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TABLE OF CONTENTS

Volume I BASIC RATEMAKING TECHNIQUES

1. Werner 1 "Introduction" 1 2. Werner 2 "Rating Manuals" 11 3. Werner 3 "Ratemaking Data" 15 4. Werner 4 "Exposures" 27 5. Werner 5 "Premium" 45 6. Werner 6 "Losses and LAE" 99 7. Werner 7 "Other Expenses and Profits" 161 8. Werner 8 "Overall Indication" 177 9. Werner 9 "Traditional Risk Classification" 233 10. Werner 10 "Multivariate Classification" 269 11. Werner 11 "Special Classification" 283 12. Werner 12 "Credibility" 363 13. Werner 13 "Other Consideration" 387 14. Werner 14 "Implementation" 395 15. Werner 15 "Commercial Lines Rating Mechanisms" 429 16. Werner 16 "Claims-Made Ratemaking" 477

Volume II

17. ISO Personal Auto Manual 507 18. ASOP 13 "Trending Procedures in Property/Casualty Insurance Ratemaking" 523 19. CAS Ratemaking Statement of Principles Regarding P&C Insurance Ratemaking 529 20, AAA “Risk Classification Statement of Principles” 541 21. Feldblum "Personal Automobile Premiums: An Asset Share Approach" 563

UNPAID CLAIM ESTIMATION

22. Friedland 1 “Overview” 595 23. Friedland 2 “The Claims Process” 603 24. Friedland 3 “Understanding the Types of Data Used in Estimation of Unpaid Claims” 607 25. Friedland 4 “Meeting with Management” 619 26. Friedland 5 “The Development Triangle” 625 27. Friedland 6 “The Development Triangle as a Diagnostic Tool” 631 28. Friedland 7 “Development Technique” 641 29. Friedland 8 “Expected Claims Technique” 665 30. Friedland 9 “Bornhuetter-Ferguson Technique” 673 31. Friedland 10 “Cape Cod Technique” 707 32. Friedland 11 “Frequency-Severity Technique” 713 33. Friedland 12 “Case Outstanding Development Technique” 749 34. Friedland 13 “Berquist-Sherman Techniques” 763 35. Friedland 14 “Recoveries: Salvage and Subrogation and Reinsurance” 821 36. Friedland 15 “Evaluation of Techniques” 833 37. Friedland 16 “Estimating Unpaid Allocated Claim Adjustment Expenses” 869 38. Friedland 17 “Estimating Unpaid Allocated Claim Adjustment Expenses” 877 39. ASOP 9 “Documentation and Disclosure in Ratemaking, Reserving, and Valuations” 917 40. ASOP 43 “Property/Casualty Unpaid Claim Estimates” 925 41. CAS Reserves Statement of Principles Regarding Insurance P&C Reserves 931

NOTES Questions and parts of some solutions have been taken from material copyrighted by the Casualty Actuarial Society. They are reproduced in this study manual with the permission of the CAS solely to aid students studying for the actuarial exams. Some editing of questions has been done. Students may also request past exams directly from the society. I am very grateful to this organization for its cooperation and permission to use this material. It is, of course, in no way responsible for the structure or accuracy of the manual. Numbers in parentheses at the end of each question identify exam questions. CAS questions have four numbers separated by hyphens: the year of the exam, the number of the exam, the number of the question, and the points assigned. SoA or joint exam questions usually lack the number for points assigned. W indicates a written answer question; for questions of this type, the number of points assigned is also given. A indicates a question from the afternoon part of an exam. MC indicates that a multiple-choice question has been converted into a true/false question. Page numbers (p.) with solutions refer to the reading to which the question has been assigned unless otherwise noted. Although I have made a conscientious effort to eliminate mistakes and incorrect answers, I am certain some remain. I am very grateful to students who discovered errors in the past and encourage those of you who find others to bring them to my attention. I would also like to thank the following who in one way or another contributed to this manual: Tammy Applegate, Ed Jordan, Katy Murdza, Laurrie Raida, and Joanne Spalla. Hanover, NH 5/15/14 PJM

Werner 1 1

© 2014 ACTEX Publications, Inc. CAS Exam 5 – Peter J. Murdza

Geoff Werner and Claudine Modlin, Chapter 1: “Introduction,” in Basic Ratemaking, 2010, pp. 1–12

OUTLINE

I. INTRODUCTION

A. Insurance Pricing

1. Pricing formula

Price = Cost + Profit

2. Unlike many noninsurance products, insurance is a promise to do something in the future and thus its cost is unknown

B. Rating Manuals

1. Premium – “price the insurance consumer pays” a. Based on rate per unit of risk exposed b. Can vary significantly with risk characteristics

2. Rating manual – “document that contains the information necessary to appropriately classify each risk and calculate the premium associated with that risk”

II. BASIC INSURANCE TERMS

A. Exposure

1. Exposure – “basic unit of risk that underlies the insurance premium” 2. Unit varies greatly by line of business 3. Types

a. Written exposures – “total exposures arising from policies issued (i.e., underwritten or written) during a specified period of time

b. Earned exposures – “portion of the written exposures for which coverage has already been provided as of a certain point in time”

c. Unearned exposures – “portion of the written exposures for which coverage has not yet been provided as of that point in time”

d. In-force exposures – “number of insured units that are exposed to loss at a given point in time”

B. Premium

1. Premium – “amount the insured pays for insurance coverage” 2. Types

a. Written premium – “total premium associated with policies that were issued during a specific period”

b. Earned premium – “portion of the written premium for which coverage has already been provided as of a certain point in time”

c. Unearned premium – “portion of written premium for which coverage has yet to be provided”

d. In-force premium – “full-term premium for policies that are in effect at a given point in time”

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C. Claim

1. Policy – transaction whereby the insured pays premium “to an insurer in exchange for a promise to indemnify the insured for the financial consequences” of a covered event

2. Claim – “demand to the insurer for indemnification under the policy” 3. Claimant – insured or a third party making the demand for payment 4. Date of loss, a.k.a. accident date, occurrence date – “date of the event that caused the

loss” 5. Loss may be sudden or result from continuous or repeated exposure 6. Report date – date “the claimant reports the claim to the insurer” 7. Unreported claims a.k.a. incurred but not reported claims (IBNR) – “[c]laims not

currently known by the insurer” 8. Reported claim – claim that is known to the company 9. Open claim – claim that has not been settled 10. Closed claim – claim that has been settled 11. Reopened claim – closed claim on which further activity occurs

D. Loss

12. Loss – “amount of compensation paid or payable to the claimant under the terms of the insurance policy”

13. Paid losses – “amounts that have been paid to claimants” 14. Case reserve – “estimate of the amount of money required to ultimately settle” a claim 15. Case reserves are adjusted over time 16. Reported loss a.k.a. case incurred loss

Reported Losses = Paid Losses + Case Reserve

17. Ultimate loss – “amount of money required to close and settle all claims for a defined group of policies”

18. Reasons ultimate losses and reported losses differ a. Incurred but not reported (IBNR) reserve – “amount estimated to ultimately

settle” unreported claims b. Incurred but not enough reported (IBNER) reserve – “difference between the

aggregate reported losses at the time the losses are evaluated and the aggregate amount estimated to ultimately settle these reported claims”

8. Ultimate losses

Ultimate Losses = Reported Losses + IBNR Reserve + IBNER Reserve

E. Loss Adjustment Expense

19. Loss adjustment expense – expenses incurred “in the process of settling claims” 20. Types

a. Allocated loss adjustment expenses (ALAE) – “claim-related expenses that are directly attributable to a specific claim”

b. Unallocated loss adjustment expenses (ULAE) – “claim-related expenses that cannot be directly assigned to a specific claim”

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F. Underwriting Expenses

1. Underwriting expenses – expenses incurred in acquiring and servicing policies 2. Commissions and brokerage – “amounts paid to insurance agents or brokers as

compensation for generating business” a. Usually a percentage of premium written b. Factors affecting percentage

1) New vs. renewal 2) Quality of business 3) Volume written

3. Other acquisition costs – “expenses other than commissions and brokerage paid to acquire business”

4. General expenses – “remaining expenses associated with the insurance operations and any other miscellaneous costs”

5. Taxes, licenses, and fees – “all taxes and miscellaneous fees paid by the insurer excluding federal income taxes”

G. Underwriting Profit

1. Since ultimate policy cost unknown, insurers assume risk that is compensated by an expected profit

2. Sources of profit a. Underwriting profit a.k.a. operating income – “sum of the profits generated

from the individual policies” b. Investment income – money earned by investing insurance premium

III. FUNDAMENTAL INSURANCE EQUATION

A. Introduction

1. Insurance equation

Premium = Losses + LAE + UW Expenses + UW Profit 2. Goal of ratemaking is to balance both sides of the equation 3. CAS principle that rate to provide for all costs involved in risk transfer

B. Ratemaking Is Perspective

1. Ratemaking process involves estimation of various components of the equation 2. Use historical experience but not recoup past losses 3. CAS principle that a rate is an estimate of future expected costs; adjust historical

experience so that it is such an estimate 4. Factors to consider in adjusting historical experience

a. Rate changes b. Operational changes c. Inflationary pressures d. Changes in the mix of business written e. Law changes

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C. Overall and Individual Balance

1. Insurance equation should be balanced at both overall and individual/segment levels 2. CAS principle that rate should cover costs of individual risk transfer 3. Failure to recognize differences in individual risks produces inequitable rates

IV. BASIC INSURANCE RATIOS

A. Frequency

1. Frequency – “measure of the rate at which claims occur”

Frequency = Number of Claims

Number of Exposures

2. Usually claims are reported claims and denominator is earned exposures 3. Uses

a. Identify general industry trends b. Measure effectiveness of specific underwriting actions

B. Severity

1. Severity – “measure of the average cost of claims”

Severity = Losses

Number of Claims

Paid Severity = Paid Losses on Closed Claims

Closed Claims

Reported Severity = Reported LossesReported Claims

2. May include or exclude ALAE 3. Uses a. Provide information on loss trends b. Identify changes in claims handling practices

C. Pure Premium 1. Pure premium a.k.a. loss cost, burning cost – “measure of the average loss per

exposure”

Pure Premium = Losses

Number of Exposures = (Frequency)(Severity)

2. Usually based on reported/ultimate losses and earned exposures 3. May include or exclude LAE 4. Identifies trends attributable to both frequency and severity

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D. Average Premium

1. Average premium

Average Premium = Premium

Number of Exposures

2. Both premium and exposures should be of the same type, i.e., written, earned, in force 3. Identifies shifts in the mix of business

E. Loss Ratio

1. Loss ratio – “measure of the portion of each premium dollar used to pay losses”

Loss Ratio = Losses

Premium = Pure Premium

Average Premium

2. Usually uses total reported losses and total earned premium 3. May include or exclude LAE 4. Measures adequacy of overall and segment rates

F. Loss Adjustment Expense Ratio

1. LAE ratio

LAE Ratio = Loss Adjustment Expenses

Losses

2. Includes both ALAE and ULAE 3. Uses

a. Indicates whether settlement costs are stable b. Comparison with ratios of other insurers

G. Underwriting Expense Ratio

1. UW expense ratio

UW Expense Ratio = UW Expenses

Premium

2. Types

a. Expenses incurred at policy inception measured as a ratio to written premium 1) Commissions 2) Other acquisition 3) Taxes, licenses, and fees

b. Expenses incurred throughout the period measured as a ratio to earned premium, i.e., general expenses

c. Combine the two ratios to produce the overall ratio 3. Uses a. Comparison with changes in inflation

b. Comparison with ratios of other insurers

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H. Operating Expense Ratio

1. Operating expense ratio (OER) – “measure of the portion of each premium dollar used to pay for loss adjustment and underwriting expenses”

OER = UW Expense Ratio + LAE

Earned Premium

2. Used to monitor expenditures and profitability

I. Combined Ratio

1. Combined ratio – “combination of the loss and expense ratios”

Combined Ratio = Loss Ratio + LAE

Earned Premium + Underwriting Expenses

Written Premium

Combined Ratio = Loss Ratio + OER 2. Loss ratio should exclude LAE 3. Used to measure profitability

J. Retention Ratio

1. Retention ratio – “measure of the rate at which existing insured renew their policies upon expiration”

Retention Ratio = Number of Policies RenewedNumber of Potential Policies

2. May exclude certain policies a. Policies canceled because of death

b. Policies not renewed by an underwriter 3. Uses a. Measure competitiveness

b. As input for projecting future premium volume

K. Close Ratio

1. Close ratio a.k.a. hit ratio, quote-to-close ratio, conversion rate – “measure of the rate at which prospective insureds accept a new business quote”

Close Ratio = Number of Accepted Quotes

Number of Quotes

2. May count multiple quotes separately or as just one 3. Used to measure competitiveness

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PAST CAS EXAMINATION QUESTIONS 1. Given the following information, compute the combined ratio.

Written premium $125 Earned premium $100 Losses incurred 77 Loss adjustment expenses incurred 8 Other underwriting expenses incurred 25 Increase in prepaid expenses 5 A. 110.0 B. 103.4 C. 93.0 D. 88.0 E. None of these answers is correct. (81–7–34–1) 2. Given the following, calculate the combined ratio.

Written premium $10,000,000 Earned premium $9,000,000 Investment income 1,000,000 Underwriting expense 2,500,000 Losses and LAE incurred 6,000,000 (82–5–72b–1) 3. Given the following data, compute the combined ratio.

Written premium $9,000 Earned premium $10,000 Commissions and taxes 1,000 All other expenses 2,500 Incurred losses 6,000 (85–5–70–1) 4. What is the combined ratio based on the following data?

Written premium $11,500 Earned premium $11,000 Paid losses 5,000 Incurred losses 8,500 Underwriting expenses 4,200 A. < 100% B. ≥ 100% but < 110% C. ≥ 110% but < 115% D. ≥ 115% but < 120% E. ≥ 120% (90–3B–41–2)

5. Using the following data, calculate the company's combined ratio.

Incurred losses and loss expense $20,000,000 Investment income $3,000,000 Incurred underwriting expense 6.000,000 Earned premium 25,000,000 Written premium 32,000,000 A. < 85% B. ≥ 85% but < 90% C. ≥ 90% but < 95% D. ≥ 95% but < 100%

E. ≥ 100% (94S–3B–55–2) 6. Given the following information, what is the combined ratio?

Written premium $1,000,000 Earned premium $800,000 Expenses 200,000 Paid losses 600,000 Incurred losses 900,000

A. .800 B. .950 C. 1.000 D. 1.325 E. 1.375 (94F–3B–53–1) 7. Giving the following information, calculate the combined ratio:

Incurred underwriting expenses $2,500,000 Incurred loss adjustment expenses 3,650,000 Incurred losses 11,150,000 Written premiums 14,150,000 Earned premiums 19,000,000 A. < .90 B.≥ .90 but < .94 C. ≥ .94 but < .98 D. ≥ .98 but < 1.02 E. ≥ 1.02 (95F–3B–51–1)

8 Werner 1


1. Combined Ratio = Incurred Losses + LAE

Earned Premium + Underwriting Expenses Incurred

Written Premium

CR = (77 + 8)/100 + 25/125 = 105.0%, p. 10. Answer: E



Written Premium

CR = 6M_

/9M_

+ 2.5M_

/10M_

= 91.7%, p. 10. 3. Assume that losses include LAE.

Combined Ratio = Incurred Losses + LAE


Written Premium

CR = 6,000/10,000 + 3,500/9,000 = 98.9%, p. 10.



Written Premium

CR = 8,500/11,000 + 4,200/11,500 = 113.8%, p. 10. Answer: C



Written Premium

CR = 20M

_/25M

_ + 6M

_/32M

_ = 98.8%, p. 10.

Answer: D

6. Assume incurred losses include LAE.

Combined Ratio = Incurred Losses + LAE


Written Premium

CR = .9M_

/.8M_

+ .2M_

/1M_

= 132.5%, p. 10. Answer: D



Written Premium

CR = (11.15M_

+ 3.65M_

)/19M_

+ 2.5M_

/14.15M_

= 95.6%, p. 10. Answer: C

Werner 1 9


8. According to Werner and Modlin, which of the following is true regarding the ratemaking process?

A. Pure premiums usually contain a provision for premium taxes. B. Incurred losses are defined to be the sum of paid losses and reported losses. C. An exposure unit is a measure of risk assumed under an insurance contract. D. None of these statements are true. E. All of these statements are true. (93F–3B–61–2)

9. a. Explain how the standard economic formula, Price = Cost + Profit, relates to the fundamental insurance equation.

b. Company ABC replaced inexperienced adjusters with experienced adjusters who have a greater knowledge of the product. Explain the impact of this change on each component of the fundamental insurance equation. (10–5–11–.75/1.25)

10. Given the following information, calculate the combined ratio.

2008 earned premium $200,000 2008 incurred losses $125,000 Loss adjustment expense ratio .14 Underwriting expense ratio .25 (10–5–12–1)

11. Given the following information:

Calendar Year 2010 Written premium $280.00 Earned premium $308.00 Commissions $33.60 Taxes, licenses and fees $9.80 General expenses $36.96 LAE ratio (to loss) 8.2% Combined ratio 100%

Calculate the 2010 operating expense ratio. (11–5–8–1.25)

10 Werner 1


8. A. F, p. 8 – They equal the average loss per unit of exposure.

B. F, p. 3 – Substitute "case and IBNR and IBNER reserves" for "reported losses." C. T, p. 2

Answer: C 9. a. “The general economic formula can be tailored to the insurance industry using the basic insurance

terminology outlined in the preceding section. Premium is the ‘price’ of an insurance product. The ‘cost’ of an insurance product is the sum of the losses, claim-related expenses, and other expenses incurred in the acquisition and servicing of policies. Underwriting profit is the difference between income and outgo from underwriting policies, and this is analogous to the ‘profit’ earned in most other industries. . . . Making those substitutions, the prior formula is transformed into the fundamental insurance equation:

Premium = Losses + LAE + UW Expenses + UW Profit,” p. 5. b. The overall effect on future premium is uncertain. The effect on losses is uncertain. More

experienced adjusters may detect more fraudulent claims, reducing losses, but they could also pay out more under policy provisions with which inexperienced adjusters are unfamiliar, increasing losses. The effect on LAE is uncertain. Experienced adjusters may work efficiently, reducing LAE, but will earn higher salaries, increasing LAE. UW expenses should be unaffected. The overall effect on UW profit is uncertain, p. 5.

10. Combined Ratio = (Incurred Losses)(1 + LAE Ratio)


Written Premium

CR = ([(125,000(1 + .14)]/200,000 + .25 = 96.3%, p. 10.

11. Underwriting Expense Ratio = Commissions + Taxes, Licenses, and Fees

Written Premium + General ExpensesEarned Premium

UER = (33.60 + 9.80)/280 + 36.96/308 = .275 Operating Expense Ratio = 1 – (1 – UER)/(1 + LAE/Losses) = 1 – (1 – .275)/(1 + .082) = 33.0%, pp. 9–10.

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Geoff Werner and Claudine Modlin, Chapter 2: “Rating Manuals,” in Basic Ratemaking, 2010, pp. 13–35

OUTLINE

I. OVERVIEW A. Rules 1. Qualitative information needed to apply rating algorithm

a. Definitions b. Summary of policy forms, coverages, limitations, and exclusions c. Premium determination considerations

2. Criteria used to classify risks 3. Information on optional coverages 4. Underwriting guidelines

B. Rate Pages

1. Base risk – “specific risk profile pre-defined by the insurer” 2. Base rate – “rate applicable to the base risk” a. Not the average rate

b. If multiple coverages, multiple base rates 3. Base rate modified to produce rates for other risk profiles

a Multipliers, addends, or a mathematical expression b Discounts/surcharges and credits/debits

4. Incorporation of expenses a. Some expenses vary by premium amount; others are the same for each policy

b. Base rate may include both types of expenses or just variable expenses c. Requirement of a minimum premium assures that expenses are covered

C. Rating Algorithms

1. Rating algorithm – detailed description of “how to combine the various components in the rules and rate pages to calculate the overall premium charged for any risk that is not specifically pre-printed in a rate table”

2. Components a. Order to consider rating variables b. How rating variables are combined c. Minimum and maximum premiums d. Maximum discounts or surcharges e. Rounding rules

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D. Underwriting Guidelines

1. Decisions to accept, decline, or refer risks – based on set of characteristics 2. Company placement – low-risk and high-risk drivers may have different companies 3. Tier placement – different tiers apply to risks with the same rating characteristics but

different underwriting characteristics 4. Credits/debits under schedule rating

a. Credits/debits reflect risk characteristics b. May allow underwriter to use judgment 5. Over time underwriting criteria may be transformed into rating criteria 6. Underwriting criteria seen as proprietary information

II. RATING MANUAL EXAMPLES

A. Homeowners

1. Base rate a. Historically an all-peril base rate

b. Recently companies implement separate base rates by peril to which individual rating variable relativities apply

2. Rating and underwriting characteristics a. Amount of insurance (AOI) – $000s b. Territory – usually formed by grouping zip codes c. Protection class and construction type

1) Protection class – “ranking based on the quality of fire protection and the availability of water in the district”

2) Construction type – frame construction more susceptible to some types of losses than masonry

d. Underwriting tier – reflection of characteristics not shown in the rating manual e. Deductible – “amount of each covered loss the insured must pay” f. Miscellaneous credits, e.g., for insureds with multiple policies g. Additional optional coverages, e.g., additional coverage for jewelry

3. Expense fee – covers fixed expenses to acquire and service a policy 4. Rating algorithm

a. Multiply the base rate by the following: 1) AOI relativity 2) Territorial relativity 3) Protection class/construction type relativity 4) Underwriting tier relativity 5) Deductible credit 6) Unity less new home discount less claim-free discount 7) Unity less multipolicy discount

b. Add increased coverages and policy fee

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B. Medical Malpractice

1. Medical malpractice insurance – “type of professional liability policy that provides coverage to healthcare professionals in the event of a malpractice claim”

2. Base rates a. Exposure base – medical professional insured for one year b. Vary depending on whether employed or self-employed 3. Rating and underwriting characteristics

a. Specialty factor, e.g., obstetrics b. Part-time status c. Territory d. Claims-free discount – based on three years of experience e. Schedule rating – based on objective or subjective criteria f. Limit factors

1) Per-claim limit – “total amount the insurer will pay for all losses occurring from a single claim during the policy period”

2) Annual aggregate limit – “total amount the insurer will pay annually for all events covered in the policy period”

3) Different treatments of ALAE – within or outside the limit g. Deductible – credit if select h. Claims-made factor 1) Claims-made policies – policies whose trigger is the date of reporting,

not the date of occurrence 2) Claims must occur after the inception date of the first such policy and be

reported during the policy year 3) Maturity or step factors reflect coverage differences 4) Extended reporting endorsement – endorsement that “covers claims

that occur during the coverage period but are reported after the policy terminates”

i. Group credit – discount if policy includes more than one insured 4. Minimum premium – after all discounts applied 5. Rating algorithm

a. Multiply the base rate by the following: 1) Specialty relativity 2) Part-time status relativity 3) Territorial relativity 4) Unity less claims-free discount 5) Unity plus/less schedule rating debit/credit 6) Limit relativity 7) Unity less deductible credit 8) Claims-made factor 9) Unity less group credit

b. Apply minimum premium if applicable c. Sum for all insureds on the policy

14 Werner 2


C. US Workers Compensation Rating Manual

1. Workers compensation a. Highly regulated line b. NCCI collects and aggregates statistical WC data but several states have

independent bureaus c. Loss cost estimate – “portion of the rates that covers the expected future losses

and loss adjustment expenses for a policy” d. Insurer adjusts loss cost for the its expenses and any anticipated loss differences e. Net premium – “premium actually collected by the insurer,” including “manual

rates, premium discounts, individual rating modifications . . . and expense constants”

2. Class rate a. Classification system groups exposures with similar exposures to loss

b. NCCI has over 400 classes c. Class premium calculated by multiplying class rate times payroll divided by 100 d. Manual premium – aggregation of class premiums

3. Rating and underwriting characteristics

a. Experience rating a.k.a. experience modification – adjustment of manual premium to reflect differences between the insured risk and the average classification risk

1) Aggregate manual premium determines eligibility 2) Regulators may mandate if eligible 3) Involves comparison of prior actual and expected experience

b. Schedule rating 1) Underwriter uses judgment based on experience and internal guidelines 2) Various factors considered, e.g., premises, safety devices

c. Premium credits (e.g., for employee assistance program) not subject to an overall maximum

4. Expenses

a. Expense constant – fixed fee added “to all policies to cover expenses common to all workers compensation policies” 1) Does not vary by premium size 2) Covers expenses not included in the manual rate

b. Premium discount – discount for administrative expenses that vary with the size of the policy

c. Minimum premium – $1,500 5. Rating algorithm

a. Higher of the minimum premium and the calculated amount b. Manual premium

MP = i=1

N (Classi Rate)($Payroll for Class i), where

N - number of classes c. Multiply the manual premium by the following:

1) Unity plus schedule rating factor 2) Unity less pre-employment drug screening credit 3) Unity less employee assistance program credit 4) Unity less return-to-work program credit

d. Add the expense constant

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Geoff Werner and Claudine Modlin, Chapter 3: “Ratemaking Data” in Basic Ratemaking, 2010, pp. 36–48

OUTLINE

I. INTERNAL DATA

A. Overview

1. Quality of rates is dependent on quality and quantity of data 2. Usually ratemaking based on internal historical data of two types

a. Risk information, e.g., exposures, premiums b. Accounting information, e.g., underwriting expenses, ULAE

3. Data systems used vary from systems designed for ratemaking to general company databases

4. Actuary should review database for a. Adequacy of data specifications

b. Reasonableness and quality

B. Risk Data – Policy Database

1. Factors defining a database a. Records – “individual policies or some further sub-division of the policy” b. Fields – “explanatory information about the record”

2. Types of records a. HO – home for one year

b. WC – separate records at the class level c. Personal auto – usually separate records for each coverage and possibly for each

auto d. Separate records for before and after the amendment of a policy

3. Fields a. Policy identifier b. Risk identifier(s) – vehicles and operators c. Relevant dates – effective and termination dates for the policy and separate

coverages, amendment dates d. Premium – written premium by coverage e. Exposure – written exposure by coverage f. Characteristics – rating and underwriting variables

16 Werner 3


C. Risk Data – Claims Database

1. Records a. Each record usually reflects a transaction (payment or reserve change) related to

a specific claim b. Claims with multiple coverage or causes of loss may have separate records or are

represented via indicator fields 2. Fields

a. Policy identifier b. Risk identifiers – needed to match claim to policy database record c. Claim identifier d. Claimant identifier e. Relevant loss dates – loss date, report date, transaction date f. Claim status – open, closed, reopened, reclosed g. Claim count – not needed if each record or record collection defines a claim h. Paid loss – for different coverages can be tracked in separate fields or records i. Event identifier – extraordinary event, e.g., catastrophe j. Case reserve – for different coverages can be tracked in separate fields or records k. Allocated loss adjustment expense

1) Definitions a) Loss adjustment expenses (LAE) – “expenses incurred

handling claims” b) Allocated loss adjustment expenses (ALAE) – “expenses that

can be assigned to a specific claim and are included on the claim database”

c) Unallocated loss adjustment expenses – expenses that “cannot be assigned to a specific claim and are handled elsewhere

2) If ALAE subdivided, use additional fields 3) ULAE handled elsewhere 4) ALAE reserves may not be tracked, only payments

l. Salvage/subrogation 1) Salvage – recoveries when damaged property is “reconditioned and sold

to offset part of the payments made for the loss” 2) Subrogation – right “to recover any damages from a third party who was

at fault or contributed fault to the loss event” 3) Link such recoveries to the original claim

m. Characteristics, e.g., type of injury

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D. Accounting Information

1. Definitions a. Underwriting expenses – “expenses incurred in the acquisition and servicing of

the policies” b. Loss adjustment expenses (ALAE) – “expenses incurred in the process of

settling claims” c. Allocated loss adjustment expenses (ALAE) – loss adjustment “expenses

directly attributable to a specific claim and are, therefore captured on the claim extract”

d. Unallocated loss adjustment expense (ULAE) – loss adjustment expenses that “cannot be assigned to a specific claim”

2. Expenses tracked at the aggregate level since most cannot be assigned to individual policies or claims

3. Aggregate figures subdivided by line and state to determine expense provisions for ratemaking

II. DATA AGGREGATION

A. Objectives

1. Accurately match policy losses and premium 2. Use most recent data 3. Minimize data costs

B. Definitions

1. Calendar year aggregation – aggregation including “all premium and loss transactions that occur during the twelve-month calendar without regard to the date of policy issuance, the accident date, or the report date of the claim” a. Premiums and exposures – fixed at the end of the calendar year b. Losses

1) Calendar year paid losses – all losses “paid during the calendar year regardless of occurrence date or report date”

2) Calendar year reported losses – “paid losses plus the change in case reserves during that twelve-month calendar year”

c. Advantages 1) Available quickly 2) As typically collected, no additional expense

d. Disadvantage – premium comes from in-force policies but losses may involve policies issued many years ago

e. Appropriate for lines/coverages where losses are settled quickly

18 Werner 3


2. Accident year aggregation a.k.a. calendar-accident year aggregation, fiscal-accident year aggregation – calendar year aggregation of premiums and exposures and aggregation of “losses for accidents that have occurred during a twelve-month period, regardless of when the policy was issued or the claim was reported”

a. Losses 1) Accident year paid losses – “loss payments only for those claims that

occurred during the year” 2) Accident year reported losses – “loss payments made plus case reserves

only for those claims that occurred during the year” 3) Losses change even after the end of the year

b. Advantages 1) Better match of premiums and losses than calendar year 2) Available more quickly than policy year

c. Requires estimation of future development on known losses 3. Policy year aggregation a.k.a. underwriting year aggregation – aggregation including

“all premium and loss transactions on policies that were written during a twelve-month period, regardless of when the claim occurred, or when it was reported, reserved, or paid” a. Premiums and exposures not fixed until all policies have expired b. Losses

1) Policy year paid losses – “payments made on those claims covered by policies written during the year”

2) Policy year reported losses – “payments made plus case reserves only for those claims covered by policies written during the year”

3) Losses change even after the end of the policy year c. Advantage – best match between premiums and losses d. Disadvantage – not available as quickly as calendar or accident year data

4. Report year aggregation – aggregation that “is similar to calendar-accident [aggregation] except [that] the losses are aggregated according to when the claim was reported, as opposed to when the claim occurred;” typically used for claims-made policies

C. Overall Versus Classification Analysis

1. Overall rate level adequacy – can aggregate data by year for the product and location 2. Univariate classification analysis – aggregate by year for each rating variable studied 3. Multivariate classification analysis a. Organize data at the individual policy or risk level

b. Aggregate by year for each combination of rating variables studied

D. Limited Data

1. Use actuarial judgment to overcome data deficiencies 2. Example: use in-force premium by territory if earned premium not available

Werner 3 19


III. EXTERNAL DATA

A. Use of External Data

1. For new lines, may be necessary 2. For existing lines, may be helpful as a supplement

B. Statistical Plans

1. Regulators frequently require filing of statistical data according to a summary-based format

2. Texas Private Passenger Statistical Plan is aggregated by territory, deductible, and driver class and has he following uses: a. Set benchmark rates b. Supplement companies’ internal analyses

3. Industry organizations collect and aggregate data a. Specific organizations

1) National Council for Compensation Insurance (NCCI) 2) Insurance Services Office (ISO)

b. Organizations can analyze data or allow companies access c. Analysis may be at either overall or segment levels

4 State regulators may also make ad hoc data calls

C. Other Aggregated Industry Data

1. Fast Track Monitoring System – quarterly loss data for personal lines 2. Highway Loss Data Institute – detailed information by type of car

D. Competitor Rate Filings/Manuals

1. Companies may be required to submit rate filings with actuarial justification 2. Companies may also be required to submit manual pages needed to rate policies a. But obtaining a complete manual may be difficult

1) Only pages that that change have to be filed 2) Not required to file underwriting rules that assign insureds to tiers

b. Need to use other companies’ data with care as companies differ in regard to 1) Insureds 2) Goals 3) Expense levels 4) Operating procedures

20 Werner 3


E. Other Third-Party Data

1. General data a. Economic data, e.g., CPI b. Geo-demographic, e.g., population density c. Credit data

2. Specific data useful for certain lines a. Personal auto – DMV records b. HO – distance to fire station c. Earthquake – type of soil d. Medical malpractice – hospital characteristics e. CGL – ownership type f. WC – OSHA inspection data

Werner 3 21


PAST CAS EXAMINATION QUESTIONS 1. Accident year experience is better than policy year experience for determining automobile liability rate

levels in that it produces more accurate experience indications. (73–5–38–MC)

2. Accident year experience is better than policy year experience for determining automobile liability rate levels in that it produces a more mature body of experience at each reporting date. (73–5–38–MC)

3. Discuss briefly the advantages and disadvantages (with respect to ratemaking) of the calendar year and accident year measures of loss experience relative to each other. (77–6–46b–6)

4. Policy year statistics are the purest in that losses are strictly comparable to premiums. (78–6–20–MC) 5. Loss development factors are not required on calendar year incurred losses. (78–6–20–MC) 6. Which of the following loss ratios most accurately match the losses with the premiums intended to fund

those losses?

A. A fully developed policy year loss ratio B. A statutory loss ratio C. A trade basis loss ratio D. A calendar year loss ratio E. A fully developed calendar-accident year loss ratio (80–5–81–1)

7. According to Werner and Modlin, what advantages and disadvantages are associated with the use of

calendar year and policy year data for ratemaking? (Be brief and concise.) (88–6–42–2) 8. According to Werner and Modlin, which of the following are true?

1. Policy year premium statistics can be distorted by significant audit premiums. 2. Compared to calendar year ones, policy year statistics for the same year take longer to develop. 3. Calendar year data and calendar-accident year data differ primarily in calculating premium.

A. 1 B. 2 C. 3 D. 1,3 E. 2,3 (91F–3B–44–2) 9. According to Werner and Modlin, the accident year method of gathering statistics provides an exact

matching of losses and premiums to a specific group of insured entities. (93F–3B–27–1) 10. According to Werner and Modlin, which of the following is false regarding ratemaking using the calendar

year method?

A. The method can result in a single claim affecting several years of loss experience. B. The method is generally less accurate than the accident year method. C. The method estimates earned premium in the same manner as the accident year method. D. None of these statements are false. E. All of these statements are false. (94S–3B–60–2)

11. Of the three methods for gathering ratemaking statistics described by Werner and Modlin, the policy year

method is the only method that provides an exact match between premium and losses for a specific group of insured entities. (95S–3B–23–1)

12. According to Werner and Modlin, the formula for incurred losses is: loss reserves at end of year plus

losses paid during the year less loss reserves at beginning of year. (95F–3B–57–MC) 13. According to Werner and Modlin, calendar year statistics can have parts of a single claim being included

in several years. (95F–3B–57–MC)

22 Werner 3


Solutions are based on pp. 42–44. 1. F – Policy year data provides more accurate experience indications. 2. T.

3. 1) Calendar year data does not require development factors, whereas accident year data requires

such factors to reflect changes in loss valuation. 2) Calendar year losses and premiums do not have a close relationship as losses are affected by

reserve changes, whereas accident year losses and calendar year premiums are more closely related.

4. T. 5. T.

6. A. 7. Calendar year data is available promptly but lacks accuracy in its estimation of incurred losses because of

distortions caused by reserving inaccuracies. Policy year data provides a more accurate matching of losses and premiums but is not available promptly since the data stretch over two calendar years and is more costly since a separate system must be maintained.

8. 1. F – Substitute "calendar" for "policy."

2. T 3. F – The difference is in the calculation of losses. Answer: B

9. F – Substitute "policy" for "accident."

10. D.

11. T. 12. T. 13. T.

Werner 3 23


14. According to Werner and Modlin, the policy year method provides the best match of losses to premiums. (96F–3B–63–MC)

15. According to the Werner and Modlin, the calendar year method is the most accurate method.

(96F–3B–63–MC) 16. According to Werner and Modlin, a disadvantage of the policy year method of compiling ratemaking

statistics versus the accident year method is that the policy year method involves more delays in gathering statistics. (97F–3B–39–1)

17. According to Werner and Modlin, the only method for gathering ratemaking statistics that provides an

exact matching of losses and premiums to a specific group of insureds is the policy year method. (98S–3B–34–1) 18. According to Werner and Modlin, under the policy year method, incurred losses are not affected by

changes in reserves for events that occurred in earlier periods. (99S–3B–54–MC)

19. According to Werner and Modlin, the accident year method uses policy year earned premiums. (99S–3B–54–MC) 20. Werner and Modlin, in "Basic Ratemaking," describe three different types of experience periods by which

insurance data is compiled.

a. Describe how premiums and losses are compiled under each of the three experience periods:

i) Policy year ii) Calendar year iii) Calendar-accident year

b. State one advantage and one disadvantage associated with each type of experience period. (01–5–47–1.5ea.)

21. a. For both premium and loss data, describe the following methods for grouping ratemaking

experience: policy year, calendar year, and accident year. b. For purposes of ratemaking, which method in a. is most responsive and which method is least

responsive? (06–5–32–1.5/.5)

22. a. Briefly define "policy year," "calendar year," and "accident year loss experience." b. Which of the three performs the best with respect to responsiveness? Explain. c. Which of the three performs the best with respect to matching premiums and losses? Explain.

(07–5–53–1.5/.5/.5)

23. Identify one advantage and one disadvantage associated with using policy year incurred losses for ratemaking. (08–5–17d–.5)

24. Provide one advantage and one disadvantage associated with using calendar year incurred losses rather than accident year incurred losses for ratemaking. (09–5–22d–.5)

25. Briefly describe one advantage and one disadvantage of using calendar year losses as compared to accident year losses in a ratemaking application. (10–5–20d–.5)

26. Briefly describe one advantage and one disadvantage associated with using policy year losses for

ratemaking. (11–5–6e–.5)

24 Werner 3


14. T. 15. F – Substitute "least" for "most." 16. T. 17. T. 18. T – Incurred losses are only affected by changes in the reserves for the particular policy year. 19. F – Substitute "calendar" for "policy." 20. a. Policy year experience uses earned premiums and incurred losses arising from policies issued in a

particular twelve-year period. Calendar year experience uses financial data for a particular calendar year. Calendar year earned premium equals premiums written during that year plus the beginning unearned premium reserve less the ending unearned premium reserve. Calendar year incurred losses equals paid calendar year losses plus the ending loss reserve less the beginning loss reserve. Calendar-accident year experience uses calendar year earned premium and losses arising from accidents that occur during the particular calendar year.

b. Policy year experience provides an exact match of premiums and losses as it arises from a defined set of policies. It is less mature than the other experience. Calendar year is fully mature at the end of the year but provides the least exact match of premiums and losses. Accident year experience is a compromise between policy year and calendar year experience. It provides a more exact match of premiums and losses than calendar year experience but a less exact match than policy year experience. On the other hand, it is more mature than policy year experience but less mature than calendar year experience.

21. a. See 20a.

b. See 20b. Responsiveness reflects maturity. Thus calendar year data is most responsive and policy year data the least responsive.

22. a. See 20a. b. See 21b. c. See 20b. Policy year provides the best match. 23. See 20b. 24. See 20b. 25. See 20b. 26. See 20b.

Werner 3 25


27. When aggregating data for ratemaking purposes, two of the three general objectives are:

i) To accurately match losses and premiums for the policy. ii) To use the most recent data available.

Briefly discuss how well the following methods of data aggregation achieve these two general objectives. a. Calendar year b. Calendar/accident year c. Policy year. (13F–5–3–.5ea.)

26 Werner 3


27. See 20b.

Friedland 14 821


Jacqueline Friedland, Chapter 14: “Recoveries: Salvage and Subrogation and Reinsurance” in Estimating Unpaid Claims Using Basic Techniques, 2009, pp. 329–44

OUTLINE

I. SALVAGE AND SUBROGATION

A. Definitions

1. Salvage – “any amount that the insurer is able to collect from the sale of such damaged property”

2. Subrogation – “insurer’s right to recover the amount of claim payment to a covered

insured from a third-party responsible for the injury or damage”

B, Data Available

1. Possible situations for insurers a. Detailed information kept on case outstanding estimates and payments for the

following: 1) Salvage 2) Subrogation 3) Deductibles 4) Collateral sources

b. Only combined data for all types of recoveries kept c. Payment data, but not case outstanding, data kept d. Recoveries treated as negative claim payments and thus no separate data kept

2. Treatment a. Use development technique to quantify recoveries

b. Salvage recoveries 1) Usually for property lines 2) Tend to be fast reporting and fast settling c. Subrogation recoveries 1) Usually for liability lines 2) Tend to be slow settling

3) May produce age-to-age factors less than one

822 Friedland 14


C. Estimation Procedure

1. Term “received S&S” may be used instead of “paid S&S” to reflect payments from third parties to the insurer

2. Method #1: apply development technique to reported S&S

3. Method #2: apply development technique to received S&S

4. Method #3: use a ratio approach a. Estimate ultimate gross of S&S using paid claim development, reported claim

development, both of these, or another technique b. Construct triangle of historical ratios of received salvage and subrogation to paid

claims c. Calculate historical development factors and select CDFs to ultimate for each

accident year d. Apply the CDF to the latest ratio to project an ultimate S&S ratio; may select

other than the indicated ratio e. Apply the selected ultimate ratio to estimated claims gross of S&S to produce

projected ultimate S&S

5. Advantages of the ratio approach a. Development factors not highly leveraged b. Allows comparison of ratios, which allows adjustments in cases where

distortions caused by changes in recording procedures or unusually large claims

6. Subtract received S&S from projected ultimate S&S to produce estimated S&S recoverable

II. REINSURANCE

A, Overview

1. All claims estimation techniques can be applied to gross, ceded, or net of reinsurance claims experience

2. Two basic approaches

a. Analyze gross and ceded experience separately b. Analyze gross and net experience separately

3. Factors affecting which approach chosen

a. Data availability 1) If ceded claims coded in the same information system as gross data,

more likely to use gross and net analyses 2) If ceded claims coded in different systems, more likely to use gross and

ceded analyses 3) Data volume and quality may also be important

b. Characteristics of gross vs. ceded program c. Actuary’s personal preferences

Friedland 14 823


B. Stages of Analysis

1. At all stages, important that actuary is cognizant of the implied relationships between gross, ceded, and net claims a. At start when actuary is reviewing and reconciling the data b. During analysis when actuary uses judgment in development of an estimate c. At end when actuary evaluates various methods and makes a selection

2. Start of the analysis – check to see if net claim and net premium data are equal to of less

than the gross data a. Quota share – create triangle of net to gross claims

1) Check to see if ratios are consistent with available insurer information 2) Check to see if ratios are consistent with relationships between net and

gross premiums b. Excess of loss – examine large claims

1) Check to see if retentions and limits are consistent with excess-of-loss contracts

2) Check to see if such are consistent with information provided 3. During the analysis

a. Check to see if assumptions are consistent between gross and net or gross and ceded analyses 1) Since net claims capped because of aggregate coverage, net claim

development is frequently less than or equal to gross claim development 2) But situations exist where net development is greater than gross

development a) Captive assumes a working layer and fronting company retains

excess layer b) Large claims limited because of excess coverage

3) Actuaries differ in the order of their analysis a) Undertake gross analysis first

i) Gross data has greater volume and credibility ii) Use gross CDFs as input for selection of ceded or net

CDFs b) Undertake net analysis first

i) Gross data has more random variation because of large claims

ii) Use net CDFs as input for selection of gross CDFs c) Generally, but not always, relationship between the selected

gross and net factors should be reasonable 4) Also review the following:

a) Trend assumptions b) Expected claim ratios c) Frequency d) Severity

824 Friedland 14


4. Later stage of the analysis a. Make sure relationship between gross and net (or ceded) claims and resulting

estimates of unpaid claims are reasonable b. Net IBNR for each accident year should not exceed gross IBNR c. Need to understand treatment of prior recoveries from aggregate or stop-loss

coverages 1) Must know whether they are considered within claim development

triangles or at a later stage 2) Usually want data prior to their application

d. Goal is for an unpaid claims estimate net of both excess-of-loss and stop-loss recoveries

Friedland 14 825


PAST CAS EXAMINATION QUESTIONS 1. Given the following information as of December 31, 2008:

Accident

Year

Paid Claims Gross of S&S

Selected Ultimate Claims

Gross of S&S

Ratio of Received S&S

to Paid Claims

Development Factor to Ultimate

for S&S Ratio

2006 $15,513 $17,000 .361 1.000

2007 15,568 17,250 .379 1.007

2008 9,441 16,500 .286 1.300

a. Use the ratio method to estimate the recoverables for salvage and subrogation (S&S) for accident

years 2006–2008. b. Briefly discuss one advantage in using the ratio method to determine salvage and subrogation

recoverables. (09–6–1–1.5/.5) 2. Given the following data as of December 31, 2010:

Cumulative Paid Claims Gross of Salvage and Subrogation

Accident Year 12 Months 24 Months 36 Months 48 Months 2007 $12,200 $13,260 $13,280 $13,280 2008 12,180 13,300 13,320 2009 12,880 14,040 2010 11,980

Cumulative Received Salvage and Subrogation

Accident Year 12 Months 24 Months 36 Months 48 Months

2007 $3,074 $4,670 $4,720 $4,746 2008 3,098 4,558 4,602 2009 3,180 4,732 2010 2,858

i) Assume no further development after 48 months. ii) Use all-year simple averages for all factor selections.

Use a ratio approach to estimate ultimate salvage and subrogation recoveries. (11–5–32–3)

826 Friedland 14


1. a. 1) Calculate ultimate ratios for each accident year: UR06 = .361 UR07 = (.379)(1.007) = .3817 UR08 = (.286)(1.300) = .3718

2) Calculate ultimate S&S: USS06 = (.361)(17,000) = 6,137 USS07 = (.3817)(17,250) = 6,584 USS08 = (.3718)(16,500) = 6,135 USS = 6,137 + 6,584 + 6,135 = 18,856

3) Calculate paid S&S: PSS06 = (.361)(15,513) = 5,600 PSS07 = (.379)(15,568) = 5,900 PSS08 = (.286)(9,441) = 2,700 PSS = 5,600 + 5,900 + 2,700 = 14,200

4) Calculate S&S recoverables: SSR = USS – PSS = 18,856 – 14,200 = 4,656, pp. 329–30, 333–41. b. 1) “[T]he development factors tend not to be as highly leveraged as the development factors

based on received S&S dollars.”

2) Ultimate ratios may be adjusted to reflect the experience of the immediate preceding years, p. 330.

2. 1) Calculate paid claim development factors: CDF12-24: 1.087, 1.092, 1.090; 1.090 (ave.) CDF24-36: 1.002, 1.002; 1.002 (ave.) CDF36-48: 1.000

2) Calculate ultimate paid claims: UPC08 = 13,320 UPC09 = (14,040)(1.002) = 14,068 UPC10 = (11,980)(1.090)(1.002) = 13,084

3) Calculate ratios of received salvage and subrogation to cumulative paid claims:

Accident Year

12 Months

24 Months

36 Months

48 Months

2007 .252 .352 .355 .357 2008 .254 .343 .345 2009 .247 .337 2010 .239

4) Calculate ratio development factors: RDF12-24: 1.397, 1.350, 1.364; 1.370 (ave.) RDF24-36: 1.009, 1.006; 1.008 (ave.) RDF36-48: 1.006

5) Calculate ultimate ratios: UR08 = (.345)(1.006) = .347 UR09 = (.337)(1.008)(1.006) = .342 UR10 = (.239)(1.370)(1.008)(1.006) = .332

6) Calculate ultimate salvage and subrogation: USS = (.357)(13,280) + (.347)(13,320) + (.342)(14,068) + (.332)(13,084) = 18,518, pp. 329–30, 333–41.

Friedland 14 827



Gross Reported Claims (000s)


2006 $55,963 $62,679 $66,439 $66,439 2007 57,584 62,191 65,922 65,922

Net Reported Claims (000s)


2006 $50,367 $50,870 $51,125 $51,125 2007 37,430 40,424 42,849 42,849

Insurer has either a quota share reinsurance contract or an excess-of-loss reinsurance in place each accident year. a. Analyze the gross and net reported claims data to determine which type of reinsurance was

purchased for each accident year. Explain your reasoning. b. Briefly explain how the selection of tail factors for both net and gross reported claims should be

affected by the presence of an excess-of- loss reinsurance contract. (11–5–33–1/.5)

4. Given the following data as of December 31, 2001, use a ratio approach to estimate the ultimate salvage and subrogation for accident year 2011.

Cumulative Paid Claims Gross of Salvage and Subrogation ($000s)

Accident Year 12 Months 24 Months 36 Months 2009 15,117 16,953 16,953 2010 15,092 16,862 2011 14,727

Cumulative Received Salvage and Subrogation ($000s)

Accident Year 12 Months 24 Months 36 Months 2009 2,104 4,493 4,605 2010 1,995 4,657 2011 2,025

i) Selected cumulative development factors for the ratio of received salvage and subrogation to

paid claims are the following:

Age (months)

CDF to Ultimate

36 1.000 24 1.025 12 2.047

ii) Assume no development after 36 months. (12–5–25–1.75)

828 Friedland 14


3. a. For accident year 2006 the ratios of gross reported claims to net reported claims vary with maturity so the reinsurance is excess of loss. For accident year 2007 the ratios are constant so reinsurance is quota share, pp. 330–32, 342–43.

b. The presence of reinsurance does not affect gross tail factors. The tail factors for net reported

claims will vary with the type of reinsurance. “[I]t is generally not reasonable for the tail factor to be larger for net claims than for gross claims. Since net claims are often capped due to excess or aggregate coverage, we frequently observe net claim development patterns that are less than or equal to gross claim development patterns,” p. 331.

4. 1) Calculate paid claim development factors: 12–24 mos.: 1.121, 1.117; 1.119 (ave.) 24–36 mos.: 1.000 2) Calculate ultimate paid claims: UPC11 = (14,727,000)(1.119)(1.000) = 16,479,513

3) Calculate the ratio of received salvage and subrogation to cumulative paid claims:

RSS/CPC11 = 2,025/14,727 = .138

4) Calculate the ultimate ratio: UR11 = (.138)(2.047) = .282

5) Calculate ultimate salvage and subrogation: USS11 = (UR11)(UPC11) = (.282)(16,479,513) = 4,647,223, pp. 329–30, 333–41.

Friedland 14 829


5. Given the following information for a self-insured pool as of December 31, 2011:

Policy Year

Reported Claims Gross of Excess of Loss ($000s)

Reported Claims Net of Excess of

Loss ($000s)

Gross Cumulative Development

Factors

Net Cumulative Development

Factors

Stop Loss Limits ($000s)

2008 1,635 634 1.440 1.380 1,000 2009 3,109 625 1.760 1.620 1,250 2010 2,358 728 2.140 1.940 1,250 2011 1,897 674 2.710 2.450 1,500

i) The pool has maintained $1 million per-occurrence excess-of-loss reinsurance since inception. ii) The pool has also maintained stop-loss coverage over limits that vary over time as shown above.

Estimate the pool’s ultimate claims net of both excess of loss and stop-loss for policy years 2008 through 2011. (12–5–26–1.25)


Paid Claims Gross of Salvage & Subrogation Accident Year 12 Months 24 Months 36 Months 48 Months

2009 $2,000 $2,400 $2,500 $2,500 2010 2,100 2,300 2,400 2011 2,100 2,400 2012 2,500

Paid Salvage & Subrogation

Accident Year 12 Months 24 Months 36 Months 48 Months 2009 $98 $166 $250 $250 2010 105 163 240 2011 107 170 2012 75

i) Assume no development after age 48. ii) Ultimate claims for accident year 2012 equals $2,985. a. Using a development approach, estimate the ultimate salvage and subrogation for accident year

2012. b. Using a ratio approach, estimate the ultimate salvage and subrogation for accident year 2012. c. Briefly discuss which approach, the development or ratio approach, to select in recommending

an ultimate salvage and subrogation estimate for accident year 2012. (13S–5–24–.75/1.5/.25)

830 Friedland 14


5. 1) Calculate ultimate claims net of excess of loss but before the stop-loss limits applying net cumulative development factors to reported claims net of excess of loss.

UC08 = (634,000)(1.380) = 874,920 UC09 = (625,000)(1.620) = 1,012,500 UC10 = (728,000)(1.940) = 1,412,320 UC11 = (674,000)(2.450) = 1,651,300

2) Apply the stop-loss limits: UC08 = 874,920 UC09 = 1,012,500 UC10 = 1,250,000 UC11 = 1,500,000 UC08-11 = 4,637,420, pp. 330–32, 342–44.

6. a. 1) Calculate paid development factors: 12–24 mos.: 1.693, 1.552, 1.589; 1.612 (ave.) 24–36 mos.: 1.506, 1.472; 1.489 (ave.) 36–48 mos.: 1.000 2) Calculate ultimate salvage and subrogation: US&S12 = (75)(1.612)(1.489)(1.000) = 180.02, pp. 329-30, 337-38.

b. 1) Calculate ratios of received salvage and subrogation to cumulative paid claims:

Accident Year

12 Months

24 Months

36 Months

48 Months

2009 .049 .069 .100 .100 2010 .050 .071 .100 2011 .051 .071 2012 .030

2) Calculate ratio development factors: RDF12-24: 1.408, 1.420, 1.392; 1.407 (ave.) RDF24-36: 1.449, 1.408; 1.429 (ave.) RDF36-48: 1.000

3) Calculate the ultimate ratio: UR10 = (.100)(1.000) = .100 UR11 = (.071)(1.429)(1.000) = .101 UR12 = (.030)(1.407)(1.429)(1.000) = .060

4) Calculate ultimate salvage and subrogation. Since the calculated ultimate ratio for 2012 seems to be an aberration, select a ratio of .100.

US&S = (Ultimate Claims12)( UR12) US&S12 = (2,985)(.100) = 298.5, pp. 329–30, 333–41.

c. Use the ratio approach for the following two reasons: 1) “[D]evelopment factors tend not to be as highly leveraged as the development factors

based on received S&S dollars.” 2) Selection of an ultimate S&S ratio instead of the calculated one may be done easily, p.

330.

Friedland 14 831


7. Within the last year, an insurer implemented a new claims processing system that resulted in faster payment of claims. The claims department, however, failed to communicate this change to the actuarial department, and the actuary continued to use the paid loss development method to select the insurer’s ultimate losses. Discuss the impact of using the actuary’s calculation of ultimate losses on the reinsurance recoverable for the underlying business on an excess-of-loss-reinsurance contract where the retention has been exceeded but the limit has not yet been exhausted. (13F–5–19d–.5)


Reported Losses Gross of Reinsurance ($000,000) Accident Year

Age 12 24 36

2010 20 40 60 2011 15 30 2012 18

Reported Losses Net of Reinsurance ($000,000)

Accident Year

Age 12 24 36

2010 16 32 30 2011 14 24 2012 11

i) Each accident year has a 20% quota share reinsurance treaty. ii) Each accident year has an aggregate stop-loss treaty attaching at $30 million applied after the quota

share treaty. iii) Assume the gross data is correct.

a. Review the loss triangles above and briefly discuss whether the net data is reasonable based on both reinsurance treaties.

b. Explain and justify an approach for estimating gross, ceded, and net ultimate claim estimates. c. Predict the relationship between the gross reported loss tail factor and the ceded reported loss tail

factor. Explain the impact of both the quota share agreement and the stop-loss agreement. (13F–5–22–.5/.75/.75)

832 Friedland 14


7. Because current paid claims are now a greater percentage of ultimate claims, applying historical development factors will overstate estimated ultimate claims including those exceeding the retention The reinsurance recoverable will thus also be overstated, pp. 331-32.

8. a. Reported losses net of reinsurance are the lower of 80% of gross reported losses and $30 million.

For accident year 2010 at 24 months, the correct value is $30 million; for accident year 2011 at 12 months, the correct value is $12 million; and for 2012 at 12 months, the correct value is $14.4 million. Thus the net data is not reasonable.

b. Since net data is defective, develop gross data to ultimate and then apply the treaty provisions to

produce ceded and net ultimate claims. c. “For example, it is generally not reasonable for the tail factor to larger for net claims than for

gross claims. Since net claims are often capped due to excess or aggregate coverage, we frequently observe net claim development patterns that are less than or equal to gross claim development patterns.” Conversely, ceded reported loss tail factor will experience all of the development once a claim has passed the stop-loss limit and thus exceed the gross reported loss tail factor, pp. 330–32.

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