September 11, 2001Thomas L. Ghezzi, FCAS, MAAA

Casualty Loss Reserve SeminarCall Paper ProgramLoss Reserving without Loss Development Patterns - Beyond Berquist Sherman

2

We used a few simplifications to keep this understandable We made up the data We select development factors based on the

volume weighted average of the last three diagonals

We tried to keep to a minimum the number of slides with lots of numbers that are hard to read

3

The data is constructed to allow for variations in reporting and payment patterns Ultimate losses based on hypothetical frequency and

severity assumptions Annual trend of 5% per year

1% frequency 4% severity

We include ten years in the data Ten year total ultimate losses of $766.5 million

Hypothetical development patterns applied to the hypothetical ultimates to derive loss development data Variation in the patterns used to create

hypothetical scenarios

4

We derived four scenarios to test the accuracy of various reserving techniques Scenario 1 (“Base Scenario”) - Stable

settlement and reserving patterns Scenario 2 - Case reserve strengthening

Assumes about six months acceleration in reporting pattern

Scenario 3 - Settlement rate acceleration Assumes about six month acceleration in claim

settlement and loss payment patterns Scenario 4 - Case reserve strengthening and

settlement rate acceleration Assumes about six month acceleration in

reporting and payment patterns

5

The loss reporting and payment patterns underlying the base scenario are as follows

0%

20%

40%

60%

80%

100%

120%

12 24 36 48 60 72 84 96 108 120Maturity (Mos)

Pct.

of U

ltim

ate

Pct. ReportedPct. Paid

6

In a stable environment, loss reserving is easy. An incurred loss triangle might look like this ... Stable Settlement and Reserve Patterns

Evaluation Age in MonthsYr 12 24 36 48 60 72 84 96 108 1201 22.6 37.9 49.0 53.3 59.8 60.6 60.9 60.9 60.9 60.92 23.8 39.8 51.5 55.9 62.8 63.7 64.0 64.0 64.03 25.0 41.8 54.0 58.7 66.0 66.9 67.2 67.24 26.2 43.9 56.7 61.6 69.3 70.2 70.55 27.5 46.1 59.6 64.7 72.7 73.76 28.9 48.4 62.5 68.0 76.47 30.3 50.8 65.7 71.48 31.9 53.4 69.09 33.4 56.110 35.1

Age Interval in MonthsYr 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-Ult1 1.676 1.292 1.087 1.124 1.013 1.005 1.000 1.000 1.0002 1.676 1.292 1.087 1.124 1.013 1.005 1.000 1.0003 1.676 1.292 1.087 1.124 1.013 1.005 1.0004 1.676 1.292 1.087 1.124 1.013 1.0055 1.676 1.292 1.087 1.124 1.0136 1.676 1.292 1.087 1.1247 1.676 1.292 1.0878 1.676 1.2929 1.67610

7

… and a paid triangle might look like this ... Stable Settlement and Reserve Patterns

Evaluation Age in MonthsYr 12 24 36 48 60 72 84 96 108 1201 8.1 17.7 32.8 45.3 48.7 53.1 56.8 60.9 60.9 60.92 8.5 18.6 34.5 47.6 51.1 55.8 59.7 64.0 64.03 8.9 19.5 36.2 49.9 53.7 58.5 62.7 67.24 9.4 20.5 38.0 52.4 56.4 61.5 65.85 9.9 21.5 39.9 55.1 59.2 64.56 10.3 22.6 41.9 57.8 62.27 10.9 23.7 44.0 60.78 11.4 24.9 46.29 12.0 26.110 12.6

Age Interval in MonthsYr 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-Ult1 2.183 1.856 1.379 1.075 1.090 1.070 1.072 1.000 1.0002 2.183 1.856 1.379 1.075 1.090 1.070 1.072 1.0003 2.183 1.856 1.379 1.075 1.090 1.070 1.0724 2.183 1.856 1.379 1.075 1.090 1.0705 2.183 1.856 1.379 1.075 1.0906 2.183 1.856 1.379 1.0757 2.183 1.856 1.3798 2.183 1.8569 2.18310

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… and simple projections all give the same resultIncurred Loss Development

Selected 1.676 1.292 1.087 1.124 1.013 1.005 1.000 1.000 1.000 1.000To Ultimate 2.692 1.606 1.244 1.144 1.018 1.005 1.000 1.000 1.000 1.000

Ult Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4 Yr 3 Yr 2 Yr 1 Projected $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5 $67.2 $64.0 $60.9 Actual $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5 $67.2 $64.0 $60.9 Difference $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0

Paid Loss Development

Selected 2.183 1.856 1.379 1.075 1.090 1.070 1.072 1.000 1.000 1.000To Ultimate 7.519 3.444 1.856 1.345 1.251 1.147 1.072 1.000 1.000 1.000

Ult Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4 Yr 3 Yr 2 Yr 1 Projected $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5 $67.2 $64.0 $60.9 Actual $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5 $67.2 $64.0 $60.9 Difference $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0

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Introducing changes to the settlement and case reserving patterns expose weaknesses in traditional loss development analyses

30%

40%

50%

60%

70%

80%

90%

100%

12 24 36 48 60 72 84 96 108 120Maturity (Mos)

Pct.

of U

ltimate

Base - % ReportedActual % Rept - Scen. 2Est. % Rept - Inc'd LDF

Scenario 2 - Case Reserve Strengthening Traditional loss

development factor (LDF) projection based on incurred data will underestimate the amount of strengthening

This results in over-projection of ultimate losses

Ten year total projection is $796.0 million $29.5 million higher than

the actual ultimates of $766.5 million

The misestimate for 12 months alone causes the projected ultimates to be too high by 17.8% ($111.4 m vs $94.5 m)

10

Changes in the settlement rate and payment patterns can be even more significant of a distortion

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

100%

12 24 36 48 60 72 84 96 108 120Maturity (Mos)

Pct.

of U

ltimate

Base - % PaidActual % Paid - Scen. 3Est. % Paid - Paid LDF

Scenario 3 - Settlement Rate Acceleration Traditional LDF projection

using paid losses results in over-projection of ultimate losses

Ten year total projection is $840.7 million $74.2 million higher

than the actual ultimates of $766.5 million

This error causes a

38% over-projection

on the latest year

($130.8 m vs $94.5 m)

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Loss reserving in a changing claim settlement or case reserving environment requires advanced techniques, and significant judgment Berquist-Sherman (PCAS LXIV, p123)

Judgmental adjustments to “prior diagonals” to approximate the settlement rate and or case reserve levels on the current diagonal

Adjusted

Actual

Adjusted

Loss

Development

Factors

Adjusted loss development pattern applied to the unadjusted (actual) data

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The techniques in this call paper adjust the latest diagonal instead of the prior data Ultimate Closed Claim Severity Technique

Projects ultimate losses using traditional methods Calculates implied unpaid loss triangle

Repeat this approach for claims to get estimated unclosed claims triangle

Ratio of the unpaid loss triangle to unclosed claim triangle gives the estimated unclosed claim severity triangle

minus equalsProjected

Ultimates

Paid toDate

EstimatedUnpaid

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The unclosed claim severity triangle is used to estimate the latest diagonal severities consistent with the historical data Stable Settlement and Reserve Patterns

Implied Ultimate Unclosed Claim Severity ($000s)Year 12 24 36 48 60 72 841 83.5 107.4 118.3 147.9 208.5 194.6 287.52 86.8 111.7 123.0 153.7 216.8 202.3 298.93 90.3 116.1 127.9 159.8 225.3 210.3 310.84 93.9 120.7 132.9 166.1 234.3 218.6 323.15 97.6 125.5 138.2 172.7 243.5 227.36 101.4 130.5 143.7 179.6 253.27 105.5 135.6 149.3 186.78 109.6 141.0 155.39 114.0 146.610 118.5

Fitted Last Diagonal: $118.5 $146.6 $155.3 $186.7 $253.2 $227.3 $323.1

Ultimate Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4

Est'd Unclosed Claims: 692 436 255 112 62 42 15Implied Ult. Outstanding: $82.0 $63.9 $39.5 $21.0 $15.6 $9.5 $4.7Paid to Date: $12.6 $26.1 $46.2 $60.7 $62.2 $64.5 $65.8Implied Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Actual Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Difference: $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0

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When there are changes in patterns, this method replaces the “distorted” latest diagonal with an adjusted diagonal consistent with prior periods Case Reserve Strengthening

Implied Ultimate Unclosed Claim Severity ($000s)Year 12 24 36 48 60 72 841 83.5 107.4 118.3 147.9 208.5 194.6 287.52 86.8 111.7 123.0 153.7 216.8 202.3 298.93 90.3 116.1 127.9 159.8 225.3 210.3 310.84 93.9 120.7 132.9 166.1 234.3 218.6 323.15 97.7 125.7 138.6 173.7 245.3 229.86 101.8 131.0 144.6 181.6 256.97 108.3 140.1 156.9 203.68 114.3 148.4 167.89 124.6 163.310 142.8

Fitted Last Diagonal: $121.3 $147.4 $155.8 $186.7 $253.2 $227.3 $323.1

Ultimate Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4

Est'd Unclosed Claims: 692 436 255 112 62 42 15Implied Ult. Outstanding: $83.9 $64.2 $39.7 $21.0 $15.6 $9.5 $4.7Paid to Date: $12.6 $26.1 $46.2 $60.7 $62.2 $64.5 $65.8Implied Ultimate Losses: $96.5 $90.4 $85.9 $81.7 $77.8 $74.1 $70.5Actual Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Difference: $2.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0

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The second new technique in this paper does not use loss development factors for any year Incremental Closed Claim Severity Method

Calculates incremental paid losses and closed claims for each year between evaluation points

Calculates incremental closed claim severity triangle

The historical incremental closed claim severities are used to estimate future incremental severities

Historical closed claim data is used to estimate future incremental closed claims

Increm.Paid

Losses

Increm.ClosedClaims

Increm.ClosedClaims

Severitydivided by equals

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The “sumproduct” of severities and closed claims “below the diagonal” provides an estimate of the remaining closed claim severities by year Stable Settlement and Reserve Patterns

Incremental Closed Claims in Age Interval in MonthsYear 0-12 12-24 24-36 36-48 48-60 60-72 72-84 84-961 368 230 165 132 47 18 26 142 371 232 167 133 48 19 26 143 375 235 168 134 48 19 27 154 379 237 170 136 49 19 27 155 382 239 172 137 49 19 27 156 386 242 173 138 50 19 27 157 390 244 175 140 50 20 28 158 394 247 177 141 50 20 28 159 398 249 179 143 51 20 28 1510 402 252 180 144 52 20 28 16

Incremental Paid Claim Severity in Age Interval in Months ($000s)Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 84-961 22.1 41.7 91.8 94.6 72.4 238.9 143.7 287.52 22.9 43.3 95.4 98.3 75.2 248.4 149.3 298.93 23.8 45.1 99.2 102.2 78.2 258.2 155.3 310.84 24.8 46.9 103.1 106.3 81.3 268.5 161.4 323.15 25.8 48.7 107.2 110.5 84.5 279.1 167.8 335.96 26.8 50.6 111.5 114.8 87.9 290.2 174.4 349.27 27.8 52.6 115.9 119.4 91.3 301.6 181.4 363.08 28.9 54.7 120.5 124.1 95.0 313.6 188.5 377.49 30.1 56.9 125.2 129.0 98.7 326.0 196.0 392.310 31.3 59.1 130.2 134.1 102.6 338.9 203.8 407.8

Sumproduct: $118.5 $146.6 $155.3 $186.7 $253.2 $227.3 $323.1

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When there are changes in patterns, this method mostly avoids the “distorted” diagonals Settlement Rate Acceleration

Incremental Closed Claims in Age Interval in MonthsYear 0-12 12-24 24-36 36-48 48-60 60-72 72-84 84-961 368 230 165 132 47 18 26 142 371 232 167 133 48 19 33 73 375 235 168 134 48 28 24 74 379 237 170 136 62 15 25 75 382 239 172 151 48 15 24 86 386 242 240 86 49 16 23 87 390 325 161 87 47 17 25 98 470 252 163 91 46 17 24 99 475 254 159 95 47 18 25 910 480 238 170 101 50 19 27 9

Incremental Paid Claim Severity in Age Interval in Months ($000s)Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 84-961 22.1 41.7 91.8 94.6 72.4 238.9 143.7 287.52 22.9 43.3 95.4 98.3 75.2 248.4 181.5 298.93 23.8 45.1 99.2 102.2 78.2 244.8 177.3 310.84 24.8 46.9 103.1 106.3 104.9 310.8 184.3 323.15 25.8 48.7 107.2 113.9 98.0 323.1 167.8 335.96 26.8 50.6 113.7 117.6 101.9 290.2 174.4 349.27 27.8 70.8 114.5 122.3 91.3 301.6 181.4 363.08 38.6 69.1 119.1 124.1 95.0 313.6 188.5 377.49 40.1 71.8 125.2 129.0 98.7 326.0 196.0 392.310 41.7 59.1 130.2 134.1 102.6 338.9 203.8 407.8

Sumproduct: $114.9 $144.5 $154.2 $176.1 $244.0 $211.6 $323.1

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These severities are used to estimate ultimate losses

Settlement Rate Acceleration

Ultimate Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4Implied Unclosed Severity: $114.9 $144.5 $154.2 $176.1 $244.0 $211.6 $323.1Est'd Unclosed Claims: 614 353 187 98 48 32 7Implied Future Payments: $70.5 $51.1 $28.8 $17.2 $11.7 $6.8 $2.4Paid to Date: $20.0 $37.3 $55.0 $63.0 $65.0 $66.8 $68.2Implied Ultimate Losses: $90.5 $88.4 $83.8 $80.2 $76.7 $73.6 $70.5Actual Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Difference: ($4.0) ($1.7) ($2.0) ($1.4) ($1.1) ($0.4) $0.0

Stable Settlement and Reserve Patterns

Ultimate Losses Yr 10 Yr 9 Yr 8 Yr 7 Yr 6 Yr 5 Yr 4Implied Unclosed Severity: $118.5 $146.6 $155.3 $186.7 $253.2 $227.3 $323.1Est'd Unclosed Claims: 692 436 255 112 62 42 15Implied Future Payments: $82.0 $63.9 $39.5 $21.0 $15.6 $9.5 $4.7Paid to Date: $12.6 $26.1 $46.2 $60.7 $62.2 $64.5 $65.8Implied Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Actual Ultimate Losses: $94.5 $90.0 $85.7 $81.7 $77.8 $74.1 $70.5Difference: $0.0 $0.0 $0.0 $0.0 $0.0 $0.0 $0.0

19

In summary, the new methods provide significant improvement in projection accuracy As with all techniques, they produce the correct

result in a stable environment With changes in case reserve adequacy and/or

settlement rates, they are much more accurate

20

All methods work when life is stable and predictable Stable Settlement and Reserve Patterns

Loss Development Ult. Closed Claim IncrementalActual Technique Severity Technique on Closed

Ultimate Incurred Paid Incurred Paid ClaimYear Losses Losses Losses Losses Losses Severity

(1) (2) (3) (4) (5) (6) (7)Estimated Ultimate Losses1 $60.9 $60.9 $60.9 $60.9 $60.9 $60.92 64.0 64.0 64.0 64.0 64.0 64.03 67.2 67.2 67.2 67.2 67.2 67.24 70.5 70.5 70.5 70.5 70.5 70.55 74.1 74.1 74.1 74.1 74.1 74.16 77.8 77.8 77.8 77.8 77.8 77.87 81.7 81.7 81.7 81.7 81.7 81.78 85.7 85.7 85.7 85.7 85.7 85.79 90.0 90.0 90.0 90.0 90.0 90.010 94.5 94.5 94.5 94.5 94.5 94.5

Total $766.5 $766.5 $766.5 $766.5 $766.5 $766.5

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But the adjusted methods are more accurate when things are changing

Strengthening and Acceleration

Loss Development Ult. Closed Claim IncrementalActual Technique Severity Technique on Closed

Ultimate Incurred Paid Incurred Paid ClaimYear Losses Losses Losses Losses Losses Severity

(1) (2) (3) (4) (5) (6) (7)Estimated Ultimate Losses1 $60.9 $60.9 $60.9 $60.9 $60.9 $60.92 64.0 64.0 64.0 64.0 64.0 64.03 67.2 67.2 67.2 67.2 67.2 67.24 70.5 70.5 71.3 70.5 70.5 70.55 74.1 74.2 75.7 74.2 74.2 73.66 77.8 78.0 80.6 77.1 77.1 76.77 81.7 83.6 85.6 81.3 82.5 80.28 85.7 88.9 94.7 84.1 86.2 83.89 90.0 97.3 109.9 89.4 93.0 88.410 94.5 111.4 130.8 94.5 98.6 90.5

Total $766.5 $796.0 $840.7 $763.1 $774.2 $755.9

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These new techniques do not necessarily produce a better adjustment than the traditional advanced techniques. However... They may be more understandable to company

management They allow explicit reflection of known changes in

mix of business or other factors that affect trend They allow easy combination of case reserve and

settlement rate adjustments They work equally well with calendar year changes

and accident year changes They reflect recent claim frequency experience They provide reasonableness testing for more

traditional methods

23

We used many simplified approaches and assumptions. Refinements are possible Use unpaid claim severities instead of unclosed More sophisticated forecasting techniques Blending with “post-change” experience Reasonableness testing

implied loss ratios, severities, pure premiums Sensitivity testing