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Introduction to Reinsurance Exposure Rating

CAS Ratemaking SeminarSession REI-47

March 12, 2001 - Las Vegas

Ira Kaplan ikaplan@gcr.com

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Exposure Rating Objectives:Estimate Expected Excess Losses

Analyze the premium profile Estimate the expected loss

ratio Estimate the layering of the

expected losses

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Treaty Submission:Information Needed

Premiums by policy limits•What business exposes the layer to

loss? Premiums by G.L. class code

•How does the business expose the layer to loss?

Historic loss ratios• This takes us from premiums to losses

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Exposure Rating Assumptions:Policy Limits Profiles

Premium Distribution by Policy Limit: Limit Est. ‘01 Premium % of

Total• 100/100 $7,000,000

17.5%• 300/300 8,520,000 21.3• 500/500 10,000,000 25.0• 1000/1000 14,480,000 36.2

$40,000,0004

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Exposure Rating Assumptions:GL class profiles

100% Premises/Operations 100% Table 2

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Distribution of Premium to Layer Premium Distribution by Policy Limit:

Limit Premium Retention 100 Xs100 Xs 200

100/100 7,000 7,000 0 0300/300 8,520 6,842 1,066 612500/500 10,000 7,379 1,150 1,4711000/1000 14,480 9,641 1,502 3,336

40,000 30,862 3,717 5,420

NOTE: All values in thousands6

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The distribution of losses to layer is not

the same as the distribution of

premiums to layer - alae

- risk load7

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Distribution of Premium and Expected Loss to Layer: Policy Limit $500/$500

Premium LossLayer Distribution Distribution

0-100 73.8% 67.8%

100-20011.5% 14.7%

Above 200 14.7% 17.5%8

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Selection of Direct ELR

Review historic experience Test reserve adequacy Understand business plan changes Review rate level changes Selection: 40% (excl. alae)

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Allocation of Premium & Loss to Layer

Limit Retention 100 Xs100 Xs200 Total100/100 Premium 7,000 0 0 7,000 Loss 2,800 0 0 2,800300/300 Premium 6,842 1,065 612 8,520 Loss 2,551 552 304 3,408500/500 Premium 7,379 1,150 1,472 10,000 Loss 2,714 588 698 4,0001000/1000 Premium 9,641 1,502 3,336 14,480 Loss 3,537 766 1,485 5,792

Total Premium 30,862 3,717 5,421 40,000 Loss 11,602 1,907 2,490 16,000

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ALAE and combination losses need to be

included

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ALAE by Layer

Retention 100 Xs100 Xs200 TotalPremium 30,862 3,717 5,421 40,000

ExpLoss 11,603 1,907 2,490 16,000ALAE% 42.9% 20.9% 18.6% 36.6%ALAE 4,988 398 465 5,851Loss&ALAE 16,591 2,304 2,956 21,851L&LAE Ratio 53.8% 62.0% 54.5% 54.6%

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Loss Ratios by Layer

0

0.10.2

0.3

0.4

0.50.6

0.7

TotalLimits

Retention 100 xs 100 xs 200

LossLoss & alae

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Expected Frequency & Severity for $100,000 Layer

Expected Loss $1,906,650

Expected Avg Severity $ 68,207

Expected # of Claims 27.95

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How to Test the Exposure Rating Indications

Review the premium profile selections

Review the selected ELR Consider the appropriateness of

the ISO loss curves Look at actual loss information

• Experience Rating

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Pro Rata ALAELoss ALAE L & ALAE

Total 640 320 960600 x 400 240 120 360

Ceded Loss x Direct Expenses + Ceded LossDirect Loss

= Ceded Loss x (Direct Expense + Direct Loss) Direct Loss

= Ceded Loss x ( 1 + Direct Expense )

Direct Loss

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ALAE Treatment - case 1Trended Loss 640Trended ALAE 320Layer 600xs400

ALAEProrata Added To

Loss ALAE Total TotalRetained 400 200 600 400In Treaty 240 120 360 560Above Treaty 0 0 0 0Total 640 320 960 960

0

200

400

600

800

1000

1200

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ALAE Treatment - case 2Trended Loss 920Trended ALAE 460Layer 600xs400

ALAEProrata Added To

Loss ALAE Total TotalRetained 400 200 600 400In Treaty 520 260 780 600Above Treaty 0 0 0 380Total 920 460 1380 1380

0200400600800

1000120014001600

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ALAE Load Can Vary

By layer - as seen earlier Model with two way variability

• Load % decreases by limit• ALAE is then allocated to layers

– One allocation formula for Pro Rata– A more complicated one for Added To

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Introduction to Reinsurance Exposure Rating? NOT!

Intro to Excess of Loss Reinsurance Exposure Rating approach to estimating Loss&ALAE for GL

“Basics of Reinsurance Pricing” by David R. Clark, Exam 6 Study Note

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“Basics of Reinsurance Pricing”

Proportional Treaties Property Per Risk XS Casualty Per Occurrence XS

• WC, Umbrella, AADs Aggregate Distributions Property Cat Final Price -

• risk loads, expenses, etc.