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Waterside Re

                                

Introduction to Experience Rating

Joy Takahashi - American Re Broker Market

CAS Ratemaking Seminar

Session REI-39

March 7, 2002

Tampa, FL

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Introduction to Experience Rating

Classical Burning Cost Method Frequency Based Method

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Classical Burning Cost MethodBasic Steps

Obtain large loss listing and calculate nominal excess losses in layer (i.e. 100k xs 100k).

Apply trend factors; cap at policy limits.

Apply loss development factors.

Divide losses by adjusted subject premium to derive an expected loss cost.

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Classical Burning CostStep 1 - Collect data

1 97 255,692 300,000 100,000 5 97 75,324 0 6 97 130,235 100,000 014 98 1,152,028 1,000,000 100,00019 99 175,274 75,27438 01 360,044 1,000,000 100,000

Total 5,747,914 997,631

Log AY Rptd Loss Pol Limit Loss in Layer

Note: Losses include ALAE. Not all losses are displayed.

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Classical Burning CostStep 2 - Trend

Trend Trended Policy Loss in

Log AY Factor Loss Limit Layer

1 97 1.338 342,174 300,000 100,000

5 97 1.338 100,801 801

6 97 1.338 174,284 100,000 0

14 98 1.262 1,454,409 1,000,000 100,000

19 99 1.191 208,754 100,000

38 01 1.060 381,647 1,000,000 100,000

Total 6,907,025 1,234,012

Total w/ freq trend 1,312,100

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Classical Burning CostStep 3 - Loss Development

Trended XS Ultimate

AY Loss in Layer LDF Loss in Layer

97 251,500 1.238 311,300

98 300,100 1.485 445,600

99 212,200 2.302 488,500

00 442,700 4.604 2,038,100

01 105,500 41.432 4,370,300

Total 1,312,100 7,653,800

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Classical Burning CostStep 4 - Divide by Subject Premium

Nominal Trended Tr & Dev

AY Adj SEP $ % $ % $ %

97 12,763 144.4 1.1% 251.5 2.0% 311.3 2.4%

98 18,233 215.5 1.2% 300.1 1.6% 445.6 2.4%

99 23,133 175.3 0.8% 212.2 0.9% 488.5 2.1%

00 26,460 362.5 1.4% 442.7 1.7% 2,038.1 7.7%

01 31,500 100.0 0.3% 105.5 0.3% 4,370.3 13.9%

Est ‘02 40,000 400.8 1.0% 533.6 1.3% 967.5 2.4%

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Classical Burning CostPotential Problems

Presence or absence of a few large claims drives the indicated rates.

Order of application of development, trend and capping makes a difference.

Trending individual claims past policy limits. Impact of current policy limit profile vs. historicals. History not reflective of current situation: reserving

practices, type of business, coverage, etc.

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Frequency Based MethodBasic Steps

Estimate # of claims above a data limit (e.g. 28 claims > $50,000).

Use size of loss curves to project # of claims above the retention (e.g. 14.4 claims > $100,000 retention).

Distribute the projected counts by policy limit; eliminate counts with policy limit below retention (e.g. 12.25 claims if 15% of exposure has $100,000 limits).

Use size of loss curves to project average severity of claims in layer (e.g. $69,495 sev. in 100 x 100 layer).

Multiply frequency by severity to get total losses. Divide by adjusted subject premium to get expected

loss cost.

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Frequency BasedStep 1 - Project # of Claims Above Data

Limit

Detrended Actual Freq Clm Cnt Projected

AY Data Limit # > DDL Trend Dev Fctr # > DL

97 37,363 6 1.104 1.050 6.96

98 39,605 8 1.082 1.155 10.00

99 41,981 5 1.061 1.559 8.27

00 44,500 13 1.040 2.339 31.63

01 47,170 5 1.020 5.847 29.82

Selected 50,000 28.00

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Frequency BasedStep 1a - Selection Process

Projected Projected

AY # > DL Adj SEP Frequency # @ 02 Levels

97 6.96 12,763 .545 21.8

98 10.00 18,233 .549 21.9

99 8.27 23,153 .357 14.3

00 31.63 26,460 1.196 47.8

01 29.82 31,500 .947 37.9

Selected 40,000 .700 28.00

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Frequency BasedStep 2 - Project # of Claims Above

Retention

Projected

Limit Retention # > Ret.

50,000 xs 50,000 28.00

100,000 xs 100,000 14.41 *

300,000 xs 200,000 7.22 *

500,000 xs 500,000 2.84 *

* Note: these were derived from pareto size-of-loss curve frequency formula: N X [(DL + B)/(R + B)] ^ Q

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Frequency BasedStep 3 - Include Impact of Policy Limits

Projected # Clms by Pol Limit New

Limit Retention # > Ret 100 300 500 1MM # > Ret

50,000 50,000 28.00 4.20 5.60 7.00 11.20 28.00

100,000 100,000 14.41 2.16 2.88 3.60 5.76 12.25

300,000 200,000 7.22 1.08 1.44 1.81 2.89 6.14

500,000 500,000 2.84 .43 .57 .71 1.14 1.14

‘02 Policy Limit Distribution: 15% 20% 25% 40%

Note: Claims below line are eliminated from the layer due to policy limits.

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Frequency BasedStep 4 - Estimate Loss $ in Layer

Projected Avg Sev. Loss Cost

Limit Retention # > Ret. in Layer in Layer

100,000 100,000 14.41 69,495 1,001,423

100,000 100,000 12.25 69,495 851,210

Note: Average severities are from pareto size-of-loss curve severity formula: [(R+B)/(Q-1)] X {1 - [(R+B)/(R+L+B)]^(Q-1)}

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Frequency Based MethodStep 5 - Divide by Subject Premium

Subject Selected Loss Cost

Earned Prem. $ %

40,000,000 851,210 2.1%

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Frequency Based MethodPotential Problems

Credibility of claim count development factors Adjustment of development factors by data

limit Picking an appropriate data limit Testing of size-of-loss assumptions

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Frequency Based MethodAdvanced Techniques

Goal: Fitting individual claim data to size-of-loss curve.

» Trend individual claims to common accident date.» Develop trended individual claims to ultimate, using

report year development factors if available.» Fit developed and trended claims to size-of-loss curve.» Test curve with actual data and industry curves.» Use new fitted curve in frequency based method to

derive new loss cost.

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Frequency Based MethodAdvanced Techniques

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0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Ave

rag

e S

eve

rity

Actual Pareto

Comparison of Actual and Fitted Average Severities (in 000’s)

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Experience RatingComparison of Methods

Classical Burning Cost Original Alternative

Est. Losses $ 1,089,100 967,500

Est. Loss Cost % 2.7% 2.4%

Frequency Based Mtd Original Co. Fitted

Est. Losses $ 851,210 955,118

Est. Loss Cost % 2.1% 2.4%

Selected 1,000,000 2.5%