Objective 4 - Reserving

Question 1

Definitions of claim reserves and component parts

Answer 1

1. Valuation date - the date at which reserves are estimated
2. Incurral or loss date - the date the event which establishes a reserve or liability occurs (such as the date of disability)
3. Service date - the date a service is actually rendered
4. Reporting date - the date the claim is reported
5. Payment date - the date payment is made on a claim
6. Lag - the period of time between two dates
   a. Reporting lag - the time between incurral and reporting dates
   b. Service lag - the time between incurral and service dates
   c. Payment lag - the time between incurral and payment dates
   d. Accrual lag - the time between service and payment dates
7. Claim reserve - an estimate of the amount remaining to be paid on a claim for an event that occurred prior to the valuation date

Question 2

Additional considerations in establishing claim reserves (in addition to ASOP #5 considerations)

Answer 2

1. Incurral dating method
2. Reserve basis - statutory, GAAP, and tax bases differ in their use of margin, interest rates, etc.
3. Interest - reserves for claims with long payouts may be discounted to reflect interest
4. Controls and reconciliation - the data should be tested for accuracy
5. Insurance characteristics - reserves vary depending on the type of risk covered
6. Reserve cells - set up separate cells for each homogenous category of business
7. Managed care features - such as discounts and provider risk sharing arrangements
8. Trends
9. Seasonality
10. Claim administrative expenses - set up a a reserve equal to a percentage of the claim reserve
11. Morbidity assumptions - for long-term claims, morbidity is reflected in continuance tables
12. Diagnosis-based tabular reserves - some companies have begun using different morbidity bases for different causes of disability
13. Use of the case reserves method - very labor intensive, so only recommended for small blocks

Question 3

Advantages and disadvantages of stochastic approaches for reserving

Answer 3

Advantages:
1. Provides explicit guidance for establishing provision for adverse deviation in the reserves
2. Provides guidance on potential variability in reported earnings and reserve levels
3. Allows for quantification of variability in items such as seasonality and claim trend
4. Allows for improved evaluation of reserve estimates (by knowing the variability of the estimate)
Disadvantages
1. Some audiences that are unfamiliar with this approach may have a false sense of confidence in the approach because of its sophistication
2. May be too complex to be used by all individuals who must perform related functions (such as forecasting and pricing)
3. Not every process can be modeled rigorously

Question 4

Stochastic modeling techniques for reserving

Answer 4

1. Fitting a parametric distribution to the data - this technique works best when the process being modeled is stationary over time
2. Ordinary least squares regression - this allows for investigation of the effects of specific explanatory variables, such as trend or seasonality (limited applicability due to assumption of normality)
3. Generalized linear models - these models improve upon ordinary regression models because they allow for cases when the dependent variable being modeled is either bounded (e.g., must be greater than zero) or not normally distributed
4. Stochastic time series models - these are useful for handling situations where values are correlated across time (e.g., seasonal or cyclical patterns)
5. Monte Carlo simulation - this approach is of significant practical value when combining results from any of the other techniques

Question 5

Considerations when developing a stochastic approach to reserve estimation

Answer 5

1. Availability of data - historical data is needed to validate the model and assumptions
2. Appropriateness of data - consider whether the processes reflected in the historical data are representative of the process being modeled going forward
3. Access to statistical software - lack of access to or understanding of modeling software will limit the available choices for modeling techniques
4. Appropriateness of the model - this can be validated through goodness-of-fit testing, residual analysis, and hold-out sample evaluation
5. Covariances of modeled estimates - when reserve estimates are calculated through component estimates, the covariance between these components must be estimated

Question 6

Features of LTD and LTC contracts to consider when setting reserves

Answer 6

1. Periodic benefits - benefits typically equal some specified monthly or daily amount
2. Long-term benefit periods
3. Elimination periods
4. Optional benefits - these may affect the timing or amount of monthly payments (e.g., partial disability benefits and cost of living adjustments)
5. Integration of benefits - these plans often coordinate benefits with Social Security and Medicare
6. Limitations and exclusions - some claims are excluded (such as intentionally self-inflicted injuries) or subject to limited periods (such as mental and nervous claims)

Question 7

Types of long-term claims and reserve methods

Answer 7

1. Open claims - claims currently being paid (uses tabular reserves). Reserve = V(n) = Sum over t=n to BP(Benefit(t) * Continuance(t) * InterestDiscount(t)), where
   Benefit = monthly benefit (may vary over time due to product provisions)
   Continuance = the probability of a claim continuing to receive payments in the future
   Interest discount = the factor to reflect the time value of money
   n = current time period
   BP = benefit period
2. Pending claims - claims that have been reported but payments have not yet begun.
   Reserve for claims that are still in the elimination period = pending factor * tabular reserve
   Reserve for claims that have completed the elimination period = pending factor * (tabular reserve + accumulated value of past payments not yet made)
3. IBNR claims = claims that have been incurred but have not been reported to the company. The reserve can be estimated using either the lag method or the loss ratio method.

Question 8

Methods for evaluating claim reserve adequacy

Answer 8

1. Runoff studies (commonly done by incurral year) - previous reserve balances are compared to subsequent claim payments and reserve balances, with adjustments for interest
2. Actual to expected claim termination rate studies (commonly done by claim duration) - compares the actual claim terminations to the expected claim terminations based on the table used for reserving.
3. Experience studies - typically involves a gross premium valuation. The reserve is adequate if PV of future gross premiums + reserve > PV of future claim cost

Question 9

Health reserves definitions

Answer 9

1. Active life reserves - contract plus unearned premium reserves for contracts not in claim status
2. Claims adjudication - the process of determining eligibility for payment and establishing the payment amount
3. Claim liability - established when the claim event has occurred but payment has not been made
4. Contract reserves - the portion of premium collected in early durations that is intentionally designed to help pay for anticipated higher claims in later durations
5. GAAP reserves - may use more realistic assumptions and include explicit methods of revenue matching
6. Incurred date - date on which the obligation to pay was established (look at contractual obligation)
7. Lag - period from incurral to payment
8. Loss adjustment expense - the liability related to the cost of processing claims that have been incurred but not yet paid
9. Premium deficiency reserves - set up when it is determined (using a gross premium valuation) that future premiums plus current reserves are not sufficient to cover future claims payments and expenses
10. Provider liabilities - liabilities for withholds or other contractually-arranged payments to providers, not related to a single claim event
11. Unearned premium reserves - premium collected but allocated to a period of time after the valuation date
12. Valuation date - date as of which the statements, balances, and estimates are prepared

Question 10

Types of reserve reporting

Answer 10

1. Regulatory reporting - concerned with solvency and policyholder protection, so conservative
2. GAAP reporting - “realistic with provision for adverse deviation”
3. Experience reporting for employers and providers - typically less sophisticated except for financial settlement and pricing reviews. For settlements, allow a 3 month run-out period to minimize the size of the estimated reserve.
4. Valuations for acquisitions - reserves are material to profitability, so they are often a focal point of negotiations. There is often a final settlement after several months to revisit the purchase price and assess the impact of claim reserves.

Question 11

Types of claim liabilities and reserves

Answer 11

1. Due and unpaid liabilities (reported, adjudicated, and processed, but not paid) - is usually small. Itemize or base on historical averages.
2. In course of settlement - system may record receipt and run report. Otherwise, use simple method such as average claim times number of claims.
   Incurred and reported = due and unpaid + in course of settlement
3. IBNR - project by using existing payment data to develop average expected claims or claim payment patterns
4. Loss adjustment expenses - usually a percentage of unpaid claims liability
5. Present value of amounts not yet due (aka “unaccrued”) - an estimate of future amounts due on known open claims (commonly for disability or LTC claims)
6. Resisted claims - usually reserved seriatim assuming 100% of claim paid and possibly damages (usually in known litigation situations)
7. Outstanding accounting feed (may overlap with due and unpaid liability) - acknowledged by unpaid
8. Deferred maternity or other extended benefits - the loss is triggered before the valuation date, but benefits are deferred by contractual provisions
9. Other special reserves - such as for waiver of premium due to disability

Question 12

Methods of estimation for claim reserves

Answer 12

1. Case reserves - direct enumeration on a claim-by-claim basis. Typically used only when there are very few claims. Can’t use for IBNR.
   a. Examiner’s method - estimate ultimate payment and deduct what’s already been paid
   b. Average size claim method - the number of reported claims times an average claim amount minus the amount already paid
2. Projection method (aka formula or factor method) - develop a historical claim rate as a function of some measure of exposure. Then apply this rate to projected exposure. The most common approach is: projected PMPM claim costs * member months - claims already paid
3. Loss ratio method (aka claim cost method) - use wehre volume is low or to validate other methods. (loss ratio * earned premium = claims already paid)
4. Tabular method - apply a factor to open claims to calculate reserve. Typically used for LTC or disability. Can’t use for IBNR.
5. Development method (aka lag, completion, or triangulation method) - projects historical clam lag pattern into the future to estimate the reserve based on experience data
6. Emerging development method techniques (see separate list)
7. Stochastic approaches - methods where a probabilistic statement can be made about the level and adequacy of the reserve amount. Any of the methods discussed previously can be given a stochastic treatment.

Question 13

Characteristics of coverages for which the development method works well

Answer 13

1. Ability to record incurral and payment dates for each claim
2. Fairly consistent lag patterns
3. Short incurral periods relative to the ultimate run out (monthly is preferred)
4. A sufficient volume of business in each cell, in order to obtain reasonably stable results
5. Availability of either earned premium or exposure data (for volume adjustments and smoothing)

Question 14

Steps of the development method

Answer 14

1. Summarize data by incurral vs. paid month to get a claims triangle
2. Sum cells of the claims triangle to get cumulative incurred and paid claims
3. Develop age-to-age development factors (ratio of month to month cumulative claims)
4. Can use various methods to smooth the age-to-age development factors (see separate list)
5. Calculate age-to-ultimate development factors (called completion factors) from the smoothed age-to-age factors
6. Divide each month’s paid claims by its completion factor to get ultimate incurred claims
7. Subtract paid claims from the ultimate incurred claims to get unpaid claims liability

Question 15

Smoothing methods to apply to development factors

Answer 15

1. Simple averaging - average development factors for each lag month (3 month average is very current, 12 month average is smoothest but may bury trends)
2. Removing bumps - throw out the high and low factors and use 6 of the last 8 or 10 data points. Or remove large “shock” claims from the claim triangle and analyze them separately.
3. Weighted averaging - give more credibility to most recent results (sum of digits, squared sum of digits, constant declining percentage)
4. Other types of means - harmonic (use the reciprocal of the “mean of reciprocals”) or geometric (the nth root of the “product of n observations”)
5. Dollar-weighted methods (prior methods have been ratio weighted) - compute smoothed age-to-age factors directly by averaging the payment amounts for a given lag month and then dividing by the average for the prior lag month.
6. Per member age-to-age ratios - before calculating age-to-age ratios, divide payments in each lag by the exposure for that lag. Then use one of the above methods.

Question 16

Methods for adjusting development method reserve estimates for recent months

Answer 16

Replace completion factors that are less than 40% to 70% with estimates based on:

1. Projection method
2. Loss ratio method, or
3. Credibility-weighted average of development method results with the projection or LR method results

Question 17

Emerging development method techniques

Answer 17

1. Multiple triangles - this technique looks at claim triangles in both the traditional way (claims paid by service date) and in a new way (claims reported by service date)
2. Time series and other statistical projections (also referred to as “regression methods”) - these techniques use advanced statistical and computer tools to help in projecting claims. Uses include:
   a. Project payment patterns for partially complete incurral months (using statistical or time series techniques - instead of development factors - to complete claims)
   b. Project PMPM costs that can be applied in projection method techniques

Question 18

Process for building in conservatism in claim reserves

Answer 18

1. Development method - can incorporate conservatism in the completion and projection factors. But usually use most likely factors and add an explicit margin to the reserve.
2. Tabular reserves - margins are typically included in the assumptions made to calculate the tabular factors
3. Projection methods - add margins to the trend assumptions that are used to project costs per unit
4. Loss ratio methods - margins can be explicit or implicit, depending o the choice of loss ratio

Question 19

Assumptions needed to estimate premium deficiency reserves

Answer 19

PDR = PV of future claim costs and expenses less PV of future premiums and current reserves (all types of reserves: contract, claim, and premium)
(Use assumptions that are realistic, rather than conservative)
1. Rate increases - must be reasonable and likely to be implemented and approved
2. Enrollment - cannot project that new entrants will improve morbidity unless there is historical experience to justify this assumption
3. Lapses - should reflect any potential antiselection, particularly if induced by rating actions
4. Expenses - if other policies can be expected to cover overhead, then zero overhead costs may be assumed (reflect only operating costs)
5. Claims trend - reflect reasonable increases in claim costs
6. Interest rates - reasonable interest rate assumptions should be used to discount deficiencies
7. Taxes - these reserves are calculated on an after-tax basis
8. Provider arrangements
a. Provider settlements under risk sharing arrangements should not be used to offset claims unless they have been specifically determined and billed to the providers
b. Include capitations as claim costs at the level currently negotiated. Recognize that if the provider goes insolvent, the discounts are lost and costs will rise.
9. Reinsurance - the calculation of the reserve is usually net of reinsurance

Question 20

Types of outcome-based contractual reserves

Answer 20

1. Employer-based contractual liabilities - need to recognize liabilities for contracts where the employer shares the risk of emerging claims experience. The most common is the contractual Claims stabilization reserve (CSR) = Prior period CSR + premiums earned + interest credits - claims incurred - risk and retention charge.
2. Provider liabilities - for example, capitation payments owed, withholds, bonuses and incentives, stop loss settlements, and anticipated insolvency of capitated providers

Question 21

Steps for using the authorization method to project claims

Answer 21

1. Gather data on the number of authorized services as of the valuation date
2. Adjust authorized services - adjust for differences between initial authorizations and actual services rendered. Differences arise due to appeals, poor data, and issues with coordination of benefits and enforceability of rules
3. Calculate an average cost per service rendered - this average cost is frequently a blend of provider contractual amounts and actual payments made
4. Estimate incurred claims - multiply the number of services by the cost per service
5. Calculate the estimate IBNR - equals the estimated incurred claims minus the amount of paid claims to date

Question 22

Calculating provider liabilities

Answer 22

1. Risk-based payments - liabilities are based on projected contractual pay out, which is commonly defined as the difference between experienced and targeted costs. Settlements are often done several months after the period ends so reserves play a minimal role.
2. Bonus or incentive contracts - estimates are normally based on utilization studies
3. The impact of stop-loss provisions should be considered and a PAD should be included

Question 23

Reserve standards for the different types of financial statements

Answer 23

1. Statutory statement - the focus is on ensuring solvency, so reserves tend to be conservative
2. GAAP statement - the focus is on matching profit streams with revenue streams, with a lesser degree of conservatism (through provisions for adverse deviation)
3. Tax statement - IRS standards make sure profits beyond a set level are recognized, and therefore taxed, immediately
4. Embedded value based statement - may be needed for international companies. Standards are set by the International Accounting Standards Board.

Question 24

Types of premium reserves

Answer 24

1. Unearned premium - reserve for the premium that has been received to cover the portion of the coverage period which hasn’t yet occurred (usually a pro-rata portion of the last premium received)
2. Premium paid in advance - reserve for premiums paid in advance for future coverage periods
3. Premium due and unpaid - an asset is created on the statement for the amount of premium that is expected to be received
4. Policy reserves (aka contract reserves, active life reserves) - money set aside to account for current funding of costs over the future lifetime of a policy

Question 25

Formulas for policy reserves on a per original issued policy basis

Answer 25

1. Notation:
   ipx = probability of survival to duration i for a policy issued at age x
   v^t = (1 + annual interest rate)^-t = present value factor
   z,iCx = claim cost at age x, duration i, and issue year z
   z,iPx = net premium at age x, duration i, and issue year z
2. Prospective formula at time t:
   z,tVx = PV(future claims) - PV(future net premiums) = Sum over i=t to omega(ipx * v^(i-t) * (z,iCx - z,iPx))
3. Retrospective formula at time t:
   z,tVx = sum over i=0 to t-1(ipx * v^(i-t) * (z,iPx-z,iCx))
4. Two-year full preliminary term prospective formula at time t:
   z,tVx,2PT = tpx * sum over i=t-2 to omega(i-t+2px+t * v^(i-t+2) * (z,iCx+2 - z,iPx+2)) for years 2 and beyond
   z,tVx,2PT = 0 for years 0 and 1
5. A modified method to reflect annual inflation (j) on both the claims and premiums:
   z,tVx = sum over i=t to omega(ipx * v^(i-t) * (z,iCx - z,iPx) * (1 + j)^i)

Question 26

Formulas for policy reserves on a per surviving policy basis

Answer 26

1. Prospective formula at time t:
   z,tVx,s = Sum over i=t to omega(i-tpx_t * v^(i-t) * (z,iCx - z,iPx))
2. Retrospective formula at time t:
   z,tVx,s = sum over i=0 to t-1(1 / t-ipx+i * v^(i-t) * (z,iPx - z,iCx))
3. Two-year full preliminary term prospective formula at time t:
   z,tVx,2PT,s = sum over i=t-2 to omega(i-t+2px+t * v^(i-t+2) * (z,iCx+2 - z,iPx+2)) for years 2 and beyond
   z,tVx,2PT,s = 0 for years 0 and 1
4. A modified method to reflect annual inflation (j) on both the claims and premiums:
   z,tVx,s = sum over i=t to omega(i-tpx+t * v^(i-t) * (z,iCx - z,iPx) * (1 + j)^i)

Question 27

Formula for deferred acquisition cost (DAC) reserves

Answer 27

1. Notation:
   z,iEx = Deferrable expenses at age x, duration i, and issue year z
   iPx,E = net expense premium at age x, duration i, and issue year z
2. The formula ( on a per surviving policy basis):
   z,tDACx,s = sum over i=0 to t-1(1 / t-ipx+i * v^(i-t) * (z,iEx - z,iPx,E))

Question 28

Types of policies for which policy reserves are required

Answer 28

1. Contracts that use level premiums

2. Contracts where the value of the future benefits at any time exceeds the value of future net premiums

Question 29

Reasons why a deficiency reserve may be needed

Answer 29

1. A policy is noncancelable, so premium rates cannot be raised
2. Regulators are unlikely to allow the premium rates to rise to self-sufficient levels
3. The size of increases needed might trigger an antiselection spiral if that makes it impossible to ever break even

Question 30

Purposes of health plan auditors

Answer 30

1. Help ensure plans are properly spending their money
2. Look for the following types of errors and fraud:
   a. Errors in coding claims - these account for about 3% of claim payments
   b. Misinterpretations - for example, the plan may be paying 100% on some services where the member also paid a copay
   c. Outright fraud - such as providers billing for services that weren’t rendered and members getting prescriptions they don’t need and reselling the drugs on the street for large profits

Question 31

Ways in which health plans will implement ICD-10

Answer 31

1. Remediation - modify all applications to accommodate ICD-10
2. Replacement of all applications
3. Neutralization - create crosswalks from ICD-10 to ICD-9, even though some codes don’t crosswalk well (CMS will be using this approach initially)

Question 32

Advantages of stochastic reserving models (IBNR)

Answer 32

1. A reserve range is reported, including a worst-case reserve amount
2. The model can produce an explicit probabilistic statement
3. The model can forecast future claims, trends, and reserves
4. The model can handle seasonality and changing lag patterns
5. It can produce actuarial work faster than with traditional models
6. Sensitivity analysis can be done
7. It produces confidence intervals

Question 33

IBNR Methods

Answer 33

1. Exposure methods:
   a. Loss ratio method
   b. PMPM method
2. Basic Development Methods:
   a. Straight-average lag with average periods of 3, 6, 9, 12 months
   b. Straight-average lag without outliers
   c. Geometric average lag
   d. Harmonic average lag
   e. Dollar-weighted average lag
3. Cross-Incurral Period Method
4. Hybrid Chain-Ladder Methods:
   a. Hybrid loss ratio method with outliers removed
   b. Bornhuetter-Ferguson with straight-average lag
   c. Gunnar-Benktander with straight-average lag
   d. Credibility-weighted with straight-average lag
5. Paid PMPM Method
6. Stochastic Methods

Question 34

Observations on IBNR methods

Answer 34

1. Lag methods consistently had the highest standard deviations. More advanced average lag methods and hybrid methods are much better alternatives to straight average methods
2. For rapidly-completing blocks, the results of the Paid PMPM method appeared closest to the mean and had the lowest standard deviation (proprietary)
3. Seasonality of claims can have a material impact on the mean error
4. Applying a method that relies on premium for its calculations requires adjustment and likely actuarial judgment
5. There is a material risk to IBNR accuracy when removing large claims from the dataset (methods without outliers)
6. Care should be taken in determining which method to choose for different medical insurance block types

Question 35

Principles for determining premium deficiency reserves

Answer 35

According to the AAA PDR work group

1. Situations that result in a PDR being established include:
   a. A block of business expected to have near-term losses
   b. A block of business expected to be profitable in the near term, but long-term guarantees will cause it to be unprofitable over the projection period
2. Should minimize false positives - no PDR should be required unless there is a meaningful potential for loss
3. Should minimize false negatives - a PDR should be required whenever there is an expectation for loss

Question 36

Contract groupings for premium deficiency reserve calculations

Answer 36

1. Contracts should be grouped in a manner consistent with how policies are marketed, serviced, and measured
2. Deficiencies on a product can be offset by profits on other products within its group, but not by profits in other contract groupings
3. The recommended groupings from the Health Reserves Guidance Manual are:
   a. Comprehensive major medical
   b. LTC
   c. Income protection (disability income)
   d. Limited benefit plans