Tammy Tomczyk, ASA
© 2003 GRASP Study Manuals
OVERVIEW OF THE MANUAL
When I sat for the SOA Course 8M exam, I found that no one had yet developed a thorough,
comprehensive study guide. As a result, I had to create my own detailed set of notes. Having an infant
daughter and a 2 ½ year old son, I knew that my study time would be limited. Therefore, I summarized all
of the material so that I would be able thoroughly review the entire syllabus several times.
As part of my exam preparation, I also created a set of integrated lists, comparative tables, and developed
several practice problems. Those notes that helped me pass the exam formed the basis for this study
guide. I hope that they will benefit you as much as they did me. Below is a description of what you will find
in the manual.
I.
Detailed Outline of the Core Readings
 This section outlines each chapter and study note included on the syllabus. The material within
each chapter is presented in the same order as it appears in the original readings, which makes
it easy to look something up when you need to refer back to the source for greater detail. The
objective was to provide enough detail here so that reference back to the readings them selves
would be minimal (that Managed Care Handbook is heavy to carry around). At the same time, I
confined my notes to the material as presented, including extra detail only where it was needed
to clarify a complex topic.
II.
Condensed Outline
 This section mirrors the detailed outline with respect to the order that the material is
presented. Subject matter remains grouped by the chapter that it was presented, however all
of the supporting detailed explanations have been excluded, leaving only the major points from
each chapter. This section is great for memorization.
III.
Integrated Lists
 This section takes list type information that overlaps between multiple readings and combines
it. For example, rather than memorize a list of characteristic for underwriting groups and
another list of characteristics for underwriting individuals, I created one list of underwriting
characteristics since the two separate lists have many items in common. Then, at exam time if
a question is asked only about group underwriting, I could pick from that list the items that
apply to groups. The condensed outline is good for determining which list items apply in each
case.
IV.
Summary Comparison Tables
 This section contains a group of tables for topics where a “Compare the advantages and
disadvantages of ……” question could be asked. It includes only the major points and is great for
memorizing. There are also tables that compare different methods or models. For example, a
table that compares characteristic of case management with disease management.
V.
Practice Problems

While there are no real complex formulas to memorize for this exam, there are quite a few
exam points allocated to math problems. Most of the material implicitly, rather than explicitly,
leads to the potential for math type questions. This section is a group of practice problems
that I created for myself when studying. With reservation, I have included suggested
solutions, however they are based on my interpretation of the readings as many of the them do
not present actual problems, but rather the background needed to solve a problems.
Canadian Handbook of Flexible Benefits
Chapter 2 – Elements of Flexible Benefits
A flexible benefit plan allows employees to decide among types of benefits, levels of
coverage, and forms of compensation.
Design Approaches
1. Opt-Up-or-Down
 Employer pays for specified level of benefits
 Opt-down and receive credits
 Opt-up and pay with payroll deduction or credits from opting down elsewhere
2. Core + Options + Credits
 Choose from a range of options with the lowest being the core (needed from a
public relations standpoint)
 Pay for options with employer credits or payroll deductions
3. Health Care Expense Account
 Added to a flex plan
 Employer funds in Canada; in US employee can contribute too
 Used for unreimbursed health care expenses
 Provides benefits on a tax free basis
4. Combination
 Core + options + credits + health care expense account
Advantages of Flex Plans to Employers
1.
2.
3.
4.
5.
Allows for management of costs
Meets the diverse needs of employees
Allows offering a greater variety of benefits
Perceived value added
Tax advantages
Sources of Funds for Choice Making System
1. Rearrangement of Existing Dollars
 Allows employees to increase/decrease benefits in specific areas
 Opt-up-or-down approach
Canadian Handbook of Flexible Benefits
Chapter 2 – Elements of Flexible Benefits
2. Cutback From Existing Level
 Core + option + credit approach
 Used when current benefits exceed employee, needs or cannot be afforded
 Core benefits are offered along with additional credits to buy new benefits
3. Introduction of New Money
 Employee money through payroll deduction
 Employer money as a flat dollar, percent of salary, or profit related
Pre-tax vs. After Tax Deductions



Pre-tax credits are more powerful
Credits are taxed based upon how they are spent
Credits used to purchase life insurance are taxable income to the employee
Areas of Choice
Medical
 Benefits are fairly constant with choice among deductible, coinsurance, managed
care, and maximums
Term Life
 Options can vary by age/gender or be a flat rate
 Employee contributions can be pre-tax or post-tax
Disability
 Choices include employee vs. employer contributions and tax implications, pay
replacement levels, and waiver
Vacation Time
 buying and selling vacation days
 Some employers only allow one or the other
Special Considerations
1. Adverse Selection
 Employees choose options that provide the most coverage at the least cost, based
upon their anticipated use
 Can be controlled through the design of a flexible program
Canadian Handbook of Flexible Benefits
Chapter 2 – Elements of Flexible Benefits
Methods to Control Antiselection
a.
b.
c.
d.
e.
Restrict drastic changes in coverage from year to year
Subsidize cost to encourage broad participation for some coverages
Credit less than full value for waivers
Group coverages with predictable expense with those that are less predictable
Use health care expense accounts for predictable expenses
2. Waivers of Coverage
 May be limited to certain areas
 May not be allowed below a core level
Health Care Expense Accounts






Employee directs credits into their account each year
Changes throughout the year are not allowed unless there is a family status change
Eligible expenses are submitted by the employee for reimbursement and paid from the
account
In Canada, Contributions cannot come from employee payroll deductions and maintain
tax favorable status
In the US, unused deposits at the end of the year are forfeited
In Canada, unused deposits at the end of the year may be forfeited or carried
forward
a. If election is made to carry forward unused deposits, unused deposits can be
carried forward one year and offset against expenses from the next year
b. If election is made to carry forward expenses, unused deposits are forfeited at
the end of the year but expenses in excess of deposits can be carried forward one
year to be offset against deposits from the next year
Sources of Funds
 Employer contributions
 Credits from tradeoffs
 Salary reductions (U.S. only)
Types of Benefits
 Deductibles
 Coinsurance
 Vision care
 Orthodontia
Canadian Handbook of Flexible Benefits
Chapter 2 – Elements of Flexible Benefits
Health Care Expense Accounts are Popular Because:
 Allows expansion of benefits offered to employees with little or no additional cost
to the employer
 Encourages employees to self-insure predictable expenses, thus reducing adverse
selection
 Tax benefits
Actuarial Standards of Practice #18
Long Term Care Insurance
Purpose – standard for designing, pricing, funding or evaluating LTC
Scope – individual and group, riders, self insured plans
Select Definitions
Activities of Daily Living (ADLs)
 Basic functions used to measure personal functionality (eating, toileting, bathing)
Long Term Care
 A range of health services including:
a. Adult Day Care
 Social and health services provided in a group setting outside the home
b. Custodial Care
 Care to help a person perform ADLs provided by people without professional
medical skills
 Performed in many settings (home, nursing home, assisted living facilities
c. Home Care
 Skilled nursing or therapy received in the home
d. Hospice Care
 Care for terminally ill people and counseling for their families
e. Intermediate Nursing Care
 Daily, but not 24-hour nursing care
 Often involves a lot of custodial care
f. Respite Care
 Temporary care that allows volunteers and family members a break from care
g. Skilled Nursing Care
 Care provided by nurses and therapists, but generally not in a hospital
Coverage and Plan Features

Consider eligibility, covered services, benefit amounts, and payment duration
Plan features needing special attention
1. Acceleration of benefits under a life policy
2. Other product providing LTC benefits
3. Other programs providing LTC benefits such as HMOs, PPOs, EPOs, etc.
4. Services provided by retirement communities
Actuarial Standards of Practice #18
Long Term Care Insurance
Assumption Setting


Consider experience data and adjust for expected changes
Consider appropriate provisions for adverse deviation
1. Morbidity
 Should be consistent with plan features
 Consider incidence, termination, and benefits when estimating claim costs
Considerations for setting claims costs:
a. Cost varies by type of benefit (nursing home, home care, etc.)
b. There is a substitution effect among benefits
c. Demand increases when there is insurance
d. Consider benefits available from other programs
e. The availability of LTC services impacts utilization and therefore cost
f. Selection
g. Mortality
2. Mortality
 Consider selection and classification
 Select an appropriate mortality table
3. Voluntary Lapse
 Consider the method of marketing, product and premium competitiveness, premium
mode, payment method, nonforfeiture benefits
4. Expenses
 Should be consistent with the business plan and method of delivery
5. Taxes
 Be consistent with the tax reserve basis of the plan
 Consider all types (premium tax, income tax, etc)
6. Investment Income
 Be consistent with the return on the assets that support the products
7. Mix-of-Business
 Reflect the age, gender, marital status, distribution system, underwriting class,
and plan options of anticipated distribution
Actuarial Standards of Practice #18
Long Term Care Insurance
8. Change-Over-Time Assumptions
 Reflect expected changes in the assumptions
Premium Rate Recommendations


Required reserves include:
Premium Reserves
Contract Reserves
Claim Reserves
Can use the same method as health insurance
Sensitivity Testing


Do prior to finalizing the assumptions
Do more testing for less credible assumptions
Cash Flow Testing

Important because of the long term nature of benefits
Experience Monitoring



Compare the prior assumptions with emerging experience
Assess implications of any differences
If industry data are used, apply new data in a timely fashion
Communication and Disclosure
1. Documentation
 Assumptions, processes used and data sources
2. Disclosure
 Disclose the sensitivity of actuarial work to variations in assumptions
3. Actuarial Opinion
 This ASOP doesn’t require an actuarial opinion
Reasons LTC Work is Challenging
1.
2.
3.
4.
Data is limited
Benefits change rapidly
New financing approaches
UW, marketing, and claim payment practices vary under different LTC plans
Actuarial Standards of Practice #18
Long Term Care Insurance
5. Changes in consumer behavior
 Changes in utilization as more insurance in available
 Control of nursing home beds
 Medical advances
 Attitudes toward nursing homes
 Divorce rates
 Government funding
 New LTC services
Provisions in LTC Plans
1. Eligibility
 An elimination period may have to be satisfied
 Must show medical necessity
 Must use covered services
2. Covered Services
 May be integrated into one lifetime maximum
3. Benefit Amount
 Can be fixed or related to cost
4. Benefit Duration
 Consecutive days
 Benefit days covered
 Maximum dollar benefit
Other Features Affecting the Cost




Alternative plan of care provision (covers substitutes)
Shortened benefit periods from a non-forfeiture option
Restoration of benefits
Provider discounts
Existing Practice



Reliance on noninsured data and emerging experience for pricing
Much sensitivity testing is done due to long term nature of benefits
There is a sensitivity to cash flow requirements and investment strategies
SN 8GM – 206 - 00
Variation by Duration in Small Group Medical Claims
Overview



Study measures variation in small group costs by duration
Claims costs vary by duration since issue as a result of underwriting and pre-existing
condition limitations
Claims were adjusted to remove differences due to benefits, area, time period and
demographics
Study Results:
business
- Claim costs rise for 4-6 years and then level out
- Guarantee issue business has higher claims cost than underwritten
- Highest claims were for the smallest and largest groups (claims cost
by size exhibit a U-shaped pattern)
- Absence of pre-ex results in higher costs later on
Methodology
1. Participating Companies
 7 companies in small group market
 data from 1988 and 1989 with runout through early 1991
2. Data Collection Guidelines
 Data was collected by month for the first 3 years, then by year for years 4-6,
then grouped 7+
 Separated by underwriting method, group size, and pre-ex limitation
a.
b.
c.
d.
e.
f.
only groups size 1 – 25 were studied
major medical plans with deductibles <= $500
incurred claims before reinsurance were used
duration is number of months since issue
exposure was broken into single vs. other categories
pre-ex grouped by # of months of required coverage before pre-existing
conditions are covered
SN 8GM – 206 - 00
Variation by Duration in Small Group Medical Claims
3. Data Adjustments
a. Benefits
 52 broad categories of adjustment factors were developed
b. Area
 3 digit zip code adjustment factors were used
c. Trend
 13% annually
d. Demographics
 Age, sex, family status
4. Data Credibility and Limitations
 Short form underwriting includes no pre-ex
 All guarantee issue has 12 month pre-ex
 Some newly underwritten employees are included at each duration
5. Exposure
 70% was short form underwritten
 1/3 was size 2-4, 1/3 was size 5-9
 92% had 12 month pre-ex
SN 8GM – 206 - 00
Variation by Duration in Small Group Medical Claims
Results


Driven by underwriting method, size, and pre-existing limitations that are applied
Composite of single and family costs were used
1. Underwriting Method
Durational Adjustment
 Long and short forms are steep in the first two years, then level off. (About a
30% lower claim cost in the first year vs. the second year)
 Guarantee issue doubles in the second year and then levels off at its ultimate claim
level
Durational Adjustment Factors
Based on Underwriting Method
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1
2
3
4
5
6
7+
Duration
Long Form
Short Form
Guarantee Issue
Claim Cost
 Guarantee issue has significantly higher claim costs in the first three years, but
ultimate runs at about the same level as underwritten business
Claim Costs by Duration
Based on Underwriting Method
200.00
180.00
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
1
2
3
4
5
6
Duration
Underwritten
Guarantee Issue
7+
SN 8GM – 206 - 00
Variation by Duration in Small Group Medical Claims
2. Size
Durational Adjustment
 The same general durational pattern applies for all sizes, given the underwriting
method is the same
 Small groups have a somewhat steeper slope in the early years
Durational Adjustment Factors
Based on Group Size
1.65
1.45
1.25
1.05
0.85
0.65
0.45
1
2
3
4
5
6
7
Duration
Size 1
Size 10 - 14
Size 2 - 4
Size 15 - 25
Size 5 - 9
Claim Cost
 Claim costs exhibit a U-shaped pattern by group size
 Groups size 5 – 9 have the lowest claim cost
Claim Cost by Duration
Based on Group Size
185.00
165.00
145.00
125.00
105.00
85.00
65.00
Size 1
Duration 1
Size 2 - 4
Size 5 - 9 Size 10 - 14 Size 15 - 25
Duration 3
Duration 7+
SN 8GM – 206 - 00
Variation by Duration in Small Group Medical Claims
3. Pre-Existing Condition Limitation
Durational Adjustment
 The durational slope for groups with no pre-ex limitation is steeper than for those
that have a 12 month pre-ex limitation
Durational Adjustment Factors
Based on Pre-ex Limitation
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1
2
3
4
5
6
7+
Duration
No Pre-ex
12 Month Pre-ex
Claim Cost
 Consistency in the first 2 years between no pre-ex and 12 month pre-ex
 No pre-ex policies have significantly higher costs in the later years

Claim Costs by Duration
Based on Pre-ex Limitation
205.00
185.00
165.00
145.00
125.00
105.00
85.00
65.00
1
2
3
4
5
Duration
No Pre-ex
12 Month Pre-ex
6
7+
TSA XXXIV
Cumulative Anti-Selection Theory
The study assumes that a large group of people are all underwritten at time zero. Due to
underwriting, all people included are healthy at time zero. As time passes people’s health
deteriorates.
The Classical Model assumes that individual’s claims follow a durational curve, with low
claims immediately after being underwritten, and increasing as time passes.
The Cumulative Antiselection (CAST) Model assumes that people are either select
(healthy) or impaired (unhealthy). Everyone is select at the time of underwriting. Over
time, people move from healthy to impaired, impaired to healthy, or merely lapse from
the group. This model assumes that as time passes and some people begin to become
unhealthy, more of the healthy people lapse as a result of rate increase.
Reasons loss ratios on mature health blocks begin to decay:
 Insured are more able to quantify the probability of a health claim than a life claim
 Lapse rates are higher and impaired lives remain covered
Definitions and Assumptions




Separate the block into two groups, healthy and unhealthy lives
Assume the select period is the duration of the policy
Total claims are an increasing function of duration
Claim costs for healthy and impaired groups are only a function of attained age
Active Lives
alx = number of active healthy lives
ilx = number of active impaired lives
lx = alx + ilx = total number of lives
il[x]
= 0 as a result of underwriting
Claim Costs
aS[x] + t = claims cost in year t for the al[x] + t people in the active healthy population
iS[x] + t = claims cost in year t for the il[x] + t people in the active impaired population
iS[x] + t
= k2 * aS[x] + t
k2 is the ratio of impaired claim costs to healthy claim costs (e.g. if an impaired person
generates 2.5 times as many claims as a healthy person, then k2 would be 2.5)
TSA XXXIV
Cumulative Anti-Selection Theory
k2 does not vary with [x] and t
The antiselect period is the period during which the claim costs exceed the “ultimate”
claims costs
Probability of Lapse
 Healthy lives can either stay healthy, become impaired or lapse
 Impaired lives can either stay impaired, become healthy or lapse
qai[x]+t = probability that a healthy life currently age x+t, that was underwritten at age x
becomes impaired during the next year (excludes recoveries from il to al)
aq[x]+t
iq[x]+t
iq[x]+t
= probability a member of al[x] + t lapses
= probability a member of il[x] + t lapses
= k1 * ( aq[x]+t – u ) + u
0 < k1 < 1
u = base lapse rate = lapses that are independent of the individual’s health
( aq[x]+t – u ) = voluntary lapses by the active healthy population
This says that the impaired lives lapse rate is the underlying base lapse rate, plus a
percentage of the voluntary lapse rate of the healthy population. In otherwords, the
impaired lives have a voluntary lapse rate that is lower than the healthy population.
Rearranging the right side of the equation we can look at it another way:
iq[x]+t
= k1 * ( aq[x]+t ) + (1 - k1 ) * ( u )
This says that the impaired lives lapse rate is a weighted average of the base lapse rate
and the lapse rate of the active healthy population
As t increases, the lapse rate approaches u
Cumulative Antiselection Theory (CAST) Model



Assumes that healthy lives are always select (incur claims at the select rate)
The number in force at each duration is the same as in the classical model
Assume that the classical model’s aggregate claim cost is correct
TSA XXXIV
Cumulative Anti-Selection Theory
l0 * S0(d) = al0 * aS0(d)
l1 * S1(d) = al1 * aS1(d) + il1 * iS1(d)
*notation without an “a” or “i” subscript to the left implies the classical model
The probability of becoming impaired, qtai is proportional to aSt(d)
Example From Pages 218-219 of the Study Note
1,000 people are underwritten at time 0
Select factors are .55 in year 1, .68 in year 2, and 1.04 thereafter
K1 = 0, K2 = 5, u = 0.10
The Classical Model assumes that everyone incurs claims at the rate of 55% of the
tabular claim cost in year 1, 68% of the tabular claim cost in year 2 and 104% of the
tabular claim cost in years 3+
The CAST Model assumes that in every year, the healthy people incur claims at the rate
of 55% of the tabular claim cost, and the impaired people incur claims at the rate of
K2*55% of the tabular claim cost (in this example, the impaired people incur claims at the
rate of 5*55% or 275% of the tabular claim cost)
Year 1
The tabular claim cost in year 1 is $91.10 (Table 1, Column 3)
Since the cast model assumes everyone is select in the first year, both models assume
the aggregate claims in year 1 = .55 x 91.10 x 1,000
= 50,105* (Table 1, Column 7 and Table 2 Column 6)
*The numbers vary slightly due to rounding
l1 = l0 * (1 - q0) = 1,000 * (1 - .4) = 600
TSA XXXIV
Cumulative Anti-Selection Theory
Year 2
The tabular claim cost in year 2 is $95.10 (Table 1, Column 3)
The Classical Model assumes everyone’s claim cost in year 2
S(d)
= 0.68 * St(d)
= 0.68 x 95.10
= 64.668
Total Cost for the 600 remaining contracts = 600 x 64.668
= $38,801 (Table 1, Column 7)
The CAST Model assumes the healthy people’s claim cost in year 2 is:
(d)
aS
= .55 * St(d)
= .55 * 95.10 = 52.31 (Table 2, Column 5)
The claim cost for the impaired lives in year 2 is:
(d)
iS
= 5 * aS(d)
= 5 * 52.31 = 261.53
Since it is assumed that the Classical Model’s aggregate claim cost is correct, we
can set up the following equation:
38,801
= al1 * aS1(d) + il1 * iS1(d)
= al1 * 52.31 + (600 - al1) * 261.53
Solving we can get the number of healthy and impaired lives in year 2:
al1 = 9 = 565
il1 = 600 – 564.539 = 35.4603 = 35
Total Cost for the 600 remaining contracts = 565 x 52.31 + 35 x 261.53
= 38,709 (Table 2, Column 6)
We can now calculate the transition probability from active to impaired status as:
qai0 = 35.4603 / 1,000 = 0.355
TSA XXXIV
Cumulative Anti-Selection Theory
Remaining Columns
Since it is assumed that the probability of becoming impaired, qtai is proportional to aSt(d)
we can calculate that ratio:
qai0 / aS0(d) = 0.355 / 50.10 = .0007077
From here, we can fill in Table 2, Column 5 using the relationship:
Table 1, Column 3 x 0.55
We can fill in Table 2, Column 4 using the relationship:
Table 2, Column 5 x .0007077
We can fill in Table 2, Column 3 using the following:
ilt
=
=
=
=
x qait-1
ai
alt-1 x q t-1
ai
alt-1 x q t-1
ai
alt-1 x q t-1
alt-1
+
+
+
+
ilt-1
ilt-1
ilt-1
ilt-1
x iqt-1
x [k1 x ( aq[x]+t ) + (1 - k1 ) x ( u )]
x [0 x ( aq[x]+t ) + (1 - 0 ) x ( 0.10 )]
x 0.90
For example, for year 5:
il5
= al4 x qai4 + il4 x 0.90
= 187 x 0.042 + 65 x 0.90
= 66
We can fill in Table 2, Column 2 using the following:
alt
= lt - ilt
For example, for year 5:
al5
= l5 - il5
= 214 – 66
= 148
TSA XXXIV
Cumulative Anti-Selection Theory
Ratio of Loss Ratios

The ratio of the loss ratios of the classical to the CAST model at duration n is:
Rn =
=
Classical Loss Ratio =
CAST Loss Ratio
ln * S(d) / ln * PC
.
(d)
(d)
(aln * aS + iln * iS ) / ln * PM
[(PM) * (ln * S(d))] / [(PC) * (aln * aS(d) + iln * iS(d))]
(rearranging terms)
PC = Classical Premium
PM = CAST Premium
As n -> ∞, Rn -> 1
Factors Causing a Variation in Anti-selection at the Time of a Rate
Increases.





Size of increase
History of prior increases, both frequency and size
Availability of replacement coverage with comparable benefits of comparable cost
Health of family
Size of premium (dollars, not percentage increase)
Summary Comparison of the Two Models





If k2 (the ratio of impaired to select claim cost) is large, there will be no voluntary
lapses and k1 will equal 0
The steeper slope of the loss ratio under the CAST Model means higher reserves
Low early loss ratios means the classical model allows high claims to pass unnoticed
and uncorrected; the CAST Model justifies a higher initial premium
The CAST Model breaks lapses into two components, base lapses and antiselective
lapses; the Classical Model only assumes lapses that vary by duration
The loss ratio under the CAST model is lower than the classical model in the early
durations and greater in the later durations