Sec D PDRs & Oth Reserves

Question 1

Principles for determining premium deficiency reserves

Answer 1

• According to the American Academy of Actuaries 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 2

Assumptions needed to estimate premium defiency reserves

Answer 2

• 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 - operating costs must be reflected. If other policies can be expected to cover overhead, then zero overhead costs may be assumed
  5. Claims trend - reflect reasonable increases in claim costs
  6. Interest rates - reasonable interest rate assumptions should be used to discount deficiencies
  7. Taxes - reserves should be 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 is the provider goes insolvent, the discounts are lost and costs will rise
  9. Reinsurance - the calculation of the reserve is usually net of reinsurance
• The last point comes from the Premium Deficiency Resrves Discussion Paper*

Question 3

Contract groupings for premium deficiency reserve calculations

Answer 3

1. Contracts should be grouped in a manner consistent with how policies are marketed, serviced and measured
2. Deficiencies on a product can be offest 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

Question 4

Reasons why a deficiency reserve may be needed

Answer 4

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 that makes it impossible to ever break even

Question 5

Types of premium reserves

Answer 5

1. Types of active life reserves:
   a) Unearned premium reserve (UPR) - reserve for the premium that has been booked to cover the portion of the coverage period whic hasn’t yet occurred
   i) Is usually a pro-rata portion of the last gross premium received (gross UPR)
   ii) But when a company holds policy reserves, the gross UPR is replaced by a net UPR that is based on the net premium used in calculating policy reserves
   b) Policy reserves (contract reserves) - this is the portion of premium collected in early durations that is intentionally designed to help pay for anticipated higher claims in later durations. Is needed for products where the claims costs increase with age while premium is level
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

Question 6

Types of outcome-based contractual reserves

Answer 6

1. Employer-based contractual liabilities - need to recognize liabilities for contract 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. Accruals for refunds needed to achieve minimum loss ratios, such as the ACA medical loss ratio requirement
3. Provider liabilities - for e.g., capitation payments owed, withholds, bundled payments, bonuses & incentives, stop loss settlements, and anticipated insolvency of capitated providers

Question 7

Formula for deferred acquisition cost (DAC) reserves

Answer 7

1. DAC = AV {deferrable expense} - AV {net expense premiums}
2. The notation:

_i^zE_x= deferrable expenses at age x, duration i, and issue year z

_i^zP_x^E= net expense premium at age x, duration i, and issue year z

3. The formula on a per surviving policy basis:

_t^zDAC_x^s= SUM_{<span>(i=0 to t-1)</span>} {[1 / _t-ip_x+i] * v^i-t * [_i^zE_{x - i}^zP_x^E]}

Question 8

Alternative approaches for estimating liabilities with the development method

Answer 8

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. Other kinds of lag triangles - some actuaries bucket payments into weekly cells and then apply the traditional development method
3. Time series and other statistical projections (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 9

Smoothing methods to apply to development factors

Answer 9

1. Simple averaging - average development factors for each lag month (3 month average is more current; 12 month average is smoother but may bury trends in payment patterns)
2. Removing bumps - throw out the high and low factors and average the rest. May also remove large “shock” claims from the claim triangle and analyze them separately
3. Weighted averaging - give more credibility to most recent results. Approaches include sum of digits, squared sum of digits, and 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) - average cumulative payments consecutive lag months and then compute age-to-age factors as the ratio of those averages
6. Per member age-to-age ratios - divide payments per lag by exposure to create PMPM payments, and then apply the dollar-weighted approach as before

Question 10

Methods for adjusting development method reserve estimates for recent incurral months

Answer 10

• Completion factors for the most recent months are typically too small to be credible and should be replaced using one of the following methods:*
  1. Loss ratio method
  2. Projection method
  3. Credibility-weighted average of completion estimates with estimates based on the projection or loss ratio method. Weights are usually assigned based on how close the completion factor is to 1.000, with the most recent month often receiving zero completion credibility

Question 11

Steps of the development method

Answer 11

1. Summarize the data by incurral month vs paid month to get a claims triangle
2. Sum the cells of the 1st claims triangle to get cumulative paid claims by incurral month
3. Calculate age-to-age development factors as the ratios of month to month cumulative claims
4. Smooth the month-to-month variations in age-to-age development factors. Various methods are used to do this
5. Calculate age-to-ultimate development factors (called completion factors) from the smoothed age-to-age factors
6. Divide each incurral month’s cumulative paid claims by its comletion factor to get the fully incurred claims
7. Subtract cumulative paid claims from the fully incurred claims to get the unpaid claims liability

Question 12

Types of coverages for which the development method works well

Answer 12

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 for medical)
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 13

Considerations when developing a stochastic approach to reserve estimation

Answer 13

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 14

Advantages and disadvantages of stochastic approaches for reserving

Answer 14

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 15

Stochastic modeling techniques for reserving

Answer 15

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
3. Generalized linear models - these models improve upon ordinary regression models because they allow for cases where 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 16

Formulas for policy reserves

Answer 16

1. The notation:

_ip_x= probability of survival to duration i for a policy issued at age x

v^t= (1 + annual int rate) ^-t = present value factor

^z_iC_x= claim cost at age x, duration i, and issue yr z

^z_iP_x= net premium at age x, duration i, and issue yr z

2. Prospective formula on a per original policy basis:

^z_tV_x= PV {future claims} - PV {future net premiums}

= SUM_{(i=t+1 to w)}{_ip_x * v^i-t * ^z_iC_x} - SUM_{(i=t to w)}{_ip_x * v^i-t * ^z_iP_x}

3. Prospective formula on a per surviving policy basis:

^z_tV^s_x= SUM_{(i=t+1 to w)}{_i-tp_x+t * v^i-t * ^z_iC_x} - SUM_{(i=t to w)} {_i-tp_x+t * v^i-t * ^z_iP_x}

4. Retrospective formula on a per original policy basis:

^z_tV_x= SUM_{(i=0 to t-1)}{_ip_x * v^i-t * ^z_iP_x} - SUM_{(i=1 to t-1)}{_ip_x * v^i-t * ^z_iC_x​}

5. Retrospective formula on a per surviving policy basis:

^z_tV^s_x= SUM_{(i=0 to t-1)}{[1/_t-ip_x] * v^i-t * ^z_iP_x} - SUM_{(i=1 to t-1)}{[1/t-ip_x] * v^i-t * ^z_iC_x​}

6. Two-year full preliminary term method - for the first 2 years, ^z_tV^2PT_x=0. Thereafter, the reserve is calculated using the regular policy reserve formulas, but calculated as if the policy begins as time 2
7. A modified method to reflect annual inflation (j) on both the claims and premiums - use the formulas above and multiply both the claims and net premiums terms by (1+j)ⁱ

Question 17

Types of policies for which policy reserves are required

Answer 17

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