Study Notes and Published Refences - Note SN 81-303 - ACTUARIAL REVIEW OF RESERVES AND OTHER A.S. LIABILITIES

Overview

audit - "critical review" process of complex org, transaction, operation or inventory
final objective of an audit - communicate clearly to the auditee an authoritative opinoin on such org (etc) being audited, in the least time, at the least cost, and with least disruption of operations

Applicable Professional Stds Regarding Actuarial Review of Reserves

AAA yearbook discusses
- standards for "Qualified Actuary"
- Recommendation 7 - Statement of Actuarial Opinion
- Recommendation 9 - Materiality
materiality is an important principle
- there comes a point wehre a small amt of increased accuracy may not justify the extra assembly or reviewing expense
- "a difficult professional judgement"
Valuation Actuary - appointed by co board
- determines appropriate reserves
  - render a report to mgmt of reserve determination techniques employed
  - statement of appropriateness of assets supporting reserves

General Principles of a Satisfactory Audit

Be certain of Audit Objectives
- communication is necessary to see if objectives consistent w/ estimated cost
- customer should know what audit will/won't include (scope of audit)
- attempt to communicate objective helps customer clarify and thefine the most efficient objective
Plan Audit in Advance
- prior to beginning detail checks
  - gain overall knowledge of components of inventory being audited
  - develop plan of review for each component
Sampling Principles to remember
- test each element fully (insofar as possible)
- pay extra attention to
  - new plans, new benfits, operations that have undergone recent changes
  - stratificatoin so that all methods and procedures used to obtain results included in sample adn tested
Prior Audit s/b reviewed
- guide to planning current audit
- point out errors from past and where current review s/b concentrated
Customer should have one audit coordinator through whom all Q&A funnel
Have physical copy of document "checking to" for numerical audit
Leave no links in audit trail untested
Audit Report
- brief descr of review process used
  - detailed decription in auditors own files
- nature of operation being audited (briefly described)
- should resemble previous reports (if periodic)
  - comment on material observations and recommendations from last report
Auditee s/b given draft to review
State all objects adn recommendations resulting from audit in specific and measuralbe terms

Reserve Assembly Process

financial provides schedule of tiems needed for completing annual statement
- date needed
- item needed
- person repsonsible for sending data
- distribution list showing recipients fo data
- typical co might have schedule which counts backwards
- main objectives of assembly process
  - speed
  - contril
  - paying attention to official AS instructions

Auditing Life Insurance Reserves and Related Actuarial Items

Five categories of effective reserve audit techniques
- spot checks
- independent full recomputations
- tests of aggregate progress of reserve from one fiscal period to another
- tests of relationships of reserve items to toher financial itmes and stability when comparing to previous periods
- tests of reserve adequacy
first four test to see if calced as tehy are supposed to be calced
fifth "good and sufficient" testing
- tests of approx valn method - could be in first, second or last test

Spot Checks (tests of inventory, test calcs, transactional checks and policy traces)

sampling - random, systematic, stratified
systematic - every nth element (after elements ordered)
- generally superior validity to random sample since form of stratification
stratefied - "forced representativeness" sampling techinque
- closes confidence interval substantially
- when an error of principle is discovered, systematic (or otherwise stratefied) sample can be used to estimate effect of error on entire block of business
tests that involve sampling
- tests of inventory are made to assure no major errors of ommission or commission
  - depending on situation
    - compare major reserve assemble worksheets to previous year to assure no categories omitted
      - at same time, look for unusual growth/dimunition of amts
    - check chain of process used to go from reserve detail to financial statement exhibit
    - identify all pol # blocks
      - select systematic sample of pols
      - trace through orig records
      - if inforce, what components and for what amounts
- tests of calculations (spot checks)
  - same sample from inventory tests good starting point
  - spot checks can include
    - retrieval of folder and checking that all listed policy benefits reserved properly
    - check of policy or contract language to see if reserveing methods proper and all inclusive
    - direct contact w/ insured to verify policy elements
- transactional checks of reserves and due premiums
  - if surrendered in current policy year, policy shouldn't be part of reserve inventory
  - if life premium past due-date, s/b paid, loaned, or net due prem asset
  - direct reserve s/b in sync w/ corresponding reins ceded reserve
- policy trace
  - pick a policy and follow it through calendar year
  - should be in inventory for
    - EOY net def prem
    - BOY net due prem
    - EOY net due prem
    - BOY SV due and unpaid
    - EOY SV due and upaid
    - BOY reserve
    - EOY reserve
    - BOY claim liab
    - EOY claim liab

Independent Full Recomputations

only done if it can be done in a cost efficient manner

Tests of Aggregate Progress of Reserve From One Fiscal Period to the Next

Analysis of Increase in Reserve Checks
- Formula I
  - C - tabular cost of mort for the year
  - I - req'd int for the year
  - (C-I) / ([0]m(x) + 1/2P) historically and check for smoothness of trend
  - C / avt amt @ risk = approx qx => find x= avg attained age historically and analyze progress
- Formula II
  - annuity type reserves
  - separate by type - dis life, supp con, normal annuities
  - reserves released by death or recovery (A) used to back into (T) tablular reserves released
  - t/([0]m(x) + 1/2(P-Payments)) = approx death/recovery rate
    - = approx avg decremental rate from underlying valn table
  - review historical treand
- Formula III
  - I s/b = approx (avg credited rate) * ([0]m + 1/2(P-Payments))
  - "roll forward" approach
    - + BOY acct value
    - + net prem deposits
    - - admin charges/pol fees
    - - COI charges
    - - benefit prems
    - - acct values released by termination
  - compare against acct value @ valn
    - delta s/b int credited to block
  - once roll forward proved
    - create historical table of (act value - reserve) / acct value
  - roll forward is test of engine that drives machine, not machine
Check of Increase in Life reserve/$1m over time
- review smoothness of incremental progress
- when comparing current to prior, use current year renewal only (no current NB)

Tests of Relationships of Reserve Items to Other Financial Items (Units of Measurement) And Stability Therein From One Fiscal Period to Another

examples
- Group Unearned Prem Reserve -> incurred group prems (collected & delta due prems)
- Substd Extra Prem reserve -> total incurred prem
- ADB reserves -> ADB inforce
- Ordinary Dis Reserve -> ann prems to be waived, inforce
purpose: spot unusual trends
- well suited for
  - net due and deferred prems
  - ancillary benefit reserves
  - reserves for nondeduction of fractional prems

Tests of Reserve Adequacy

traditional definition of adequate - actuary's best estimates
- reserve plus future prems and int make good and sufficient provision for future benfits adn expenses
three common tests of adequacy
- loss ratio tests
- gross prem valn methods
- claim runoff tests on dis life reserves, claim reserves, loss reserves
Loss Ratio tests ("check students guide and see what they say"
Gross Prem Valn (aka Prospective Asset Share)
- GPV(t) = sum([B(s)+E(s)-P(s)]*v^(s-t-1)*[s-t-1]p(x+t)) from s=?? to infinity
- PVBP(t) - pv book profit - Anderson's Method
  - =[t]V - GPV(t) where [t]V = Stat Reserve
  - > 0 -> reserve officially heald exceeds best estimate provision (a good thing)
- adjust cells for fractional durations for calendar year calc
  - discount 1/2 year, add future gross due and def prems less expenses and expected benefit
  - subtract mean reserve and net due & def prems - [t]V*v^(1/2)*[1/2]p(x+t-1/2)
- A&H blocks - adjusted loss ratio approach
  - historical look at sum of incurred claims and incr active life reserves
  - sufficient margin at EOY t woudl be
    - + revised PV future profits
    - - reserve according to an up-to-date standard
    - + reserve actually held
Claims Runoff Tests
- loss triangles
- gaining popularity due to high-speed computers -> multiple scenario CF surplus proj
- diff between GP valn and CF surplus proj
  - indiv assets tracked as to actual income, redemptions, taxes
  - multiple scenarios run, usually w/ different int rate paths
  - diff int rate paths & assumed behavior patterns shoudl show consistent relationship
- as review of CF projections, two circumstances
  - reviewer of another actuary's CF projections
    - both methodology and experience assumptions s/b reviewed
  - testing another actuary's reserve adequacy by performing own CF projections
- other "good and sufficient" test
  - that an approx vlan method is accomplishing its goals
    - approximating well the trad, more detailed method
    - making good and sufficient provision for liability it purports to represent
  - historical analysis of formula II type reserve (payment annuity) to see if T-A released generally positive
    - if so, decrement assumption may render reserve inadequate

Conclusions

remember certain priorities
- errors of principle more important than clerical errors/typos
- priority to large items vs smaller ones due to time restrictions
- when selelcting samples for spot checking, think diversity
- priority to new plans and products along w/ procedural changes
- once on-site audit finished, final reports s/b given priority over actuary's other work

Healthy Skepticism

"developed a healthy skepticism concerning data and other info proffered by others"
"apply a test of reasonableness to all figures you are given"

Appendix A - "Qualified Actuary" Standards

Education
- pass exams and take CE
  - genearl and actuarial math
  - life and health policy forms and coverage
  - divs, reins, and tax laws
  - investment and valn of ins co assets
  - valuatin and liabs
  - valn and nonf laws for jurisdiction
Experience
- 3 eyars responsible experience (recent) under qualified supervision

Appendix B - Recommendation 7 - Statement of Actuarial Opinion

list items and amts on whch the actuary opines
common stds adn sound actuarial principles - dictated by ASOPs, recommendations, etc
contract provisions such as fractional prems paid beyond date of death, conversion rights, etc
check valn reqs in state of domicile
reserve adequacy - GP valns < reserves held => ok
comments on changes in actuarial assumptions or methods
include who you are and who you work for

Appendix C - Recommendation 9 - Materiality

a difficult professional judgement
consider decision-making framework of typical user of actuary's work and their probable response
quantitative and qualitative consideration

Appendix E

Analysis of degree of improvement in validity by changing from random to stratified
blah blah blah

Appendix F - Analysis of Increse in Reserves

Formula I - [0]M + P + I - C - V_D - V_T = [1]M (life)
Formula II - [0]M + P + I + (T-A) - Pmts = [1]M (life annuities)
Formula III - [0]M + P + I - Pmts - [1]M (int only reserves)
Life Insurance
- [0]M,[1]M - 12/31 reserves
- P - tabular net prems collected
- I - req'd int for year
- C - tabular cost of mort for year
- V_D, V_T - reserves release by death/other than death
- (C-I) = ([0]M + P) - ([1]M + V_D + V_T)
- I = i*(1/2)*([0]M +[1]M + V_D + (C-I)) wehre i = reserve rate of int
- C is balancing item = (C-I) + I
Life Annuities
- T - annuity reserves expected to be released by deaths of annuitants according to valn table
- A - annuity reserves actually released by death during year
- Pmts - actual amts paid to annuitants during year
- (T-A+I) = ([1]M + Pmts) - ([0]M + P)
- I = i*(1/2)*([0]M + [1]M - (T-A+I))
- (T-A) = (T-A+I) - I
Int Only Reserves
- I = ([1]M + Pmts) - ([0]M + P)

Copyright © 2004 Steve Welander.
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