Insurance Abstract
A method that combines into one insurance policy, perils which tend
to offset each other, the offsetting being manifested by negative
correlations in the payouts of benefits for the offsetting pair
or pairs of risks. The method includes, selecting a population of
potential policyholders to be insured and dividing the population
of potential policyholders into several subpopulations; the probability
distributions of which are estimated for payments of benefits to
policyholders in a particular subpopulation. Followed by estimating
a plurality of statistical properties of benefit payouts for at
least two perils. Furthermore, specifying at least one statistical
property based upon its relation to an acceptable risk level. Finally,
creating at least one combined policy that meets the specified statistical
property and pays out benefits in the event that at least one of
the perils occurs.
Insurance Claims
1. A method for forming a multiperil insurance policy with prespecified
statistical properties for a selected population of potential policyholders
the members of which are treated as substantially homogeneous, and
the probability distributions of which are estimated for payments
of benefits to policyholders, the method comprising: (a) estimating
a plurality of statistical properties of benefit payouts for at
least two negatively correlated perils; (b) specifying at least
one of said statistical properties based upon its relation to an
acceptable risk level; (c) creating at least one insurance policy
contract between at least one insurer and at least one insured that
meets the specified statistical property and insures against both
of said at least two negatively correlated perils by obligating
said at least one insurer to pay out benefits to said at least one
insured in the event that any of said at least two perils occurs;
and (d) paying, by the insurer, benefits to the insured after any
of said at least two perils occurs.
2. The method in accordance with claim 1, wherein said at least
two perils further comprises three perils, in which at least two
of said three perils are negatively correlated.
3. The method in accordance with claim 1, further comprising fixing
the benefit levels for the life of the policy at the time the policy
is issued.
4. (canceled)
5. A method for forming a multiperil insurance policy with prespecified
statistical properties for a selected population of potential policyholders,
the members of which are treated as substantially homogeneous, and
the probability distributions of which are estimated for payments
of benefits to policyholders, the method comprising: (a) estimating
a plurality of statistical properties of benefit payouts for at
least two negatively correlated perils; (b) specifying at least
one of said statistical properties based upon its relation to an
acceptable risk level; (c) creating at least one insurance policy
contract between at least one insurer and at least one insured that
meets the at least one statistical property and insures against
both of said at least two negatively correlated perils by obligating
said at least one insurer to pay out benefits to said at least one
insured in the event that any of said at least two perils occurs;
(d) fixing the benefit levels for the life of the policy at the
time the policy is issued; and (e) paying, by the insurer, benefits
to the insured after any of said at least two perils occurs.
6. A method for forming a multiperil insurance policy with prespecified
statistical properties for a selected population of potential policyholders,
the members of which are treated as substantially homogeneous, and
the probability distributions of which are estimated for payments
of benefits to policyholders, the method comprising: (a) estimating
a plurality of statistical properties of benefit payouts for at
least three perils, at least two of which are negatively correlated;
(b) specifying at least one of said statistical properties based
upon its relation to an acceptable risk level; (c) creating at least
one insurance policy contract between at least one insurer and at
least one insured that meets the specified statistical property
and insures against both of said at least two negatively correlated
perils by obligating said at least one insurer to pay out benefits
to said at least one insured in the event that any of said at least
three perils occurs; and (d) paying, by the insurer, benefits to
the insured after any of said at least three perils occurs.
7. The method in accordance with claim 6, further comprising fixing
the benefit levels for the life of the policy at the time the policy
is issued.
Insurance Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] This invention relates generally to a method for forming
an insurance policy and more specifically a method for forming a
multiperil insurance policy.
[0003] 2. Description of the Related Art
[0004] In the past, it has been difficult for an insurance provider
to prepare a comprehensive plan for an individual that is not too
risky for the insurance provider to cover and yet not too expensive
for the individual. Typically, an individual who wishes to purchase
life insurance, an annuity and long term care (LTC) insurance can
purchase these forms of protection separately. However, the high
premiums for these policies often limit the individual to only being
able to purchase inadequate coverage.
[0005] There is a high degree of uncertainty in setting premiums
for private longterm care insurance, which leads to high premiums
in order to provide a safety factor for the insurer. Uncertainty
also leads to premiums that are not guaranteed for the life of the
contract, but which may be increased as time passes; that is, these
premiums are not "noncancellable", but only "guaranteed
renewable". Policyholders often drop their coverage because
of steep premium increases and then are left with no LTC insurance
when they need it. In addition, the pricing of LTC insurance is
difficult for several reasons. Among those are estimating the use
of nursing home services and homehealthcare services, the future
costs of these services, along with adverse selection.
[0006] The LTC policies on the market are apparently not very attractive
to many individuals. It has been found that only 2.2% of the elderly
and 1.6% of the near elderly have private LTC insurance coverage.
In addition, many people do not annuitize annuities; only about
2% of annuities are ever annuitized. So the key feature (and basis
for the product's name) is seldom utilized. This is despite the
need for reliable retirement income to replace the pension check
of prior generations.
[0007] Each of these three types of insurance, as sold in standalone
policies, is subject to substantial adverse selection, when compared
with the general population. Therefore, it is the object and feature
of the invention to provide a method for forming a multiperil combined
insurance policy.
BRIEF SUMMARY OF THE INVENTION
[0008] The invention is a method that combines into one insurance
policy, perils which tend to offset each other. The offsetting is
manifested by negative correlations in the payouts of benefits for
the offsetting pair or pairs of risks.
[0009] The method includes, selecting a population of potential
policyholders to be insured and dividing the population of potential
policyholders into several subpopulations. Next, the probability
distributions for payments of benefits to policyholders in a particular
subpopulation are estimated. A plurality of statistical properties
of benefit payouts are estimated for at least two perils and at
least one statistical property is specified based upon its relation
to an acceptable risk level. Finally, a combined policy is created
that meets the specified statistical property and pays out benefits
in the event that one or more perils occur.
[0010] The method is used to create a multiperil insurance policy
preferably combining long term care (LTC) insurance, life insurance
and an annuity as the perils. This method is advantageous over standalone
policies because the correlation coefficient for payouts of benefits
for life insurance and an annuitized annuity is, in principle, negative
one (1). Whatever the correlation coefficients between LTC and
both life insurance and an annuitized annuity, whether they are
positive or negative, a combined policy can be designed to meet
a specified statistical property such as the coefficient of variation
property. For all of the models formulated, the correlation coefficient
between LTC and an annuitized annuity is a moderatesized positive
number, and the correlation coefficient between LTC and life insurance
is a moderately larger negative number. By using the preferred method,
an insurer can sell the combined policy for a smaller premium than
each of the policies separately because there is need for a smaller
"cushion" against variability in payouts of benefits,
and because using the same mortality table for all of the perils
in the policy reduces the expected payout, compared with using a
separate mortality table for each peril.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0011] FIG. 1 is a table illustrating the preferred method of the
present invention.
[0012] FIG. 2 is a table illustrating the embodiment of FIG. 1
with inflation protection.
[0013] FIG. 3 is a table illustrating a prior art embodiment.
[0014] FIG. 4 is a table illustrating a prior art embodiment with
inflation protection.
[0015] FIG. 5 is a table illustrating a comparison between the
embodiment of FIG. 1 and the embodiment of FIG. 3.
[0016] FIG. 6 is a table illustrating a comparison between the
embodiment of FIG. 2 and the embodiment of FIG. 4.
[0017] In describing the preferred embodiment of the invention,
which is illustrated in the drawings, specific terminology will
be resorted to for the sake of clarity. However, it is not intended
that the invention is limited to the specific term so selected and
it is to be understood that each specific term includes all technical
equivalents, which operate in a similar manner to accomplish a similar
purpose.
DETAILED DESCRIPTION OF THE INVENTION
[0018] Insurers operate within a riskbasedcapital environment.
However, by utilizing the preferred method to formulate a combined
policy so that the combined policy has the same risk (coefficient
of variation) as an annuitized annuity, the insurer can substitute
a combined policy that protects against multiple perils for an annuitized
annuity with no impact upon its actual risk profile.
[0019] A Brief Example of the Preferred Method.
[0020] To begin an insurer selects the perils that will be incorporated
into the multiperil policy. In this example the perils selected
include longterm care insurance (LTC), an annuitized annuity, and
life insurance. These three perils are selected because at least
two of the perils are somewhat negatively correlated. Negative correlation
between two quantities means that large values of one of the quantities
tend to be associated with small values of the other quantity, and
vice versa. For example, an annuitized annuity and a life insurance
policy have a negative correlation with each other because an annuitized
annuity, by definition, is paid during a lifetime of an individual,
while a life insurance policy is only paid after the insured has
died.
[0021] The insurer must select the population to be insured and
divide the population of potential policyholders into several subpopulations
or risk classes such that the members of each subpopulation can
be treated as reasonably homogeneous.
[0022] For each subpopulation, the insurer will obtain or estimate,
using both a mortality table and a morbidity table for the members
of the subpopulation, probability distributions for the payments
of benefits to policyholders in that subpopulation. The insurer
then estimates the statistical properties of the benefit payouts
for the three selected perils.
[0023] Next, the insurer specifies one statistical property, based
upon its relation to an acceptable risk level, which the combined
policy will be designed to meet. Initially, this statistical property
will preferably be that the coefficient of variation of the payouts
for the combined policy equals the coefficient of variation for
the annuitized annuity. The reason the annuitized annuity is preferably
selected is because an annuitized annuity is a lowrisk policy for
an insurer to write. However, other properties could be chosen.
The coefficient of variation is the standard deviation of the benefit
payouts divided by the expected value of the benefit payouts.
[0024] The insurer creates at least one, but preferably a variety
of combined policies that meet the specified statistical property
that pays out benefits for any of the perils that occur. The benefit
levels for the three risks to be insured must be chosen, and some
sample benefit levels are illustrated in FIG. 1 columns C, D, and
E. This step will specify the multiperil policy. The creating of
the combined policy proceeds by selecting a benefit level for LTC,
such as $2000 per month and then selecting a series of possible
values for the annuitizedannuity benefit level, such as $200 per
month, $300 per month, $500, $700, $1000, $1500, $2000, $2500 or
$3000 per month.
[0025] For each of the pairs of benefit levels selected, the insurer
calculates the lifeinsurance face amount that will make the combined
policy fulfill the specified condition on the coefficient of variation.
[0026] This process can then be repeated for several values of
the LTC benefit level, such as $3000 per month, $4000 per month,
$5000 per month, et cetera. Since all benefit levels can be doubled,
tripled or multiplied by any other positive real number without
changing the specified statistical property of the combined policy,
this last step can be done very easily.
[0027] Following is a schedule showing, in each row, the benefit
levels for a variety of possible of combined policies, as illustrated
in FIG. 1, all of which have the same risk structure as a pure annuitized
annuity. See FIG. 2, columns C, D, and E for a combined policy with
inflation protection built in to the policy. TABLEUS00001 Annuitized
LTC Life Annuity Benefit Insurance $200 $2,000 $36,617 300 2,000
28,090 500 2,000 18,979 700 2,000 14,176 1,000 2,000 10,113 1,500
2,000 6,628 2,000 2,000 4,764 2,500 2,000 3,605 3,000 2,000 2,813
[0028] The relative levels of the benefit payouts are then fixed
at the chosen (by the insured) levels, such as $2000 LTC benefit,
$3,000 annuitized annuity and $2,813 face amount of life insurance
for the life of the policy. This avoids adverse selection by the
policyholder during the life of the policy. For example, suppose
a policyholder sees his/her doctor who says, "You are very
healthy. You will `live forever`." The policyholder may be
inclined to go to the insurance agent and say "Switch everything
to an annuityno more life insurance." However, suppose instead
the doctor said, "You are full of cancer. You won't live four
months." The policyholder now would like to change everything
to life insurance, because an annuity, which pays until death, will
not be very valuable. This fixing of values at the time at which
the policy is issued just affects the situation AFTER the policy
has been issued.
[0029] How the Method Works:
[0030] The preferred method uses a Monte Carlo simulation program
to attain the results illustrated in FIG. 1. Beginning with simulated
age 65, the method is repeated year after year until the probable
death of the simulated individual. Benefit payments for each peril
for each year are calculated and, at the simulated death, the present
values of the annual payouts are discounted back to age 65 and summed.
Many simulations can be run for various circumstances and summary
statistics are then calculated for each group of simulated individuals.
[0031] In order to obtain the results shown in FIG. 1, morbidity
and mortality tables are selected and incorporated into the simulation.
Morbidity tables for a simulated individual to enter a nursing home
in a particular year and for that individual's length of stay can
be adapted from Tables 19 and 20 of the "Brookings/ICF Long
Term Care Financing Model: Model Assumptions" (U.S. Department
of Health and Human Services, February, 1992). At least one mortality
table is chosen to simulate the overall probability of an individual's
death in that year. For example, one of the following mortality
tables can be chosen: [0032] "In Sickness and in Health: An
Annuity Approach to Financing LongTerm Care and Retirement Income"
by Murtaugh, Spillman and Warshawsky, The Journal of Risk and Insurance,
2001 [0033] 2001 [insurance] Commissioners Standard Ordinary mortality
table [0034] 1980 [insurance] Commissioners Standard Ordinary mortality
table [0035] The annuity mortality table and the overall population
mortality table from Table 1.1, in the book, "The role of Annuity
Markets in Financing Retirement" by Brown, Mitchell, Poterba
and Warshawsky, The MIT Press, 2001 (referred to below as Reference
A). However, a person having ordinary skill in the art will recognize
that these are only examples of morbidity and mortality tables and
any variety of published tables can be used.
[0036] When designing a multiperil policy that includes an annuitized
annuity, longtermcare insurance and life insurance, the preferred
statistics calculated include: [0037] the sample average to estimate
the expected payout for the three perils and age at death; [0038]
the standard deviation for each of these four quantities; [0039]
the correlation coefficient between each of the three pairs (AnnuityLTC),
(LTCLife Ins) and (AnnuityLife Ins). However, as will be recognized
by a person having ordinary skill in the art, other summary statistics
can be calculated.
[0040] Several dozen simulation runs, each simulation run being
comprised of several thousand simulated lives, can be made based
upon the following considerations. Each simulated person's health
in accordance with the Brookings/ICF model is classified as: [0041]
1 no disability [0042] 2 unable to perform at least one "instrumental
activity of daily living", such as, doing heavy work or doing
light work, preparing meals, shopping for groceries, walking outside,
managing money [0043] 3 unable to perform one of the "activities
of daily living", such as, eating bathing, dressing, toileting,
getting in and out of bed [0044] 4 unable to perform two or more
of the "activities of daily living" Each simulated year
there is a probability that an individual will change from the current
state of disability to another state of disability. It is assumed
that at age 65 an individual is properly classified into one of
these four categories.
[0045] Simulations can be performed with no "inflation protection"
for the benefit levels, as illustrated in FIG. 1. That is, benefit
levels do not change from year to year. Alternatively, simulations
can be performed with annuity payments increasing 3 percent each
year, LTC payments increasing 5 percent each year and with no change
in the face amount of the life insurance, as illustrated in FIG.
2. As a person having ordinary skill in the art will recognize,
many other inflationprotection patterns can be utilized, but the
one chosen is a typical pattern.
[0046] In all cases the general pattern is the same. For a chosen
LTC benefit level, one can set an annuity benefit level and find
the corresponding amount of life insurance required to meet the
specified value for the coefficient of variation of the combined
policy. The larger the annuity benefit, the smaller the face amount
of life insurance required, and vice versa. For each specific combined
policy (that is, for each set of values of the LTC benefit and annuity
benefit) the smaller the imposed design value of the coefficient
of variation or the smaller the specified amount of risk, the larger
the face amount of life insurance required, and vice versa.
[0047] The design property used for the combined policy is that
the coefficient of variation (CV) of the combined policy equals
the CV for the annuity component of the combined policy. In FIG.
1 column J the CV equals 0.413132. There are many other choices
that one could make, but this example uses a comparison with which
insurers are familiar and comfortable, namely, the risk associated
with an annuitized annuity.
[0048] Alternatively, if inflation protection is added to the benefits
of a policy, this will change the value of the CV for the annuity
component. As illustrated in FIG. 2, the CV is thus 0.483843 as
shown in the calculations in Column J. Including inflation protection
is somewhat more risky. The result would be a greater face amount
of life insurance in each row.
[0049] There are other possible choices of statistical design parameters
for a combined policy. For example, one could specify that a combined
policy satisfied a specified riskreturn relationship. Furthermore,
one could use a statistical property other than a coefficient of
variation as the design parameter. For example one could require
that the combined policy lie on a specified riskreturn line or
that it have a specified total expected benefit payout. Alternatively,
one could impose two conditions instead of one that the combined
policy must meet. For example, a specified value for the coefficient
of variation and that the skewness property is equal to or less
than a specified value. Other properties, which can be used, are
the 95.sup.th percentile benefit payout, the average of the largest
ten percent of payouts and the average of the largest thirtyfive
percent of payouts.
[0050] All of the cases mentioned above represent instances in
which there are three components in the combined policy. More complex
applications could involve four or more perils, which would lead
to choosing four or more benefit levels in designing a combined
policy. It is also noted that the method can be applied to a case
in which there are just two perils.
[0051] Terminology and inputs to the calculation of the benefit
levels for the combined policy include: TABLEUS00002 Subscript
1 refers to the (annuitized) annuity 2 refers to the LTC insurance
3 refers to the life insurance.
[0052] E denotes estimate of the expected value of a benefit payout
[0053] S denotes standard deviation of a stream of benefit payouts
[0054] R denotes correlation coefficient between two of the benefit
payout streams Thus, for example, [0055] E.sub.1 denotes estimate
of expected payout for the annuity component [0056] S.sub.2 denotes
standard deviation for the LTC component [0057] R.sub.23 denotes
correlation coefficient between the LTC and life insurance payouts
[0058] For example assume that calculations have been made for
the benefit levels of:
[0059] $1,000 per month for the annuity
[0060] $2,000 per month for the LTC benefit and
[0061] $100,000 for the face amount of life insurance.
[0062] To form a specific combined policy, an insurer introduces
factors A, B, and C, respectively, which multiply the three benefit
levels just described. Thus, TABLEUS00003 A equal to 0.5 corresponds
to an annuity of 0.5 times $1,000 or an annuity of $500 per month
B equal to 1 corresponds to an LTC benefit of $2,000 per month C
equal to 0.4 corresponds to a life insurance face amount of $40,000.
[0063] A specific policy is designed by choosing the values of
A, B, and C. The expected payout for a combined policy denoted by
A, B and C is E=A E.sub.1+B E.sub.2+C E.sub.3. The variance (square
of the standard deviation) for the combined policy will be Var =
A 2 .times. S 1 2 + B 2 .times. S 2 2 + C 2 .times. S 3 2 + 2 .times.
AB .times. .times. S 1 .times. S 2 .times. R 12 + 2 .times. BCS
2 .times. S 3 .times. R 23 + 2 .times. ACS 1 .times. S 3 .times.
R 13 The coefficient of variation for the combined policy, CV, equals
the square root of Var (above) divided by E.
[0064] The design parameter for this example will be that the coefficient
of variation for the combined policy will equal the coefficient
of variation for the annuity component of the combined policy; the
latter will be denoted as CV.sub.1: CV.sub.1 equals A S.sub.1 dividedby
A E.sub.1 or S.sub.1/E.sub.1
[0065] The design condition will be that CV equals CV.sub.1. For
convenience and to avoid square roots, square both sides. Thus,
from above, the equation that embodies the design condition is:
[ A 2 .times. S 1 2 + B 2 .times. S 2 2 + C 2 .times. S 3 2 + 2
.times. AB .times. .times. S 1 .times. S 2 .times. R 12 + 2 .times.
BCS 2 .times. S 3 .times. R 23 + 2 .times. ACS 1 .times. S 3 .times.
R 13 ] [ AE 1 + BE 2 + CE 3 ] 2 equals .times. [ S 1 / E 1 ] 2 All
of the E's, S's and R's are known quantities from the results of
a simulation run.
[0066] There is thus one equation relating A, B and C. First, to
set the scale for the combined policy, set B=1. Note that if A,
B and C are all doubled, the equation is unchanged. There is now
one equation in A and C. If a value is assigned to A, then a quadratic
equation is formed in the one unknown C, which specifies the face
amount of life insurance that is required for the designated values
of A and B. A quadratic equation has two roots, which may be real
or complex. A real solution may be positive or negative. Of course,
it is only positive, real values of C, which yield useful results.
[0067] One key to the success of the method in producing a multiperil
policy with specified statistical properties is fixing the benefit
levels for the various components when the policy is issued and
keeping them fixed throughout the life of the policy. The purpose
of fixing the benefit levels at the time at which the policy is
issued is to avoid adverse selection by the policyholder during
the life of the policy. A combined policy is designed to meet certain
specified statistical properties over the life of the insurance
contract and part of meeting these specified properties is keeping
the benefit levels unchanged.
[0068] Comparison to Known Methods:
[0069] Considering three standalone policies, the riskbasedcapital
requirements for the annuity and life insurance policies are small
percentages of the premiums, but the riskbasedcapital requirement
for a standalone LTC policy will be a much larger percentage of
the premium than for annuity and life insurance policies. However,
it seems reasonable to apply that same low riskbasedcapital requirement
to the entire premium of the combined policy if that combined policy
has been designed to have a coefficient of variation as small as
or even smaller than the coefficient of variation of a standalone
annuity. Thus, a significantly smaller amount of capital should
be required to be retained by the writing insurer to support a combined
policy than to support three standalone policies with the same
benefit levels.
[0070] The combined policy can be compared to previous methods
of preparing standalone policies both with and without inflation
protection. FIGS. 3 and 4 are tables illustrating the results of
calculations using a known method for preparing standalone policies.
The total present value of payouts is shown in column M in both
FIGS. 5 and 6. This number is analogous to column I in FIGS. 1 and
2 for the combined policy. Column U shown in FIGS. 5 and 6 illustrates
the difference in policy payouts for the insurer when using the
preferred method for preparing a combined policy versus preparing
a standalone policy using a prior known method. The differences
are very beneficial to an insurer when using the preferred method.
There are two components to the reduction in expected payouts First,
for the combined policy the same mortality table is used for all
of the perils, rather that an annuity mortality table for the annuity
portion of the combined policy and a life insurance mortality table
for the life insurance component. Secondly, the reduced risk regarding
the LTC insurance peril, especially, leads to a proposed reduction
in risk based capitol (RBC) for a combined policy. This proposed
reduction in RBC times the insurer's cost of capital yields an estimate
for the insurer's saving in the cost of RBC.
[0071] Additional Comparison
[0072] The following demonstrates that combined policies can be
designed that are less risky than both annuitized annuities and
life insurance when following the preferred method. The statistic
used for comparison is the 95.sup.th percentile benefit payout.
[0073] The coefficient of variation (CV) is used to design combined
policies and to compare them with annuitized annuities and life
insurance policies. As noted elsewhere, various other design properties
can be chosen for designing combined policies. These alternatives
include, but certainly are not limited to, the average of the ten
percent largest in the distribution of payouts and a benefitpayout
quantity which is "at least as much as is needed in 95 percent
of the trials" in simulation runs. These statistics are rather
similar in behavior. The riskbased capital requirements for life
insurance in the 2004 National Association of Insurance Commissioners
(NAIC) publication seem to be based upon this "95 percent of
the trials" statistic. This 95percentofthetrials statistic,
which is virtually identical with the 95.sup.th percentile benefit
payout, is used to make comparisons of combined policies with annuitized
annuities and with life insurance policies.
[0074] The following analyses are based upon simulation runs only
for the following two situations: [0075] Mortality table: overall
population, 2001, reference A [0076] Singlepremium policies issued
at age 65 [0077] Initial state of disability: no disability [0078]
Riskfree discount rate: 5 percent [0079] Males only
[0080] Inflation protection: TABLEUS00004 Situation one Run [A]
3% for the annuitized annuity. 5% for the longterm care benefits
0% for the face amount of the life insurance. Situation two Run
[B] no inflation protection
[0081] The combined policies are designed to meet specified values
of the coefficient of variation. The smaller the coefficient of
variation, the less risky the corresponding combined policy. Each
combined policy is compared with an annuitized annuity and a life
insurance policy, each of whose benefit levels are adjusted so that
the expected payouts of benefits are the same for all three policies
in a particular comparison.
[0082] For a particular comparison, the 12,000 simulated payouts
for the pure annuitized annuity are sorted and the 601.sup.st largest
payout is selected (because 600 is five percent of 12,000). Next,
the payouts for the corresponding combined policy are sorted and
the 601.sup.st largest payout is selected. Finally, the payouts
for the pure life insurance policy are sorted and the 601.sup.st
largest payout is selected.
[0083] Table I, below, illustrates the level of risk of combined
policy, compared with annuitized annuity and with life insurance,
as measured by what is essentially the amount of the 95th percentile
benefit payout. The table is only a brief summary of the results
of the calculations. TABLEUS00005 TABLE I riskiness of comb. policy
compared with inflation monthly LTC coefficient annuitized life
protection* annuity benefit life insurance of variation** annuity
insurance 350 $3,000 $2,000 $42,590 0.4838 greater greater 350 3,000
2,000 99,476 0.44 greater smaller 350 3,000 2,000 137,413 0.4131
smaller smaller 350 3,000 2,000 156,898 0.4 smaller smaller 350
3,000 2,000 220,498 0.36 smaller smaller 350 3,000 2,000 291,384
0.32 smaller smaller *350 inflation protection means a 3% annual
increase in the annuity payments, a 5% annual increase in LTC benefits
and no increase in life insurance benefits. **0.4838 is the coefficient
of variation for the annuitized annuity under the conditions of
this simulation run with 350 inflation protection and 0.4131 is
the coefficient of variation for a simulation run under the same
circumstances but with no inflation protection.
[0084] In each case, a combined policy becomes less risky as the
coefficient of variation to which it is designed is reduced. The
topmost entries are for a $3000 monthlyannuitized annuity benefit,
which is relevant for estate planning in the context of choosing
a monthly income level and then choosing for the LTC benefit level
the incremental amount of income, which is desired if LTC benefits
are needed. This display includes inflation protection, as described.
[0085] In comparison, the second group, which is for a $1000 per
month annuitized annuity benefit, requires a smaller coefficient
of variation before the combined policy becomes smaller in risk
than the two standalone comparison policies.
[0086] The value 0.4838 is the coefficient of variation for the
annuitized annuity with the specified inflation protection and 0.4131
is the corresponding coefficient of variation for the annuitized
annuity without inflation protection. The bottom two displays show
similar results for the cases without inflation protection.
[0087] Alternative Uses for the Preferred Method
[0088] There are many alternative uses for the preferred method.
For example, employee benefits or individual or group insurance
coverage can be calculated using the preferred method, such as combining:
[0089] routine health care and/or preventive health care [0090]
major medical insurance [0091] disability income insurance [0092]
life insurance
[0093] Preventive health care and routine health care are low enough
in variability to act similarly to an annuity when part of a combined
policy. Major medical insurance and/or disability income insurance
(for people under fifty years of age) will be analogous to LTC insurance.
Life insurance will play its usual role of being negatively correlated
with routine health care and/or preventive health care.
[0094] Medical spending accounts (medical savings accounts) plus
highdeductible major medical insurance are used more frequently
today. Adding life insurance to this combination would enable the
design of a combined package, which meets a specified coefficient
of variation.
[0095] In addition, financial planning for parents with disabled
children can be calculated using the preferred method. For example,
suppose a parent chose to purchase an annuitized annuity today of
X dollars a month for the life of the parent and purchased for the
dependent child an annuity of Y dollars per month that would begin
upon the death of the parent and continue until the death of the
child. There will be a strong negative correlation in the amounts
of money, which the insurer will be called upon to pay out in benefits
for these two annuities. The longer the parents' lives, the shorter
and further in the future will be the payments to the child, and,
vice versa.
[0096] Thus, there is a basis for designing a combined policy to
meet a specified coefficient of variation even before bringing in
consideration of insurance for perils such as LTC insurance, major
medical insurance and life insurance for both or either of parent
and child. However, there are special considerations involved in
this area, and they go well above and beyond simply designing an
appropriate combined policy.
[0097] Finally the approach of the combined policy will be very
useful for estate planning. Broadly speaking, a person doing estate
planning will have assets such as 401K accounts, 403Bs, definedbenefit
pensions, mutual funds, portfolios of stocks and bonds, et cetera.
The essential challenge is to use the assets at a rate which will
provide a comfortable style of living without exhausting the assets
before death and enabling the retiree to meet healthcare needs
and longtermcare needs as they arise, as well as providing monthly
income. A second desire of retirees is to have a "nest egg"
to give to the next generation. Those planning estates can then
choose how to divide their assets between a combined policy and
leaving those assets invested elsewhere.
[0098] Expressed in terms of planning for one person, a suitable
first step will be to choose the benefit level for the annuitized
annuity, probably with inflation protection such as a three percent
increase in the benefit level year.
[0099] Next, the planner can choose the incremental level of monthly
LTC benefit needed if and when the person enters a nursing home
or needs home health care. Note that this LTC benefit level does
not need to be the total cost of nursing home care because the monthly
annuitizedannuity benefit will continue. Again, one would probably
choose inflation protection, such as a five percent increase in
benefit each year. The insurance underwriter will then calculate
the face amount of life insurance required to meet the statistical
property or properties for which the combined policy is to be designed.
[0100] This method is advantageous over standalone policies because
the correlation coefficient for payouts of benefits for life insurance
and an annuitized annuity is, in principle, negative one. In addition,
by using the same mortality and morbidity tables for pricing all
of the risks in the combined policy, the combined policy will yield
total expected benefit payouts that are less than the sum of the
expected payouts for the corresponding standalone policies for
the same group of risks. For example, for the mortality and morbidity
tables used here a pure annuitized annuity of $1,134 per month has
the same expected benefit payout and the same standard deviation
of payouts as the combined policy with a $1,000 per month annuity,
a $2,000 per month LTC benefit and a $6,556 life insurance policy.
The skewness and the kurtosis of the payouts are reasonably similar.
Thus, one would anticipate that an insurer would be essentially
indifferent between writing these two policies. A policyholder could,
on the other hand, in effect, "trade" $134 per month of
a $1,134 per month annuitized annuity income for the LTC and life
insurance coverage. Thus the approach of the combined policy will
be very useful for retirement planning.
[0101] While certain preferred embodiments of the present invention
have been disclosed in detail, it is to be understood that various
modifications may be adopted without departing from the spirit of
the invention or scope of the following claims.
