Intermediate Track II September 2000 Minneapolis, Minnesota 1
This Session Will Discuss 1. Bornhuetter-Ferguson Method 2. Average Hindsight Method 3. Average Incremental Paid Method 2
BORNHUETTER- FERGUSON METHOD 3
Bornhuetter-Ferguson Method Summary: Project IBNR based on expected losses and the percentage of ultimate losses which are currently unreported. The Bornhuetter-Ferguson method is a combination of Expected Loss Ratio Method (loss ratio x premium) Paid or Incurred Loss Development Method (paid or incurred losses x loss development factor) 4
Bornhuetter-Ferguson Method Steps to Project Ultimate Loss (1) Calculate Expected Losses (2) Calculate IBNR Factor (3) Calculate IBNR Reserve (4) Calculate estimated ultimate losses. 5
Bornhuetter-Ferguson Method Assumptions Earned Premium = $1,250 Incurred Losses = $600 Expected Loss Ratio = 65% CDF = 1.35 (derived from incurred loss development triangle) 6
Bornhuetter-Ferguson Method Step 1 Calculate Expected Losses = Expected Loss Ratio x Earned Premium Earned Premium = $1,250 Expected Loss Ratio = 65% Expected Losses = $813 (1,250 x 0.65) [Expected losses may also be projected using (pure premium x exposure) OR (frequency x severity x exposure) ] 7
Bornhuetter-Ferguson Method Step 2 Calculate IBNR Factor [IBNR Factor is the percent of ultimate losses still left to be reported] = IBNR / Ultimate Losses = Ultimate Loss - Incurred to Date Ultimate Loss = 1.000 - (Incurred to Date / Ultimate) = 1.000 - [1.000/(CDF)] CDF = 1.350 IBNR Factor = [1-1/1.350] = 26% 8
Bornhuetter-Ferguson Method Step 3 Calculate IBNR Reserve = IBNR Factor x Expected Losses Expected Losses = $813 IBNR Factor = [1-1/1.350] = 26% IBNR Reserve = [$813 x 26%] = $211 9
Bornhuetter-Ferguson Method Step 4 Calculate Estimated Ultimate Losses = Incurred Losses + IBNR Reserve Incurred Losses = $600 IBNR Reserve = [$813 x 26%] = $211 Ultimate Losses = [$600 + $211] = $811 10
Bornhuetter-Ferguson Method Advantages Easy to use Compromises between loss development and expected loss ratio methods Avoid 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 11
Bornhuetter-Ferguson Method Disadvantages Highly dependent on expected loss ratio or pure premium Requires development factors 12
Bornhuetter-Ferguson Method Comparison of Methods Given: Earned Premium = $2,000 Expected Loss Ratio = 70 % Incurred Losses to Date = $750 Development Factor = 2.00 13
Bornhuetter-Ferguson Method 1) Expected Loss Ratio Method =Earned Premium x Expected Loss Ratio =$2,000 x 70% =$1,400 2) Loss Development Method =Incurred to Date x Development Factor =$750 x 2.00 =$1,500 3) Bornhuetter Ferguson Method = Incurred to Date + Expected Losses x (1-1/Dev. Factor) =$750 + $1,400 x [1-1/2.00] =$750 + $700 =$1,450 14
Bornhuetter-Ferguson Method Comparison of Methods: Illustration of Tempering Effect Given: One additional large claim of $150 Incurred Losses to Date = $900 15
Bornhuetter-Ferguson Method 1) Expected Loss Ratio Method =Earned Premium x Expected Loss Ratio =$2,000 x 70% =$1,400 2) Loss Development Method =Incurred to Date x Development Factor =$900 x 2.00 =$1,800 3) Bornhuetter Ferguson Method = Incurred to Date + Expected Losses x (1-1/Dev. Factor) =$900 + $1,400 x [1-1/2.00] =$900 + $700 =$1,600 16
AVERAGE HINDSIGHT METHOD 17
Average Hindsight Method Summary: Estimate the expected ultimate losses for recent accident years based on hindsight average paid values per claim for more mature accident years. 18
Average Hindsight Method Data Needed Cumulative Paid Loss Triangle Cumulative Closed (Paid) Claim Count Triangle 19
Average Hindsight Method Steps to project Accident Year 1997 Ultimate Loss (1) Project ultimate losses for AY s 1993-1996 using paid loss development method (2) Project ultimate claim counts for all AY s using claim count development (3) Calculate projected payment per claim from 36 months to ultimate (4) Calculate total future payments for AY 1997 (5) Calculate estimated ultimate losses for AY 1997 20
Average Hindsight Method Accident Year 1997 - Step 1 Project ultimate losses for AY s 1993-1996 using paid loss development method 21
Average Hindsight Method XYZ Auto Insurance Company Cumulative Paid Losses ($000) Accident Months of Development Year 12 24 36 48 60 72 84 1993 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 1994 60.2 97.0 118.5 130.7 136.6 141.0 1995 75.5 120.1 147.0 162.4 171.0 1996 91.9 147.1 180.2 197.0 1997 115.0 184.1 226.4 1998 146.5 233.4 1999 181.1 22
Average Hindsight Method XYZ Auto Insurance Company Development of Paid Losses Months of Development Acc Year 12-24 24-36 36-48 48-60 60-72 72-84 84-Ult 1993 1.600 1.228 1.098 1.050 1.035 1.021 1.000 1994 1.611 1.222 1.103 1.045 1.032 1995 1.591 1.224 1.105 1.053 1996 1.601 1.225 1.093 1997 1.601 1.230 1998 1.593 3 year avg 1.598 1.226 1.100 1.049 1.034 1.021 1.000 Selected 1.050 1.035 1.020 1.000 CDF 1.108 1.056 1.020 1.000 Diagonal 197.0 171.0 141.0 119.7 Ultimate 218.4 180.5 143.8 119.7 23
Average Hindsight Method XYZ Auto Insurance Company Cumulative Paid Losses ($000) Accident Months of Development Year 12 24 36 48 60 72 84 Ultimate 1993 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 $119.7 1994 60.2 97.0 118.5 130.7 136.6 141.0 143.8 1995 75.5 120.1 147.0 162.4 171.0 180.5 1996 91.9 147.1 180.2 197.0 218.4 1997 115.0 184.1 226.4 * 1998 146.5 233.4 * 1999 181.1 * Ultimate losses from Slide 23 24
Average Hindsight Method Accident Year 1997 - Step 2 Project ultimate claim counts for all AY s using claim count development 25
Average Hindsight Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year 12 24 36 48 60 72 84 1993 50 75 88 94 97 99 100 1994 55 83 97 104 107 109 1995 63 94 110 118 122 1996 70 105 123 131 1997 80 120 141 1998 93 139 1999 105 26
Average Hindsight Method XYZ Auto Insurance Company Development of Closed Claims Months of Development Acc Year 12-24 24-36 36-48 48-60 60-72 72-84 84-Ult 1993 1.500 1.173 1.068 1.032 1.021 1.010 1.000 1994 1.509 1.169 1.072 1.029 1.019 1995 1.492 1.170 1.073 1.034 1996 1.500 1.171 1.065 1997 1.500 1.175 1998 1.495 3 year avg 1.498 1.172 1.070 1.032 1.020 1.010 1.000 Selected 1.500 1.172 1.070 1.032 1.020 1.010 1.000 CDF 2.000 1.333 1.138 1.063 1.030 1.010 1.000 Diagonal 105 139 141 131 122 109 100 Ultimate 210 185 160 139 126 110 100 27
Average Hindsight Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year 12 24 36 48 60 72 84 Ultimate 1993 50 75 88 94 97 99 100 100 1994 55 83 97 104 107 109 110 1995 63 94 110 118 122 126 1996 70 105 123 131 139 1997 80 120 141 160 1998 93 139 185 1999 105 210 Ultimate claim counts from Slide 27 28
Average Hindsight Method Accident Year 1997 - Step 3 Calculate projected payment per claim from 36 months to ultimate 29
Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 36 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 36 Months Payments of Claims 36 Months 36 Mos Payment (1) (2)=Slide 24 (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1993 $119,700 $98,200 $21,500 100 88 12 $1,792 1994 143,820 118,500 25,320 110 97 13 1,934 1995 180,525 147,000 33,525 126 110 16 2,137 1996 218,372 180,200 38,172 139 123 16 2,345 Fitted forecasted value for AY 1997 $2,561 30
Average Hindsight Method Accident Year 1997 - Steps 4 & 5 Calculate total future payments for AY 1997 Calculate estimated ultimate losses for AY 1997 31
Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1997 (1) Forecasted Average Future Payment [Slide 30] $2,561 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = 160-141 19 (3) Estimated Future Loss Payments [ (1) x (2) ] $49,693 (4) Paid Losses to Date [Slide 24] $226,400 (5) Estimated Ultimate Losses [ (3) + (4) ] $276,093 32
Average Hindsight Method Steps to Project Accident Year 1998 Ultimate Loss (1) Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1997 projection) (2) Calculate total future payments for AY 1998 (3) Calculate estimated ultimate losses for AY 1998 33
Average Hindsight Method Accident Year 1998 - Step 1 Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1997 projection) 34
Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 24 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 24 Months Payments of Claims 24 Months 24 Mos Payment (1) (2)=see below (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1994 $143,820 $97,000 $46,820 110 83 27 $1,728 1995 180,525 120,100 60,425 126 94 32 1,907 1996 218,372 147,100 71,272 139 105 34 2,079 1997 276,093 184,100 91,993 160 120 40 2,277 Fitted forecasted value for AY 1998 $2,497 (2) 1994-1996 ultimates from Slide 24, 1997 ultimate from Slide 32 35
Average Hindsight Method Accident Year 1998 - Steps 2 & 3 Calculate total future payments for AY 1998 Calculate estimated ultimate losses for AY 1998 36
Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1998 (1) Forecasted Average Future Payment [Slide 35] $2,497 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = 185-139 46 (3) Estimated Future Loss Payments [ (1) x (2) ] $115,684 (4) Paid Losses to Date [Slide 24] $233,400 (5) Estimated Ultimate Losses [ (3) + (4) ] $349,084 37
Average Hindsight Method Steps to Project Accident Year 1999 Ultimate Loss (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY s 1997 & 1998 projections) (2) Calculate total future payments for AY 1999 (3) Calculate estimated ultimate losses for AY 1999 38
Average Hindsight Method Accident Year 1999 - Step 1 (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY s 1997 & 1998 projections) 39
Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 12 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 12 Months Payments of Claims 12 Months 12 Mos Payment (1) (2)=see below (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1995 $180,525 $75,500 $105,025 126 63 63 $1,675 1996 218,372 91,900 126,472 139 70 69 1,826 1997 276,093 115,000 161,093 160 80 80 2,004 1998 349,084 146,500 202,584 185 93 92 2,194 Fitted forecasted value for AY 1999 $2,399 (2) 1995-1996 ultimates from Slide 24, 1997 from Slide 32, 1998 from Slide 37 40
Average Hindsight Method Accident Year 1999 - Steps 2 & 3 Calculate total future payments for AY 1999 Calculate estimated ultimate losses for AY 1999 41
Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1999 (1) Forecasted Average Future Payment [Slide 40] $2,399 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = 210-105 105 (3) Estimated Future Loss Payments [ (1) x (2) ] $251,902 (4) Paid Losses to Date [Slide 24] $181,100 (5) Estimated Ultimate Losses [ (3) + (4) ] $433,002 42
Average Hindsight Method Advantages Relatively unaffected by changes in case reserving practices Can easily adjust trend assumptions 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 (i.e. retentions dramatically increase) Too formula-driven 43
AVERAGE INCREMENTAL PAID METHOD 44
Average Incremental Paid Method Summary: Estimate the expected ultimate losses for recent accident years based on average incremental paid values per claim. 45
Average Incremental Paid Method Data Needed: Ultimate Claim Counts Incremental Paid Loss Triangle 46
Average Incremental Paid Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year 12 24 36 48 60 72 84 Ultimate 1993 50 75 88 94 97 99 100 100 1994 55 83 97 104 107 109 110 1995 63 94 110 118 122 126 1996 70 105 123 131 139 1997 80 120 141 160 1998 93 139 185 1999 105 210 Ultimate claim counts derived in average hindsight method - Slide 28 47
Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses ($000) Accident Months of Development Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 1993 $50.0 $30.0 $18.2 $9.6 $5.4 $4.0 $2.5 1994 60.2 36.8 21.5 12.2 5.9 4.4 1995 75.5 44.6 26.9 15.4 8.6 1996 91.9 55.2 33.1 16.8 1997 115.0 69.1 42.3 1998 146.5 86.9 1999 181.1 12-24 column = Slide 24, column 3 (24 mos) - column 2 (12 mos) 48
Average Incremental Paid Method Steps to Project Ultimate Loss (1) Create triangle of incremental paid losses per ultimate claim (2) Calculate incremental payment trend factors and select projected trend factor (3) Calculate on-level incremental payments (4) Project future payment amounts (5) Calculate estimated ultimate losses 49
Average Incremental Paid Method Step 1 Create triangle of incremental paid losses per ultimate claim 50
Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Actual) Accident Months of Development Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 1993 500 300 182 96 54 40 25 1994 547 334 195 111 54 40 1995 601 355 214 123 68 1996 660 396 238 121 1997 717 431 264 1998 791 469 1999 862 Slide 48 (incremental paid losses) / Slide 47 (ultimate claims counts) 51
Average Incremental Paid Method Step 2 Calculate incremental payment trend factors and select projected trend factor. 52
Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Actual) Accident Months of Development Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 1994/93 9.4% 11.4% 7.3% 15.4% -0.8% -0.1% 1995/94 9.9% 6.2% 9.6% 10.6% 27.7% 1996/95 9.8% 11.7% 11.0% -1.6% 1997/96 8.7% 8.7% 11.0% 1998/97 10.3% 8.8% 1999/98 9.1% Select 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 6.2% = 355 / 334-1 = Slide 51 (1995) / Slide 51 (1994) - 1 53
Average Incremental Paid Method Step 3 Calculate on-level incremental payments [Trend all incremental paid amounts to current (2000) level] 54
Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (On-Level) Accident Months of Development Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 1993 503 280 136 70 48 27 1994 514 276 144 64 44 1995 501 277 146 75 1996 513 282 131 1997 512 287 1998 511 1999 Select N/A 510 280 140 70 46 27 514 = 334 x (1.09) ^ 5 = Slide 51 * (Slide 53) ^ number of years 55
Average Incremental Paid Method Step 4 Project future payment amounts [Fill-in the triangle] 56
Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Projected) Accident Months of Development Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 Total 1993 0 1994 27 27 1995 46 29 75 1996 70 50 32 152 1997 140 76 55 35 306 1998 280 153 83 60 38 613 1999 510 305 166 91 65 42 1,179 Slide 55, Selected 83 = 70 x (1.09) ^ 2 = 1996 value x (Slide 53 ^ number of years) Total = Sum across row (projected future severity) 57
Average Incremental Paid Method Step 5 Calculate estimated ultimate losses. 58
Average Incremental Paid Method XYZ Auto Insurance Company Projected Ultimate Losses Projected Paid Loss Projected Projected Projected Ultimate Accident Per Ult. Claim Future Average Ultimate Losses Year as of 12/99 Severity Severity Claims (000's) (1) (2)=see below (3)=Slide 57 (4)=(2)+(3) (5)=Slide 47 (6)=(4)x(5) 1993 $1,197 $0 $1,197 100 $119.7 1994 1,281 27 1,308 110 144.0 1995 1,361 75 1,436 126 180.5 1996 1,414 152 1,567 139 218.2 1997 1,411 306 1,717 160 275.5 1998 1,259 613 1,873 185 347.1 1999 862 1,179 2,041 210 428.6 (2) = Slide 51, summed across row 59
Average Incremental Paid Method 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 60