september 2001 new orleans, louisiana

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Intermediate Track II

September 2001New Orleans, Louisiana

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This Session Will Discuss

1. Bornhuetter-Ferguson Method

2. Average Hindsight Method

3. Average Incremental Paid Method

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BORNHUETTER-FERGUSONMETHOD

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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)

Bornhuetter-Ferguson Method

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Steps to Project Ultimate Loss

(1) Calculate Expected Losses(2) Calculate IBNR Factor(3) Calculate IBNR Reserve(4) Calculate estimated ultimate losses


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Assumptions Earned Premium = $1,250 Incurred Losses = $600 Expected Loss Ratio = 65% CDF = 1.35

(derived from incurred loss development triangle)

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Step 1 Calculate Expected Losses= Expected Loss Ratio x Earned Premium

Earned Premium = $1,250Expected 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) ]


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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 = 1.350IBNR Factor = [1 - 1/1.350] = 26%


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Step 3 Calculate IBNR Reserve= IBNR Factor x Expected Losses

Expected Losses = $813IBNR Factor = [1 - 1/1.350] = 26%IBNR Reserve = [$813 x 26%] = $211


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Step 4 Calculate Estimated Ultimate Losses= Incurred Losses + IBNR Reserve

Incurred Losses = $600IBNR Reserve = [$813 x 26%] = $211Ultimate Losses = [$600 + $211] = $811


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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


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Disadvantages

Highly dependent on expected loss ratio or pure premium Requires development factors


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Comparison of Methods

Given: Earned Premium = $2,000Expected Loss Ratio = 70 %Incurred Losses to Date = $750Development Factor = 2.00


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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


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Comparison of Methods: Illustration of Tempering Effect

Given: One additional “large” claim of $150

Incurred Losses to Date = $900


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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


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AVERAGEHINDSIGHT

METHOD

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Summary:

Estimate the expected ultimate losses for recent accident years based on “hindsight” average paid values per claim for more mature accident years.

Average Hindsight Method

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Data Needed

Cumulative Paid Loss Triangle

Cumulative Closed (Paid) Claim Count Triangle


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Steps to project Accident Year 1998 Ultimate Loss(1) Project ultimate losses for AY’s 1994-1997 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 1998(5) Calculate estimated ultimate losses for AY 1998


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Accident Year 1998 - Step 1

Project ultimate losses for AY’s 1994-1997 using paid loss development method


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XYZ Auto Insurance CompanyCumulative Paid Losses ($000)

Accident Months of DevelopmentYear 12 24 36 48 60 72 841994 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.71995 60.2 97.0 118.5 130.7 136.6 141.01996 75.5 120.1 147.0 162.4 171.01997 91.9 147.1 180.2 197.01998 115.0 184.1 226.41999 146.5 233.42000 181.1

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XYZ Auto Insurance CompanyDevelopment of Paid Losses

Months of DevelopmentAcc Year 12-24 24-36 36-48 48-60 60-72 72-84 84-Ult

1994 1.600 1.228 1.098 1.050 1.035 1.021 1.0001995 1.611 1.222 1.103 1.045 1.0321996 1.591 1.224 1.105 1.0531997 1.601 1.225 1.0931998 1.601 1.2301999 1.593

3 year avg 1.598 1.226 1.100 1.049 1.034 1.021 1.000Selected 1.050 1.035 1.020 1.000CDF 1.108 1.056 1.020 1.000

Diagonal 197.0 171.0 141.0 119.7Ultimate 218.4 180.5 143.8 119.7

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XYZ Auto Insurance CompanyCumulative Paid Losses ($000)

Accident Months of DevelopmentYear 12 24 36 48 60 72 84 Ultimate1994 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 $119.71995 60.2 97.0 118.5 130.7 136.6 141.0 143.81996 75.5 120.1 147.0 162.4 171.0 180.51997 91.9 147.1 180.2 197.0 218.41998 115.0 184.1 226.4 *1999 146.5 233.4 *2000 181.1 *

Ultimate losses from Slide 23

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Project ultimate claim counts for all AY’s using claim count development


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XYZ Auto Insurance CompanyCumulative Number of Closed Claims

Accident Months of DevelopmentYear 12 24 36 48 60 72 841994 50 75 88 94 97 99 1001995 55 83 97 104 107 1091996 63 94 110 118 1221997 70 105 123 1311998 80 120 1411999 93 1392000 105

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XYZ Auto Insurance CompanyDevelopment of Closed Claims

Months of DevelopmentAcc Year 12-24 24-36 36-48 48-60 60-72 72-84 84-Ult

1994 1.500 1.173 1.068 1.032 1.021 1.010 1.0001995 1.509 1.169 1.072 1.029 1.0191996 1.492 1.170 1.073 1.0341997 1.500 1.171 1.0651998 1.500 1.1751999 1.495

3 year avg 1.498 1.172 1.070 1.032 1.020 1.010 1.000Selected 1.500 1.172 1.070 1.032 1.020 1.010 1.000CDF 2.000 1.333 1.138 1.063 1.030 1.010 1.000

Diagonal 105 139 141 131 122 109 100Ultimate 210 185 160 139 126 110 100

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Accident Months of DevelopmentYear 12 24 36 48 60 72 84 Ultimate1994 50 75 88 94 97 99 100 1001995 55 83 97 104 107 109 1101996 63 94 110 118 122 1261997 70 105 123 131 1391998 80 120 141 1601999 93 139 1852000 105 210

Ultimate claim counts from Slide 27

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Calculate projected payment per claim from 36 months to ultimate


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XYZ Auto Insurance CompanyCalculation of Future Payment per Claim - 36 Months to Ultimate

Estimated Number of NumberEstimated Paid Estimated Ultimate Closed to Settle Average

Accident Ultimate Losses at Future Number Claims at Beyond FutureYear 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)

1994 $119,700 $98,200 $21,500 100 88 12 $1,7921995 143,820 118,500 25,320 110 97 13 1,9341996 180,525 147,000 33,525 126 110 16 2,1371997 218,372 180,200 38,172 139 123 16 2,345

Fitted forecasted value for AY 1998 $2,561

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Accident Year 1998 - Steps 4 & 5

Calculate total future payments for AY 1998

Calculate estimated ultimate losses for AY 1998


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XYZ Auto Insurance CompanyEstimated Ultimate Losses: Accident Year 1998

(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

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Steps to Project Accident Year 1999 Ultimate Loss

(1) Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1998 projection)(2) Calculate total future payments for AY 1999(3) Calculate estimated ultimate losses for AY 1999


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Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1998 projection)


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(2) 1995-1997 ultimates from Slide 24, 1998 ultimate from Slide 32



Accident Ultimate Losses at Future Number Claims at Beyond FutureYear 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)

1995 $143,820 $97,000 $46,820 110 83 27 $1,7281996 180,525 120,100 60,425 126 94 32 1,9071997 218,372 147,100 71,272 139 105 34 2,0791998 276,093 184,100 91,993 160 120 40 2,277


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Steps to Project Accident Year 2000 Ultimate Loss

(1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY’s 1998 & 1999 projections)(2) Calculate total future payments for AY 2000(3) Calculate estimated ultimate losses for AY 2000


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(1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY’s 1998 & 1999 projections)


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(2) 1996-1997 ultimates from Slide 24, 1998 from Slide 32, 1999 from Slide 37



Accident Ultimate Losses at Future Number Claims at Beyond FutureYear 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)

1996 $180,525 $75,500 $105,025 126 63 63 $1,6751997 218,372 91,900 126,472 139 70 69 1,8261998 276,093 115,000 161,093 160 80 80 2,0041999 349,084 146,500 202,584 185 93 92 2,194


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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”


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AVERAGEINCREMENTAL

PAIDMETHOD

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Summary: Estimate the expected ultimate losses for recent accident years based on average incremental paid values per claim.

Average Incremental Paid Method

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Data Needed:

Ultimate Claim Counts

Incremental Paid Loss Triangle


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Ultimate claim counts derived in average hindsight method - Slide 28


Accident Months of DevelopmentYear 12 24 36 48 60 72 84 Ultimate1994 50 75 88 94 97 99 100 1001995 55 83 97 104 107 109 1101996 63 94 110 118 122 1261997 70 105 123 131 1391998 80 120 141 1601999 93 139 1852000 105 210

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12-24 column = Slide 24, column 3 (24 mos) - column 2 (12 mos)

XYZ Auto Insurance CompanyIncremental Paid Losses ($000)

Accident Months of DevelopmentYear 0-12 12-24 24-36 36-48 48-60 60-72 72-841994 $50.0 $30.0 $18.2 $9.6 $5.4 $4.0 $2.51995 60.2 36.8 21.5 12.2 5.9 4.41996 75.5 44.6 26.9 15.4 8.61997 91.9 55.2 33.1 16.81998 115.0 69.1 42.31999 146.5 86.92000 181.1

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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


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Step 1

Create triangle of incremental paid losses per ultimate claim


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Slide 48 (incremental paid losses) / Slide 47 (ultimate claims counts)

XYZ Auto Insurance CompanyIncremental Paid Losses per Ultimate Claim (Actual)

Accident Months of DevelopmentYear 0-12 12-24 24-36 36-48 48-60 60-72 72-841994 500 300 182 96 54 40 251995 547 334 195 111 54 401996 601 355 214 123 681997 660 396 238 1211998 717 431 2641999 791 4692000 862

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Step 2

Calculate incremental payment trend factors and select projected trend factor.


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XYZ Auto Insurance CompanyIncremental Paid Losses per Ultimate Claim (Actual)

Accident Months of DevelopmentYear 0-12 12-24 24-36 36-48 48-60 60-72 72-84

1995/94 9.4% 11.4% 7.3% 15.4% -0.8% -0.1%1996/95 9.9% 6.2% 9.6% 10.6% 27.7%1997/96 9.8% 11.7% 11.0% -1.6%1998/97 8.7% 8.7% 11.0%1999/98 10.3% 8.8%2000/99 9.1%

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

6.2% = 355 / 334 - 1= Slide 51 (1996) / Slide 51 (1995) - 1

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Step 3

Calculate on-level incremental payments [Trend all incremental paid amounts to current

(2001) level]


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XYZ Auto Insurance CompanyIncremental Paid Losses per Ultimate Claim (On-Level)

Accident Months of DevelopmentYear 0-12 12-24 24-36 36-48 48-60 60-72 72-841994 503 280 136 70 48 271995 514 276 144 64 441996 501 277 146 751997 513 282 1311998 512 2871999 5112000

Select N/A 510 280 140 70 46 27

514 = 334 x (1.09) ̂5= Slide 51 * (Slide 53) ̂number of years

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Step 4

Project future payment amounts[Fill-in the triangle]


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XYZ Auto Insurance CompanyIncremental Paid Losses per Ultimate Claim (Projected)

Accident Months of DevelopmentYear 0-12 12-24 24-36 36-48 48-60 60-72 72-84 Total1994 0

1995 27 27

1996 46 29 75

1997 70 50 32 152

1998 140 76 55 35 306

1999 280 153 83 60 38 613

2000 510 305 166 91 65 42 1,179

Slide 55, Selected

83 = 70 x (1.09) ̂2= 1997 value x (Slide 53 ̂number of years)

Total = Sum across row (projected future severity)

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Step 5

Calculate estimated ultimate losses.


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(2) = Slide 51, summed across row

XYZ Auto Insurance CompanyProjected Ultimate Losses

ProjectedPaid Loss Projected Projected Projected Ultimate

Accident Per Ult. Claim Future Average Ultimate LossesYear as of 12/00 Severity Severity Claims (000's)(1) (2)=see below (3)=Slide 57 (4)=(2)+(3) (5)=Slide 47 (6)=(4)x(5)

1994 $1,197 $0 $1,197 100 $119.71995 1,281 27 1,308 110 144.01996 1,361 75 1,436 126 180.51997 1,414 152 1,567 139 218.21998 1,411 306 1,717 160 275.51999 1,259 613 1,873 185 347.12000 862 1,179 2,041 210 428.6

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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 businessCould be distorted if payout patterns change


september 2001 new orleans, louisiana

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