to use

– Quality – affected by “varied quantity”• Some ceding companies report more detail to reinsurers than

do others• As reinsurance data for reserving is organized at the level of

common detail in terms of reported data fields, this has an impact on the quality of the analysis



• Increased Variability– Primary insurers purchase reinsurance (among other

reasons) to make their results less variable (i.e. from catastrophes)

– Reinsurer data is subject to this reinsured variation

– Depending on the type of reinsurance cover, reinsurer data may BE this variation



Primary Experience Gross of Reinsurance

020406080

100120140160180

1998 1999 2000 2001 2002

Losses (in $ millions)


Primary Experience Net of Reinsurance

020406080

100120140160180

1998 1999 2000 2001 2002



Reinsurance Experience

020406080

100120140160180

1998 1999 2000 2001 2002



• Tailor-made or Atypical Contracts or Features– Many (possibly large) reinsurance contracts have features

that affect the way their experience will develop relative to other contracts with which they would otherwise be grouped

• Examples: Stop loss arrangements, loss corridors, sunset clauses, etc



• “Accumulation of Issues”– Each primary insurer faces issues (e.g. changes in reserve

adequacy, settlement patterns, etc.)– Issues affect company’s loss reserving data, and reserving

analyst has tools to neutralize the effects– Reinsurance loss reserving data is an accumulation of

primary data each of which may have these issues– Adds a further complication to the reinsurance loss

reserving process



Agenda







Applications, Complications, and Considerations

• Application of Projection Methods– Loss Development Method– Loss Ratio Method– Bornhuetter-Ferguson Method– Other Methods


Applications, Complications and Considerations

• Complications– parameter uncertainty

• Volatility in report-to-report (RTR) factors• Result can be very leveraged by tail factor selection • Loss trend factors• Expected loss ratios

– data constraints• Line of business definition• Claim count information often lacking

• Other considerations– qualitative information

• Often lack information on claims and underwriting changes at cedant level


Loss Development Method – Assumptions

• Assumes the relative change in a given year’s reported loss & ALAE from one evaluation to the next will be similar to the relative change in prior years’ reported loss & ALAE at similar evaluation points

• RTR factors measure change in reported loss & ALAE at successive evaluations

• tail factor allows for development beyond the observed experience

• Assumes the relative adequacy of the company’s case reserves has been consistent over time

• Assumes no material changes in the rate claims are paid or reported


Loss Development Method Suggestions for Tail Factors

• Industry benchmarks– RAA for excess

• Reinsurance industry data going back 40+ years• Available for treaty vs. facultative and by attachment range

– Primary sources lagged for pro-rata• ISO• A.M. Best• NCCI

• Curve fitting– Compare to benchmarks for reasonability


Loss Development MethodHow to deal with variability in Historical Development

• Refine data– Line of business mix

• At the very least need to split property vs. casualty & pro-rata vs. excess

– Treaty vs. facultative• Development patterns may differ

– Attachment points/limits• Need to understand attachment points on from ground up (FGU)

basis• How are attachment points/limits changing over time

– Assess whether or not data is still credible after making refinements


• Adjust for unique situations and claims– Commutations

• Remove from analysis, otherwise projections will be distorted– Treat any finite contracts separately

• E.g. aggregate stop loss covers – will not develop similarly to per occurrence excess

• Be watchful of traditional contracts with “finite” features– Annual aggregate deductibles, loss corridors

– Asbestos, pollution, mass tort claims should be subdivided and reviewed separately• If these claims are included in development data, the tail factor

will be overstated for more recent periods– Segregate cats, 9/11 losses, other large/unusual losses



• Supplement with benchmarks– Utilize benchmark (or weighting of benchmarks) that is most

appropriate for the book of business being analyzed. Consider:• Nature of underlying exposure (e.g. products versus premises)• Attachment points/limits• Actual historical development• Ceding company profile

– Insolvent ceding companies will cause reporting delays



Development by Line of Business

Source: RAA Historical Loss Development Study, 2005 Edition.

Exhibit A - 1

Excess ReinsuranceHistorical Loss Development

Case Incurred Losses

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Maturity (Years)

Based on combined treaty and facultative data 5 year averages; all patternsassume no development beyond oldest evaluation age in triangles.

Per

cent

age

of U

ltim

ate

Automobile Liability

General Liability Excluding Mass Torts

Workers Compensation

Medical Malpractice


Treaty vs. Facultative – General Liability


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Maturity (Years)

Based on 5 year averages; assumes the same development pattern as Exhibit A-1 beyond 33 years.

Per

cent

age

of U

ltim

ate

Treaty

Facultative

Exhibit E-2

Treaty vs. FacultativeHistorical Loss Development

General Liability Excluding Mass TortsCase Incurred Losses

Based on: Treaty - 20 Companies Facultative - 16 Companies


Impact of Attachment Points – General Liability


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21

Maturity (Years)

Based on 15 year averages; assumes the same development pattern as Exhibit A-1 beyond 21 years.

Per

cent

age

of U

ltim

ate

Current Range 1 - $1 -$180,000

Current Range 2 - $180,001 -$425,000

Current Range 3 - $425,001 -$1,800,000

Current Range 4 - $1,800,001 -$4,750,000

Current Range 5 - Greater than$4,750,000

Exhibit F-2

Impact of Attachment Pointson Historical Loss Development

General LiabilityCase Incurred Losses


Loss Development Method

• Application same as for primary business

• Results leveraged– no claims = no IBNR– large claims = large IBNR

Layer Accident

Year

Excess Loss & ALAE @ 12/31/2001 LDF

Ultimate Loss & ALAE

(3) x (4) (1) (2) (3) (4) (5)

800 x 200 1996 $1,543 1.355 $ 2,091 800 x 200 1997 1,255 1.488 1,868 800 x 200 1998 1,988 1.755 3,488 750 x 250 1999 1,868 2.336 4,364 750 x 250 2000 863 3.473 2,997 700 x 300 2001 0 8.196 0

Total $7,517 $14,808


Loss Development Method

• Paid Loss Development Method not very common for reinsurance reserving– Payment pattern is often extremely slow and erratic– may be appropriate for property or low limit proportional

business (e.g. nonstandard auto liability)


Loss Ratio Method

• Useful for new business or immature years• Need premium base and a priori expectation

regarding loss ratio• Advantage: stability

– ultimate loss estimate does not change unless the premium or loss ratio are revised

• Potential problem: lack of responsiveness– ignores actual loss experience as it emerges


Loss Ratio Method

Ultimate Loss = Earned Premium x ELR

Accident YearEarned

PremiumExpectedLoss Ratio

UltimateLoss & ALAE

(2) x (3)(1) (2) (3) (4)

1996 $ 3,994 66.5% $ 2,6561997 3,577 70.0% 2,5041998 4,161 73.5% 3,0581999 2,564 76.5% 1,9612000 2,769 78.8% 2,1822001 2,654 85.4% 2,267

$19,719 $14,628


Loss Ratio Method

• Selecting the loss ratio:– historical experience

• paid and incurred loss experience• LDF projection• adjusted to appropriate year

– rate changes– trends– coverage changes

– underwriting considerations• underwriting files• actuarial pricing• market considerations

– benchmarks (industry results)


Adjustment for Incomplete Years

• Recent underwriting or policy years may not be fully earned as of the evaluation date– may need to scale back loss development projections– apply ultimate loss ratio to earned premium as of evaluation

date• Ensure that resulting IBNR is reasonable

• Ultimate Loss Ratio = Ultimate Loss / Ultimate Premium

• Ultimate premium– project development– seek underwriter input


Agenda







Reserving Methods - Bornhuetter-Ferguson

• Essentially a blend of LDF method and Expected Loss method– begins with an a-priori estimate of expected losses

• IELR (Initial Expected Loss Ratio) x Earned Premium– splits a-priori estimate into two pieces

• expected reported losses = (IEL x % reported)• expected unreported losses(IBNR) = (IEL x % unreported)

– replaces expected reported losses with actual reported (case incurred) losses

• Restated ultimate loss estimate equals– expected unreported(IBNR) plus actual reported (case incurred)


Bornhuetter-Ferguson Method - an Example

(1) (2) (3) (4) (5) (6) (7)(2) x (3) (4) x (5) (4) - (6)

Initial Initial Expected Expected ExpectedAccident Earned Expected Expected Percent Reported Unreported

Layer Year Premium L/R Loss&ALAE Reported Loss&ALAE Loss&ALAE

800 xs 200 2000 3,994 66.5% 2,656 73.8% 1,960 696800 xs 200 2001 3,577 70.0% 2,504 67.2% 1,683 821800 xs 200 2002 4,161 73.5% 3,058 57.0% 1,743 1,315750 xs 250 2003 2,564 76.5% 1,961 42.8% 840 1,122750 xs 250 2004 2,769 78.8% 2,182 28.8% 628 1,553700 xs 300 2005 2,654 85.4% 2,267 12.2% 277 1,990

Total 19,719 14,628 7,130 7,498

Notes:(3) Based on analysis of historical accident year results adjusted for changes in retention.(5) Expected percent reported based on excess loss development patterns.


Bornhuetter-Ferguson Method - an Example (Con’t)

(8) (9) (10) (11) (12) (13)(9) - (10) (11) + (12)

Initial Expected Expected ActualAccident Expected Reported Unreported Case Inc'd Ultimate

Layer Year Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE

800 xs 200 2000 2,656 1,960 696 1,543 2,239800 xs 200 2001 2,504 1,683 821 1,255 2,076800 xs 200 2002 3,058 1,743 1,315 1,988 3,303750 xs 250 2003 1,961 840 1,121 1,868 2,989750 xs 250 2004 2,182 628 1,554 863 2,417700 xs 300 2005 2,267 277 1,990 0 1,990

Total 14,628 7,131 7,497 7,517 15,014


Bornhuetter-Ferguson Method - Advantages

• Allows for smoothing of results– LDF method understates when case incurred losses are small

• overstates if losses large (ELR may understate in this instance)• Incorporates changes in the environment

– attachment point, coverage changes, layer restructuring, price strengthening/deterioration

• Balances stability and actual loss emergence• Estimates IBNR when loss activity is sparse

– ideal for long tailed lines (umbrella, xs casualty)– redundant for short tailed lines (approximates LDF method)

• Reflects potential information found in underwriting files– underlying limits profile


Bornhuetter-Ferguson Method - Disadvantages

• Reporting pattern– expected percentage reported = 1 / LDF– difficulty in estimating pattern for LDF method also applies here

• Initial expected losses– IBNR is directly related to a-priori estimate

• double the expected losses ----> double the IBNR– importance of IELR may be lost in the analysis

• need to step back and determine % of total IBNR that is loss ratio driven• Ultimate Premium

– most recent year may be difficult to estimate• booked premium is probably under-reported due to timing lags• seek underwriting estimate


Bornhuetter-Ferguson Method -Alternative Sources of Initial Expected Losses

• Loss Ratio Method (incorporates pricing indices)• Underwriting estimate from pricing study

– by definition it is the a-priori estimate• verify that parameters for pricing and reserving are consistent

• Increased limits factors and direct premium– may be used if you feel primary company’s higher limits pricing is

inadequate• should have been incorporated in pricing study

– may also be used for changes in layer and/or attachment point• Stanard-Buhlman estimates• Frequency/Severity estimates


Example of change in layer structuringEffect on IELR

(1) (2) (3) (4) (5) (6)

Ultimate RestatedAccident Loss&ALAE Limits Loss&ALAE

Year Ratio Layer Adj Factor Layer Ratio

1999 63.5% 800 xs 200 1.00 800 xs 200 63.5%2000 66.5% 800 xs 200 1.00 800 xs 200 66.5%2001 70.0% 800 xs 200 1.00 800 xs 200 70.0%2002 73.5% 800 xs 200 1.00 800 xs 200 73.5%2003 72.7% 800 xs 200 1.05 750 xs 250 76.5%2004 74.8% 800 xs 200 1.05 750 xs 250 78.8%2005 77.1% 800 xs 200 1.11 700 xs 300 85.4%

Notes: (4) assumes that loss ratio increases 5% due to change in retention.


Stanard-Buhlman Estimate

• Essentially the Bornhuetter-Ferguson estimate with “on average” perfect information

• Uses actual loss ratio indices multiplied by average loss ratio– incorporating loss trend and pricing changes

• Balances the expected average loss ratio so that:– expected reported losses = actual reported losses


Stanard-Buhlman - an Example

(1) (2) (3) (4) (5) (6)

Average Adjusted ExpectedAcc Earned Ultimate Pricing Ultimate UltimateYear Premium L/R Index L/R Loss&ALAE

(3 x 4) (2 x 5)

2000 3,994 70.0% 0.95 66.5% 2,6562001 3,577 70.0% 1.00 70.0% 2,5042002 4,161 70.0% 1.05 73.5% 3,0582003 2,564 70.0% 1.17 81.8% 2,0972004 2,769 70.0% 1.23 86.2% 2,3872005 2,654 70.0% 1.39 97.2% 2,580


Stanard-Buhlman - an Example (continued)

(1) (2) (6) (7) (8) (9)

Expected Expected ActualAcc Earned Ultimate Percent Reported Case Inc'dYear Premium Loss&ALAE Reported Loss&ALAE Loss&ALAE

(2 x 5) (6 x 7)

2000 3,994 2,656 73.8% 1,960 1,5432001 3,577 2,504 67.2% 1,683 1,2552002 4,161 3,058 57.0% 1,743 1,9882003 2,564 2,097 42.8% 898 1,8682004 2,769 2,387 28.8% 688 8632005 2,654 2,580 12.2% 315 0

Total 19,719 15,283 7,286 7,517

Ratio of actual to expected: 1.032

Restated Loss Ratio: 72.2%


Stanard-Buhlman - an Example (continued)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Average Adjusted Expected Expected ActualAcc Earned Ultimate Pricing Ultimate Ultimate Percent Reported ReportedYear Premium L/R Index L/R Loss&ALAE Reported Loss&ALAE Loss&ALAE

(3 x 4) (2 x 5) (6 x 7)

2000 3,994 72.2% 0.95 68.6% 2,739 73.8% 2,022 1,5432001 3,577 72.2% 1.00 72.2% 2,583 67.2% 1,736 1,2552002 4,161 72.2% 1.05 75.8% 3,154 57.0% 1,798 1,9882003 2,564 72.2% 1.17 84.4% 2,163 42.8% 926 1,8682004 2,769 72.2% 1.23 88.9% 2,462 28.8% 709 8632005 2,654 72.2% 1.39 100.3% 2,661 12.2% 325 0

Total 19,719 15,763 7,515 7,517

Ratio of actual to expected: 1.000

Restated Loss Ratio: 72.2%


Stanard-Buhlman - Bornhuetter-Ferguson Method (continued)

(1) (2) (3) (4) (5) (6)(2) - (3) (4) + (5)

Initial Expected Expected ActualAcc Expected Reported Unreported Reported UltimateYear Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE

1996 2,739 2,021 718 1,543 2,2611997 2,583 1,736 847 1,255 2,1021998 3,154 1,798 1,356 1,988 3,3441999 2,163 926 1,237 1,868 3,1052000 2,462 709 1,753 863 2,6162001 2,661 325 2,336 0 2,336

15,762 7,514 8,248 7,517 15,765


Frequency Based Method - Basic Steps - Including Policy Limit Impact

• Estimate the annual number of claims above the data limit– 37.5 claims greater than $150,000

• Use size of loss curves to project the number of claims above the reinsurance retention

– 11.3 (of 37.5 claims) greater than $300,000• Use size-of-loss curves to project average severity of claims in

reinsurance layer– $239,751 average severity of claims in $700,000 excess of $300,000 layer

• Multiply the frequency and the severity projections to estimate the total ultimate losses

• Incorporate frequency/severity estimate into Bornhuetter-Ferguson method


Frequency/Severity - Estimate of claim counts above data limit

(1) (2) (3) (4) (5)

Act #> Claim IndividualDetrended Detrended Count Total

Accident Data Data Develpoment ExcessYear Limit Limit Factors Counts

6.0% (3 x 4)

2001 118,814 34 1.282 43.62002 125,943 25 1.408 35.22003 133,499 31 1.555 48.22004 141,509 22 1.927 42.42005 150,000 11 2.618 28.8

Total 123 198.2


(1) (2) (3) (4) (5) (6) (7)

SelectedProjected Subject # of

Acc. # of claims Earned On-Level Indicated Selected ExcessYear > Data Limit Premium SEP Frequency Frequency Claims

(2 / 4)

2001 43.6 50,000 63,550 0.686 43.62002 35.2 55,000 63,525 0.554 35.22003 48.2 60,000 63,000 0.765 48.22004 42.4 55,000 55,000 0.771 0.750 41.32005 28.8 50,000 50,000 0.576 0.750 37.5

Total 198.2 270,000 295,075 0.672 205.8

Frequency/Severity - Estimate of claim counts above data limit (Con’t)


Frequency/Severity - Estimation of excess losses using pareto distribution

(1) (2) (3) (4) (5) (6)

Average UltimateAccident Layer Projected # Severity Loss&ALAE

Year Limit XS Retention > $150,000 > Retention in Layer in Layer(4 x 5)

2001 800,000 200,000 43.6 14.8 178,667 2,644,2722002 800,000 200,000 35.2 13.7 178,724 2,455,6682003 750,000 250,000 48.2 16.6 206,971 3,433,6492004 750,000 250,000 41.3 14.2 207,030 2,942,1942005 700,000 300,000 37.5 11.3 239,751 2,720,579

Total 205.8 70.7 14,196,361

Notes: (4) from pareto size-of-loss curve frequency formula; Nx[(DL+B)/(R+B)]^Q(5) from pareto size-of-loss curve severity formula; [(R+B)/(Q-1)]x{1-[(R+B)/(R+L+B)] ^ (Q-1)}^Q


Frequency/Severity - Bornhuetter-Ferguson Method

(1) (2) (3) (4) (5) (6)(4) + (5)

Initial Expected Expected ActualAcc Expected Reported Unreported Reported Ultimate

Layer Year Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE

800 xs 200 2000 2,550 1,882 668 1,543 2,211800 xs 200 2001 2,644 1,777 867 1,255 2,122800 xs 200 2002 2,456 1,400 1,056 1,988 3,044750 xs 250 2003 3,434 1,470 1,964 1,868 3,832750 xs 250 2004 2,942 847 2,095 863 2,958700 xs 300 2005 2,721 332 2,389 0 2,389

Total 16,747 7,708 9,039 7,517 16,556


Recap of Methods - Ultimate Loss and ALAE

Bornhuetter BornhuetterAcc. Loss Ferguson Stanard- Frequency/ FergusonYear LDF Ratio (w/ IELR) Buhlman Severity (w/ F/S)

2000 2,091 2,656 2,239 2,261 2,550 2,2112001 1,868 2,504 2,076 2,102 2,644 2,1222002 3,488 3,058 3,303 3,344 2,456 3,0442003 4,364 1,961 2,989 3,105 3,434 3,8322004 2,997 2,182 2,417 2,616 2,942 2,9582005 0 2,267 1,990 2,336 2,721 2,389

Total 14,808 14,628 15,014 15,764 16,747 16,556


Recap of Methods -Ultimate Loss and ALAE Ratios

(1) (2) (3) (4) (5) (6) (7)

Bornhuetter BornhuetterAcc. Loss Ferguson Stanard- Frequency/ FergusonYear LDF Ratio (w/ IELR) Buhlman Severity (w/ F/S)

2000 52.4% 66.5% 56.1% 56.6% 63.8% 55.4%2001 52.2% 70.0% 58.0% 58.8% 73.9% 59.3%2002 83.8% 73.5% 79.4% 80.4% 59.0% 73.2%2003 170.2% 76.5% 116.6% 121.1% 133.9% 149.5%2004 108.2% 78.8% 87.3% 94.5% 106.2% 106.8%2005 0.0% 85.4% 75.0% 88.0% 102.5% 90.0%


Final Selection of UltimatesRules of Thumb

• LDF methods for older, more mature accident/policy periods– look at LDF/ percentage reported to determine maturity

• umbrella versus auto physical damage• Expected Loss techniques for newer, less mature accident/policy

periods– most recent or two most recent accident years

• Bornhuetter-Ferguson/ Stanard Buhlman, anywhere in between– requires judgment: (GL, umbrella, excess casualty)

• Frequency/Severity: similar to expected loss techniques– better estimate when loss ratio is unstable/unreliable

• high layers, single treaties• Benchmarks

– IBNR to case O/S ratios; loss ratios


Other Thoughts

• Look for trends, stability, shocks– are they reasonable ?

• Communicate with the underwriting and claims departments– good fodder for next underwriting audit or pricing season

• Gather knowledge on reserving philosophy (level of ACRs)– make adjustments where necessary to benchmarks

• How to handle new lines of business with no history– benchmarks, underwriting files, actuarial pricing analysis

• Incomplete underwriting year– ultimate loss & ALAE ratio using ultimate premium

• apply to estimated earned premium; look at actual case incurred• Difficult Coverages (Agg XS, deductibles, reinstatements)

– requires modeling of underlying exposures


Other Approaches (Con’t)

• Asbestos, Pollution, Other Health Hazards– Need to handle separately

• Cedant information, industry data, benchmarks• Results of exposure based modeling techniques

• Large Events / Market Losses (WTC losses)– Seek input from claims department– Utilize market information / knowledge

• Property Catastrophes– Results of models (may need to adjust)– Underwriter estimates– Traditional top-down techniques


Contact Information

• Anita Sathe, ACAS, ASADeloitte Consulting LLPPhone: (860) [email protected]

• Christopher Bozman, FCAS, MAAATowers Perrin TillinghastPhone: (215) [email protected]

• Michael Angelina, ACAS, MAAAEndurance Specialty Holdings, LtdPhone: (441) [email protected]

mailto:[email protected]



atlanta, georgia september 11, 2006 anita sathe, acas, asa – deloitte consulting llp christopher...

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