Introduction to Experience Rating Casualty Actuarial Society Reinsurance Pricing Seminar Dave Clark, Actuary and VP Munich Reinsurance America, Inc.

2 Introduction to Experience Rating Agenda:  Basic Experience Rating Methodology  Diagnostics: telling the story  Credibility weighting with exposure rate  Examples  Problems & Challenges (time permitting)

3 Introduction to Experience Rating Basic Experience Rating Methodology Steps in Experience Rating: 1.Assemble Data 2.Adjust Subject Premium to Future Level 3.Trend and Layer Losses 4.Apply Loss Development

4 Introduction to Experience Rating Basic Experience Rating Methodology (1) Assemble Data First Rule: Apples-to-Apples collection of historical subject premium and loss data Trended OnLevel Subject Premium Trended Ultimate Layer Losses Experience Rate =

5 Introduction to Experience Rating Basic Experience Rating Methodology (1) Assemble Data Second Rule: Get all the detail on historical losses 1.Include all historical losses that would trend into the layer (rule of thumb: get all losses > half of your attachment point) 2.Split out ALAE for each loss 3.Include historical policy limits (and SIR if applicable) 4.Confirm that losses are assembled by occurrence, not by claimant

6 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level  Filed [manual] rate changes  “Price-level” changes Schedule-Rating, company tiers, etc Also include “soft” changes such as terms & conditions, changes in underwriting standards, etc  Exposure Trend (for inflation-sensitive exposure bases)

7 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level Goal is to adjust historical premium to a level “as if” it has been written during the future period. The split between “rate” and “price” is not always obvious (e.g., where are LCMs or package factors included?): get a full description from the ceding company.

8 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level

9 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level Note to actuaries coming from a primary rate-filing background: In a rate filing, you typically adjust premium to the current rate level. In reinsurance pricing, you want to adjust premium to the average rate level in the future period.

10 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level Obvious observation: If the ceding company’s effective rates drop by -10% for the prospective period, but we assume that rates are “flat,” then our experience rating will be understated by 10%. Recommended Reading: Trent Vaughn’s Commercial Lines Price Monitoring; CAS Forum Fall 2004 Handouts from Chris Nyce and Brian Hughes at the 2007 CAS Ratemaking Seminar (

11 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level

12 Introduction to Experience Rating Basic Experience Rating Methodology (2) Adjust Subject Premium to Future Level

13 Introduction to Experience Rating Basic Experience Rating Methodology (3) Trend & Layer Losses  Purpose is to bring the historical value up to the average level in the future period  Typically we apply trend and then cap the trended loss at the historical policy limit  Hidden assumption: All losses trend at the same percent (trend does not vary by size of loss)

14 Introduction to Experience Rating Basic Experience Rating Methodology (3) Trend Losses:Depends on Treaty Basis: Experience Period (AY) Risks Attaching Treaty Experience Period (AY) Losses Occurring Treaty

15 Introduction to Experience Rating Basic Experience Rating Methodology (3) Trend Losses – Leveraged Effect 1,000,000 1,200,000 trend

16 Introduction to Experience Rating Basic Experience Rating Methodology (3) Trend Losses - Impact on Excess Layer All numbers are for illustration only, and not for use in pricing.

17 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate  Factors depend on Layer of Reinsurance being priced  We apply LDFs to trended layer losses so that all years are on the same basis.  Development is an aggregate loss concept  Includes new claims (“true IBNR”), development on known claims, reopening of closed claims, etc

18 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate All numbers are for illustration only, and not for use in pricing.

19 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate Problem: Most recent periods are very green and may have zero losses reported to date. Should they be included? Alternatively, if there are losses, then they are hit with huge LDF. Possible Solutions: B-F or “Cape Cod” Methods

20 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate LDF Method: Ultimate = Reported × LDF Bornhuetter-Ferguson (B-F) Method: Ultimate = Reported + Prem×ELR×(1-1/ LDF) But what ELR do we use?

21 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate “Cape Cod” method is a special case of the B-F method. The ELR is selected to be equal to the final value of the all-year average loss ratio.  Subject Premium ELR  Ultimate Loss=

22 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate “Cape Cod” ELR turns out to be calculated simply as follows:  Premium/LDF ELR  Reported Loss= Where Premium/LDF is the “exposed premium” corresponding to the loss that we would expect to have been reported to date.

23 Introduction to Experience Rating Basic Experience Rating Methodology (4) Develop Losses to Ultimate Key Formulas in “Cape Cod” Method: Subject Premium / LDFSubject Premium Reported Loss × LDFReported Loss= Cumulative % of Loss Reported = 1 / LDF

24 Introduction to Experience Rating Diagnostics: Telling the Story Does the Experience-Rating make sense?  Graphical Display  Comparisons  Prior years’ Experience Rating  Exposure Rating

25 Introduction to Experience Rating Diagnostics: Telling the Story Simple test of actual versus expected: All numbers are for illustration only, and not for use in pricing.

26 Introduction to Experience Rating Diagnostics: Telling the Story Some questions to ask when reconciling with prior rating or exposure rating:  Is the experience rating distorted by large losses?  Is the ELR used in exposure rating consistent with the ceding company’s experience? Is the ALAE the same?  How has the business changed? Is the experience even relevant?

27 Introduction to Experience Rating Credibility Credibility: Experience Rating = Projection of losses based only on what took place for this specific account Exposure Rating = A Priori estimate of losses based on information other than the specific account’s experience in the layer

28 Introduction to Experience Rating Credibility Credibility: Separating claim counts is useful for comparing experience and exposure ratings, and also for gauging credibility. A good credibility standard is: the number of claims that we would have expected to observe in the historical periods. Z = n n + k

29 Introduction to Experience Rating Credibility Credibility:Other Considerations  Stability of Experience: How much would experience rate change if we remove the largest claim or add an additional full limit loss?  Are pricing factors (LDFs, rate changes, etc) from the account or are they default values?  Do the characteristics of the ceding company match the business in the exposure rating curves?

30 Introduction to Experience Rating EXAMPLES

31 Introduction to Experience Rating Challenges We will look at two challenges that require some variation on the experience-rating: (1) Changing Mix of Business or Policy Limits Distribution (2) Inclusion of Excess or Umbrella Policies

32 Introduction to Experience Rating Challenges (1) Changing Mix of Business Wherever possible, we want the experience rating performed on homogeneous experience. That is, each historical period writes the same business as will be in the future period. A changing mix by line of business means that separate experience ratings are needed by line.

33 Introduction to Experience Rating Challenges (1) Changing Policy Limits Distribution Suppose we are pricing a 500,000 excess of 500,000 layer, but the ceding company has only recently begun writing high limit policies. How can the historical experience be used?

34 Introduction to Experience Rating Challenges (1) Changing Policy Limits Distribution (a) Trend past historical policy limits. (b) Price lower “fully exposed” layer and then use exposure-rating model relativities. (c) Adjust each historical period to the future period’s level of exposure. (d) Use curve-fitting model to historical losses. Complex Simple

35 Introduction to Experience Rating Challenges (1)Changing Policy Limits Distribution (a) Trend past historical policy limits. Advantage:  Very simple Disadvantage:  Only works if the reason that policy limits have changed is that they have drifted up with inflation.

36 Introduction to Experience Rating Challenges (1)Changing Policy Limits Distribution (b) Experience rate “fully exposed layer” Advantage:  Relatively simple Disadvantages:  Subject premium still needs to be adjusted to the average policy limit profile of future period.  Does not make use of the loss experience in the layer that we are actually pricing.

37 Introduction to Experience Rating Challenges (1) Changing Policy Limits Distribution (c) Adjust years based on exposure rating each historical period Advantage:  This is the most accurate method. Disadvantage(s):  Requires full policy limit profile for each historical period  Difficulty in explaining adjustment factors

38 Introduction to Experience Rating Challenges (1) Changing Policy Limits Distribution All numbers are for illustration only, and not for use in pricing.

39 Introduction to Experience Rating Challenges (1) Changing Policy Limits Distribution (c) Adjust years based on exposure rating each historical period The exposure rates from this table are used to “layer” the subject premium to find the portion of premium corresponding to the losses in the layer; the layered premium becomes the new “adjusted subject premium.” Note: this is a variation on the exposure adjustment described by Mata & Verheyen in their Spring 2005 CAS Forum article.

40 Introduction to Experience Rating Challenges (1)Changing Policy Limits Distribution (d) Fit curve to historical data Advantage:  Makes use of all the loss information Disadvantage(s):  Does not properly include development  Significant increase in complexity  Temptation to extrapolate beyond data

41 Introduction to Experience Rating Challenges (2) Inclusion of Excess Policies Challenges:  Proper handling of “supported” and “unsupported” excess policies  Proper application of inflation trend

42 Introduction to Experience Rating Challenges (2) Inclusion of Excess Policies Primary Policy 1M Limit Excess Policy 1M xs 1M 2M Exposed Excess Policy 1M xs 1M 1M Exposed “Supported” Excess“Unsupported” Excess

43 Introduction to Experience Rating Challenges (2) Inclusion of Excess Policies “supported” and “unsupported” excess policies (a) Combine primary and excess portions of large losses This is the right answer, but requires the ability to match loss records from the two types of policies (b) Price excess layer on a “responds ground-up” basis

44 Introduction to Experience Rating Challenges (2)Inclusion of Excess Policies Proper application of inflation trend (a) Add SIR to loss amount before trending (b) Use a higher trend percent to reflect “leverage”

Thank you very much for your attention. Dave Clark, Actuary and VP Munich Reinsurance America, Inc. © Copyright 2007 Munich Reinsurance America, Inc. All rights reserved. The Munich Re America name is a mark owned by Munich Reinsurance America, Inc. The material in this presentation is provided for your information only, and is not permitted to be further distributed without the express written permission of Munich Reinsurance America. This material is not intended to be legal, underwriting, financial, or any other type of professional advice. Examples given are for illustrative purposes only.