1999 CASUALTY LOSS RESERVE SEMINAR Intermediate Track II - Techniques

1999 CASUALTY LOSS RESERVE SEMINAR

Intermediate Track II - Techniques

SEPTEMBER 1999

RESERVE MODELS

Average Hindsight Reserve Method (Slides 2 - 12)

Average Incremental Paid Method (Slides 13 - 19)

Bornhuetter-Ferguson Method (Slides 20 - 30)

Slide 1

AVERAGE HINDSIGHT RESERVE METHOD

Goal: Estimate The Average Future Settlement Value Per Claim For . Recent Accident Years, Both For Claims Already Reported . and Future Claim Reports

Based On: Projected Ultimate Losses and Hindsight . Average Values For More Mature Accident Years

Hindsight (Current Ultimate-Historical Payments) is the . Implied Unpaid Amount

Slide 2


Data Needed

Cumulative Paid Loss Triangle

Cumulative Closed (Paid) Claim Count Triangle

Estimated Ultimate Number of Claims for All Accident Years

Estimated Ultimate Losses For Several Mature Accident Years

Slide 3


XYZ Auto Insurance Company

Cumulative Paid Losses ($000)

Accident Months Of Development .

Year 12 24 36 48 60 72 84 Ultimate

1992 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 $119.7

1993 60.2 97.0 118.5 130.7 136.6 141.0 143.8

1994 75.5 120.1 147.0 162.4 171.0 178.7

1995 91.9 147.1 180.2 197.0 220.1

1996 115.0 184.1 226.4 *

1997 146.5 233.4 *

1998 181.1 *

*To be estimated

Slide 4



Cumulative Number Of Closed Claims


Year 12 24 36 48 60 72 84 Ultimate*

1992 50 75 88 94 97 99 100 100

1993 55 83 97 104 107 109 110

1994 63 94 110 118 122 125

1995 70 105 123 131 140

1996 80 120 141 160

1997 93 139 185

1998 105 210

*Estimated using claim count development factors.

Slide 5



Calculation Of Average Outstanding Losses At 36 Months

Purpose: Project Future Settlement Dollars For 1996

Number

Estimated Estimated Number of to Settle Average

Estimated Paid Future Ultimate Closed Beyond Future

Accident Ultimate Losses at Payments Number Claims at 36 Mos* Payment . Year Losses 36 Months = (2)-(3) of Claims 36 Months =(5)-(6) =(4)/(7)

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

1992 $119,700 $98,200 $21,500 100 88 12 $1,792

1993 143,800 118,500 25,300 110 97 13 1,946

1994 178,700 147,000 31,700 125 110 15 2,113

1995 220,100 180,200 39,900 140 123 17 2,347

*Includes IBNR Claims Fitted forecasted value for AY 1996 = $2,549

Slide 6



Estimated Ultimate Losses: Accident Year 1996

(1) Forecasted Average Future Payment [Slide 6] = $2,549

(2) Number of Future Claims to Settle [Slide 5]

(Ultimate - Closed Claims) = 160 - 141 = 19

(3) Estimated Future Loss Payments [(1) x (2)] = $ 48,431

(4) Paid Losses to Date [Slide 4] = $226,400

(5) Estimated Ultimate Losses [(3) + (4)] = $274,831

Slide 7





Number




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

1993 $143,800 $97,000 $46,800 110 83 27 $1,733

1994 178,700 120,100 58,600 125 94 31 1,890

1995 220,100 147,100 73,000 140 105 35 2,086

1996 274,831 184,100 90,731 160 120 40 2,268


Slide 8










Slide 9





Number




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

1994 $178,700 $75,500 $103,200 125 63 62 $1,665

1995 220,100 91,900 128,200 140 70 70 1,831

1996 274,831 115,000 159,831 160 80 80 1,998

1997 347,664 146,500 201,164 185 93 92 2,187


Slide 10










Slide 11


ADVANTAGES

Relatively Unaffected by Changes in Case Reserving Practices Can Easily Adjust Trend Assumption Allows Separate Analysis of Frequency and Severity

DISADVANTAGES Sensitive to Payment Pattern Shifts Averages Highly Variable When Only a Few Claims May be Insufficient if Business has Significantly . . Changed (Example: Retentions Dramatically Increase) Too “Formula” Driven

Slide 12

AVERAGE INCREMENTAL PAID METHOD

Incremental Paid Losses per Ultimate Claim (Actual)


Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84

1992 500 300 182 96 54 40 25

1993 547 335* 195 111 54 40

1994 604 357 215 123 69

1995 656 394 236 120

1996 719 432 264

1997 792 470

1998 862

* 335 = (97,000-60,200) / 110

(Slide 4 @ 24 months -Slide 4 @ 12 months) / Slide 5 Ultimate

Slide 13


Trend Factors


Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84

1993/92 9.4% 11.7% 7.1% 15.6% 0.0% 0.0%

1994/93 10.4% 6.6%* 10.3% 10.8% 27.8%

1995/94 8.6% 10.4% 9.8% - 2.4%

1996/95 9.6% 9.6% 11.9%

1997/96 10.2% 8.8%

1998/97 8.8%

Select 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 9.0%

* 6.6% = 357 / 335 - 1

Slide 13 (1994) / Slide 13 (1993) - 1

Slide 14


Incremental Paid Losses per Ultimate Claim (On-level)


Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84

1992 914 503 280 136 70 48 27

1993 917 515* 275 144 64 44

1994 929 504 278 146 75

1995 926 510 280 131

1996 931 513 288

1997 941 512

1998 940

Select N/A 510 280 140 70 46 27

* 515 = 335 x (1.09 ^ 5)

Slide 13 x (Slide 14 ^ number of years) Slide 15


Incremental Paid Losses per Ultimate Claim (Projected)


Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 Total

1992 0

1993 27 27

1994 46 29 75

1995 70 50 32 152

1996 140 76 55 35 306

1997 280 152 83* 60 38 613

1998 510 305 166 91 65 42 1,179

* 83 = 70 x (1.09 ^ 2)

= 1994 value x (Slide 14 ^ number of years)

Slide 16


Projected Ultimate Losses

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

Paid Loss Projected Projected Projected Projected

Per Ult. Claim Future Ultimate Ultimate Ultimate

Accident as of Severity Severity Claims Losses ($000)

. Year 12/31/98 (Slide 16) (1) + (2) (Slide 5) (3) x (4)

1992 $1,197 $0 $1,197 100 $119.7

1993 1,282 27 1,309 110 144.0

1994 1,368 75 1,443 125 180.4

1995 1,407 152 1,559 140 218.3

1996 1,415 306 1,721 160 275.4

1997 1,262 613 1,875 185 346.9

1998 862 1,179 2,041 210 428.6

(1) = Slide 13, summed across row Slide 17


Summary

Step 1: Project Ultimate Claims

Step 2: Calculate Historical Severities

Step 3: Select Trend Factor

Step 4: Calculate On-level Severities

Step 5: Select On-level Severities

Step 6: Project Future Severities

Step 7: Multiply Total Severities by Ultimate Claims

Slide 18


ADVANTAGES

Allows separate analysis of frequency and severity trends.

Can be modified to account for changes affecting accident year severity (e.g. . deductibles, benefit changes).

Model can accommodate different trends by accident year, calendar year, or . development age.

DISADVANTAGES

Very dependent upon estimate of future inflation rates.

Less accurate for low frequency lines of business.

Could be distorted if payout patterns change.

Slide 19

BORNHEUTTER-FERGUSON METHOD

Data Needed

Earned Premium or Exposure By Year

A priori Expected Loss Ratio or Pure Premium For Each Year

An Estimate of the Percent of Dollars Unreported, Usually . Based on Loss Development Factors (LDFs)

Slide 20

BORNHUETTER-FERGUSON METHOD“IBNR” RESERVES

As of the evaluation date, there are four categories of future claims activity that . may not be reflected in either claim payments or case reserves.

1. Losses Not Yet Reported To The Company

2. Claims In Transit (Reported But Not Recorded)

3. Future Development On Known Open Claims

4. Reopenings on Claims Currently Closed

The Bornhuetter-Ferguson method and most accident year methods estimate “broad” IBNR which includes all four categories.

NOTE: The sum of (1) and (2) is termed “True” or “Pure” IBNR.

Slide 21

BORNHUETTER-FERGUSON METHODBasic Formulas

Expected Losses = Loss Ratio x Earned Premium

= Pure Premium x Exposure

= Frequency x Severity

IBNR Reserve = IBNR Factor x Expected Losses

Slide 22

BORNHUETTER-FERGUSON METHODXYZ Auto Insurance Company

Accident Year .

1996 1997 1998

(1) Earned Premium $1,250 $1,600 $2,000

(2) Expected Loss Ratio 65% 70% 75%

(3) Initial Expected Losses (1) x (2) $813 $1,120 $1,500

(4) Development Factor 1.350 1.650 2.000

(5) IBNR Factor [1 - [1 / (4)] 26% 39% 50%

(6) IBNR Reserve (3) x (5) $211 $437 $750

(7) Reported Losses at 12/31/98 $600 $700 $1,000

(8) Estimated Ultimate Losses (6) + (7) $811 $1,137 $1,750

Slide 23

BORNHUETTER-FERGUSON METHODIBNR Factor Derivation

IBNR Factor = IBNR / Ultimate Losses

= Ultimate - Incurred to Date

Ultimate

= 1.000 - (Incurred to Date/Ultimate)

= 1.000 - [1.000/(LDF-to-Ultimate)]

= 1.000 - Percent Unreported

= Percent Unreported

Slide 24

BORNHUETTER-FERGUSON METHOD


Accident Year .

1996 1997 1998

(1) Ultimate Losses

a. Expected (Slide 23, Line 3) 813 1,120 1,500

b. Estimated (Slide 23, Line 8) 811 1,137 1,750

(2) Reported Losses at 12/31/98

a. Expected (Slide 23, Line 3 - Line 6) 602 683 750

b. Actual 600 700 1,000

(3) Loss Ratio

a. Expected (Slide 23, Line 2) 65.0% 70.0% 75.0%

b. Estimated (Slide 23, Line 8/Line 1) 64.9% 71.1% 87.5%

Slide 25

BORNHEUTTER-FERGUSON METHOD

Considerations

Premium Adequacy and Expected Loss Ratios

- Sources: pricing assumptions, historical data such as Schedule P, industry data Changes in Operations:

- Reinsurance

- Longer-Tailed Lines (LDF selection more critical)

- Underlying Limits, Deductibles

- Claims Made versus Occurrence

- Claims Handling Changes in Mix of Business That May Impact Either Loss Ratios, and/or Development Patterns

Slide 26


Advantages

Easy to Use Compromises Between Loss Development and Expected Loss

Ratio Methods Avoids Overreaction: Doesn’t apply Development Factors to an Unusual Claim Occurrence Suitable for New or Volatile Lines of Business Can be Used with No Internal Loss History Can also be Used with Paid Data

Disadvantages Depends on Expected Loss Ratio or A Priori Pure Premium Requires Development Factors

Slide 27



Illustration Of Tempering Effect

One Extra

Large Claim

Expected of $150

EXPECTED LOSS RATIO METHOD

(1) Earned Premium $2,000 $2,000

(2) Expected Loss Ratio 75% 75%

(3) Projected Ultimate Losses (1) x (2) $1,500 $1,500

LOSS DEVELOPMENT METHOD

(4) Actual Reported to Date $750 $900

(5) Development Factor 2.00 2.00

(6) Projected Ultimate Losses (4) x (5) $1,500 $1,800

Slide 28



Illustration Of Tempering Effect

One Extra

Large Claim

Expected of $150


(1) Earned Premium $2,000 $2,000

(2) Expected Loss Ratio 75% 75%

(3) Expected Ultimate Losses (1) x (2) $1,500 $1,500

(4) Actual Reported to Date $750 $900

(5) Development Factor 2.00 2.00

(6) IBNR Factor 1 - [1 / (5)] 50% 50%

(7) Projected Ultimate Losses $1,500 $1,650

(4) + [(3) x (6)]

Slide 29



Illustration Of “Tempering” Effect

One Extra

Large Claim

Method Expected of $150

(1) Expected Loss Ratio Method $1,500 $1,500

(2) Loss Development $1,500 $1,800

(3) Bornhuetter-Ferguson $1,500 $1,650

Slide 30

1999 CASUALTY LOSS RESERVE SEMINAR Intermediate Track II - Techniques

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