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Pricing and profitability of
unit-linked insurance
Münchener Rück
Munich Re Group
Munich Re Group
Pricing and profitability of unit-linked insurance
1
INTRODUCTION ...............................................................................................................2
2
INITIAL CHARGES ............................................................................................................3
2.1
DIRECT INITIAL CHARGE. ...............................................................................................3
2.2
DISGUISED INITIAL CHARGE .........................................................................................4
2.3
EFFECTS OF THE INITIAL CHARGE ON PRODUCT DESIGN .......................................5
3
SURRENDER CHARGES ..................................................................................................6
4
RENEWAL CHARGES .......................................................................................................8
4.1
METHODS OF TAKING RENEWAL CHARGES...............................................................8
4.2
ALLOCATION RATES AND BID/OFFER SPREADS.........................................................9
5
CHARGES FOR ADD-ON INSURANCE BENEFITS ......................................................10
6
PRICING AND PROFIT TESTING...................................................................................11
6.1
OVERVIEW ......................................................................................................................11
6.2
EXPENSES INCURRED ..................................................................................................11
6.3
CHOOSING THE CHARGING STRUCTURE..................................................................12
6.4
THE ASSUMPTIONS REQUIRED ..................................................................................12
6.5
VALUATION AND OTHER RESERVES ..........................................................................14
7
PRICING A UNIT-LINKED POLICY .................................................................................17
7.1
EXAMPLE OF PRICING ..................................................................................................17
7.2
PROFIT TESTING RESULTS ..........................................................................................18
7.3
EFFICIENT PRODUCT DESIGNS ...................................................................................20
7.4
COMMISSION STRATEGIES .........................................................................................20
7.5
SENSITIVITY TESTING ..................................................................................................21
APPENDIX 1:
PRODUCT DESIGN AND PRICING ASSUMPTIONS FOR A SIMPLE
UNIT-LINKED PLAN..........................................................................................23
APPENDIX 2:
PROJECTION OF A POLICYHOLDER'S ACCOUNT .......................................24
APPENDIX 3:
PROJECTED INSURANCE REVENUE ACCOUNT..........................................25
APPENDIX 4:
SHAREHOLDER'S ACCOUNT..........................................................................26
BIBLIOGRAPHY............................................................................................................................28
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1
INTRODUCTION
This paper looks at the various charging methods in use for unit-linked
business and how insurers decide on the charging structure of their
unit-linked policies.
The profitability of a unit-linked product is a delicate balance between the
charges that the insurer takes from the policy and the claims for which it will
be liable plus the commission and administration expenses that it will incur.
The charges can be set in various ways such that they are expected to meet the
insurer’s profit objectives. The types of charge used and the levels at which they
are set will affect the sales and the robustness of profitability (that is, the
sensitivity of profitability to deviations of actual experience from pricing
assumptions). In particular, the problem of recouping initial costs is an issue
that the pricing actuary will have to grapple with. Any number of combinations
of initial charges, renewal charges, surrender charges, and charges for insurance
benefits may provide acceptable levels of profit. However, as will be explained
in this paper, there will be relative advantages and disadvantages of each from a
sales and/or marketing perspective. The following sections describe and discuss
in more detail the various methods of taking charges that can be used and the
advantages and disadvantages of each.
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Pricing and profitability of unit-linked insurance
INITIAL CHARGES
This section considers the various ways in which an initial charge can be taken
- either directly or in disguised form.
2.1
•
•
•
•
•
DIRECT INITIAL CHARGE
Direct initial charges can be taken in two ways:
– Zero allocation to units for a period of time (i.e. no part of the premium
is used to buy units and the insurer can therefore use this money to
cover initial expenses)
– Reduced allocation (say 50%) to units for a longer period of time
Within these two methods, there is a variety of operating practices:
– The zero or reduced allocation period can be a fixed period.
– The zero or reduced allocation period can vary according to the term
of the policy or the commission payable.
– The zero or reduced allocation period can vary according to the
premium level. Under this method, a debt or charge fund is established
at the start of the policy. This is a monetary amount, determined as
either a fixed amount or a variable amount depending on the premium
or commission payable. The unallocated premium reduces the debt or
charge fund. The balance on the debt or charge fund is deducted from
the value of units on surrender before the debt or charge fund has been
paid off. The debt or charge fund can be level, increase at a specified
rate of interest or increase in line with fund performance.
Direct initial charges best match the incidence of incurred expenses, so the
lower the allocation rate during the reduced allocation period, the better
the match with the incidence of expenses and the more robust the
profitability of the product.
Taking an initial charge means that fewer clients surrender their policies
before the initial costs have been recouped than if charges were spread
more evenly over the term of the policy. As such, there is a lesser burden
of unrecouped initial costs to spread across clients who do not surrender
and the surrender or maturity values for these clients are therefore higher
than if there is a more even charging structure.
The major disadvantage of direct initial charges is that they are easily visible
to the client and have a severe impact on surrender values in the early years
of the policy. This is often unacceptable from a marketing point of view.
2.1.1
•
•
•
•
•
•
SOME EXAMPLES OF DIRECT INITIAL CHARGE METHODS
A zero allocation period of 12 months
A 50% allocation period for 24 months
A zero allocation period of initial commission rate/60% x 12 months
A 50% allocation period of initial commission rate/60% x 24 months
A zero allocation period of 0.5 months x term of policy
A 50% allocation period of 1 month x term of policy
Methods of taking
direct initial charges
Direct initial charges
best match incidence
of expenses
Direct charges are
visible to the client
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•
•
•
2.2
Create a non-increasing debt of 5% x term of policy x annualized premium.
Assuming a 20-year policy, this gives a debt of one annual premium. This
could be paid off by
– a zero allocation period of 12 months;
– a 50% allocation period of 24 months.
Under this method the exact allocation percentages and reduced allocation
period are fairly unimportant, as on surrender before the debt is paid off,
the outstanding debt is deducted from the value of the units. Any
combination results in approximately the same as having a zero allocation
period. The difference is the investment growth of any premiums allocated
to units once the value of the units exceeds the outstanding debt (i.e. the
surrender value is positive).
Create a debt of $250 increasing at 4% per annum to be paid off by a
50% allocation period. At a monthly premium of $200, the debt would be
cleared following payment of the third monthly premium. At a monthly
premium of $25, the debt would be cleared after payment of the 21st
monthly premium.
DISGUISED INITIAL CHARGE
Making direct initial
charges less visible
Insurers have generally been reluctant to abandon the initial charge structure
and have sought instead to take initial charges in a way that is less visible to
the client. Various ways of disguising initial charges have been developed,
which are more acceptable from a marketing point of view, but the fact that
they are simply ways of making the same initial charge means that the
surrender values in the early years remain just as low. In an environment
where disclosure of early surrender values is required, the disguise becomes
rather ineffectual.
Initial units and
cancellation units
One method of disguising initial charges is to use initial or cancellation units.
Under this method, the early premiums paid are allocated to units that have
a fund management charge considerably higher than the regular fund
management charge. If the client surrenders the policy, then all future fund
management charges in excess of the regular fund management charges on
these units are taken at the point of surrender. These charges are therefore
received regardless of whether the policy is surrendered early or runs to
maturity. Ignoring any solvency requirements, the reserve needed in respect of
these units is number of units times unit price less the value of the excess
future fund management charges. This is the same as having a reduced
allocation to units in the early years and has the same effect for the insurer
as an initial charge. Depending on the precise method used the initial units
and regular units may have different prices.
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2.3
Pricing and profitability of unit-linked insurance
EFFECTS OF THE INITIAL CHARGE ON PRODUCT DESIGN
In the UK, initial units and surrender charges were introduced in the late 1970s
in response to intermediary concerns that direct initial charges put clients off
buying these products. At that time disclosure of surrender values during the
early years of the policy was not mandatory, and indeed was avoided where
possible. Surrender charges were the first method to be used, but as
administration systems became more advanced and better able to deal with
more complicated product structures, initial units became common.
Reasons why initial units
and surrender charges
were introduced
Under the initial unit structure, the client is presented with a product under
which 100% (or close to 100%) of premiums are allocated to units. This was
perceived to be the best product design from a marketing perspective. The
death benefit under this type of contract was usually the greater of the value
of units without deduction of future fund management charges (as opposed
to the surrender value from which they were deducted) and the sum insured
under the policy.
This helped to maintain the illusion to the client that close to 100% of its
premium was allocated to units all the way through the policy term. Once
regulation came into force requiring disclosure of surrender values in the early
years, the nature of the initial unit charging structure became obvious and
rendered the disguise of the structure ineffective. Most developed markets now
require disclosure of early surrender values at point of sale but the effects on
product design have varied between markets.
• In some markets the product design has reverted to the initial charge
structure. In these markets, there is downward pressure from
intermediaries on initial charges. Where intermediaries take little or no
initial commission (but charge fees instead), the insurers are able to reduce
initial charges.
• In some markets, the product design has moved towards a level charging
structure, irrespective of the initial commission paid to intermediaries.
UK regulation has
rendered disguise of the
cost structure ineffective
The level charge structure means:
• Higher surrender values in the early years
• Initial expenses are not fully recouped from early surrenders
• The insurer is exposed to the risk of an adverse early surrender experience
• Longer term surrender values and maturities are lower than under an initial
charge structure
• Better marketability
Level charge structure
In summary, the initial charge structure has two significant advantages:
• It allows the insurer to recoup initial expenses much more quickly and
as such lessens the sensitivity of profit to deviations from pricing
assumptions, especially lapse rates.
• It eventually produces superior surrender values in later years for clients.
• On the other hand, initial charges depress early surrender values, and can
prove to be a marketing disadvantage, especially if they are clearly
disclosed to the policyholder.
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Surrender charges are
used to recover
outstanding initial costs
SURRENDER CHARGES
Surrender charges (also called surrender penalties or back-end charges) are
applied when a policy is surrendered. These charges are normally used to
recover the outstanding initial costs which have not yet been recovered by
the other product charges. If a policy persists over the full product term or
(a significant portion of it), the initial costs will have been recouped.
A surrender charge protects the insurance company in the case where the
policy is surrendered and initial costs have not been fully recovered. They
are often used for policies with either no initial charge or a low initial charge.
Surrender charges can be as high as 100% of the value of units purchased
during the first year of the policy.
Reduced allocation and
surrender charges are
fundamentally different
There is a fundamental difference between reduced allocation rates and
surrender charges. Reduced allocation rates are applied to all policies whereas
surrender charges are applied only to surrendering policies.
A surrender charge of 100% of the value of the units purchased in the first year
is not equivalent to a zero allocation rate during the first year. Under the zero
allocation, the insurer allocates no money to purchase units for the policy in the
first year and thus may use the whole of the first year’s premium from all
policies to cover its expenses.
Possible investment
mismatch risk
Even with a 100% surrender charge in the first year, the insurer will have to
pay the value of the units purchased with the first year’s premium, less any
remaining surrender charge, if surrender occurs past the first year. Under this
product design, if the insurer does not actually allocate units, it exposes itself
to an investment mismatch risk. Furthermore, a reserve would have to be
established in respect of the allocation to the policy in the first year as some
(or even most) policies will be subject to a surrender penalty of less than 100%
of the value of these units. Thus, zero allocation in the first year is equivalent
to a 100% surrender charge of the first year’s investments only for policies that
surrender in the period during which the 100% surrender charge applies.
The actuary has to consider this distinction when setting the reserving basis for
the policies. Ignoring any guarantees, it would be imprudent to hold as reserve
the value of the units less the full surrender charge. On the other hand, holding
the full value of the units would be conservative given that some policies will
surrender and a surrender charge will be taken.
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Pricing and profitability of unit-linked insurance
Surrender charges themselves come in several forms:
• A scale reducing over time applied to the premiums paid in the first
year (or other suitable period)
• A scale reducing over time applied to the value of units purchased in
the first year (or other suitable period)
• A scale reducing over time applied to the value of all units
• A fixed amount reducing over time
In general, surrender penalties go down to zero after a period of time
(commonly five years, although longer periods are acceptable in some
markets). This means that after five years the surrender value is equal to the
value of units and ideally all initial expenses should have been recouped,
through a combination of surrender charges and the other charges taken from
policies. In practice this is unlikely and so fund management and other renewal
charges will need to exceed incurred renewal expenses in the later years of the
policy to recoup the remaining unrecovered initial expenses.
The longer the period over which the surrender charge applies and the larger
it is, the more it approximates to an initial charge. Policies with a low surrender
charge or a surrender charge that goes down quickly tend to have higher
renewal charges than policies with either a direct initial charge or with initial
or cancellation units.
Surrender charges reduce
as expenses are recouped
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4
RENEWAL CHARGES
4.1
METHODS OF TAKING RENEWAL CHARGES
The various ways in which renewal charges can be taken are:
• As an investment or allocation fee taken as a percentage of each premium
• As a policy fee deducted from the premium before allocation to units
• As a policy fee deducted from the funds under management by cancelling
units
• As a bid/offer spread on the price of units whereby the price at which the
client buys units is higher than the price at which the insurer will redeem
them
• A percentage of the funds under management
Covering ongoing renewal
expenses
Any or all of these can be used to cover ongoing renewal expenses and
unrecovered initial expenses. The level of any of these charges depends on the
extent to which they are required to recoup initial expenses. The lower the level
of initial charge, the higher the level of renewal charge required.
Once initial costs have all been recouped, the level of renewal charges will be
more than sufficient to meet renewal costs. This means that loyalty bonuses
can be offered to clients still paying premiums at that time. Loyalty bonuses
may be marketed as:
• Increase in the allocation rate to the policy (to more than 100% if there is a
bid/offer spread), usually after a period of time.
• Allocation of bonus units to the policy, usually after a period of time. This
is commonly used when the main source of renewal charges is the funds
under management charge and so this is at a higher rate than the market
norm. Once the initial costs have been recouped, charges are no longer
required at this level. As unit prices are generally calculated after deduction
of the management fee, applying a different fund management charge
when the policy had been in force for a certain duration would require
two sets of units with different unit prices. This would be administratively
complex, and rather than do this bonus units are allocated to the policy
at regular intervals.
• Waiver of the policy fee. This is often done once the fund value exceeds
a certain monetary value, e.g. $10,000.
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4.2
Pricing and profitability of unit-linked insurance
ALLOCATION RATES AND BID/OFFER SPREADS
There is often confusion over the use of a bid/offer spread, and it is important
to recognize that it is primarily a means of extracting an initial charge from a
single premium policy or an ongoing charge from a regular premium policy.
In this way, it acts in much the same way as the allocation rate to units. Some
simple examples will illustrate this.
Consider first a unit-linked policy where there is only one unit price, say, $1.00.
The allocation rate to units is 95% and the premium paid is $1,000. There is no
surrender penalty.
The amount of money allocated to the policy is 95% x $1,000 = $950 which
buys 950 units at $1 each. The cash value and reserve of the policy has
increased by $950. The other $50 is available to meet expenses.
Consider now a unit-linked policy where there are two unit prices. The terms
and conditions of the policy state that bid price = 95% x offer price. The
allocation to units is 100%. The offer price = $1.00 (so the bid price = $0.95).
The amount of money allocated to the policy is $1,000 which buys 1,000 units.
If the units were surrendered immediately, their value would be 1,000 x $0.95 =
$950. What this effectively means is that the actual cost of creating a unit is
$0.95; that is, $0.95 worth of assets (ignoring transaction costs) support each
unit. The cash value and the reserve of the policy have both increased by $950.
The remaining $50 is available to meet expenses.
Both methods achieve the same result – a $50 contribution to expenses. In the
first case the client has 950 units valued at $1.00 each. In the second case the
client has 1,000 units valued at $0.95 each.
Of course, a policy could have both a bid/offer spread on its units and an
allocation rate different from 100%. The final result of the combination of bid/
offer spread and allocation rate should be a sufficient contribution to expenses.
Allocation rates and
bid/offer spreads achieve
the same objective
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5
CHARGES FOR ADD-ON INSURANCE BENEFITS
Add-on insurance benefits are benefits chosen by the client that are included
in a unit-linked policy in addition to any minimal insurance coverage
automatically provided under the policy to ensure that it meets the definition
of life insurance. There is not usually an explicit charge for such minimal cover,
and the costs thereof are normally allowed for as an element of the overall
costs associated with the product.
Examples of add-on
benefits
Add-on benefits may cover people other than the main client and can consist
of life insurance, critical illness insurance, disability cover or other benefits.
In some cases, a level premium is charged for cover provided under add-on
insurance benefits and this is deducted from the premium prior to being
allocated to units. Premium rates for these benefits will reflect commission on
the main unit-linked policy. The extent to which the add-on benefit rates meet
expenses depends on how the insurer wishes to recover initial expenses and
meet renewal expenses. As the commission on the main unit-linked policy is
usually lower than the rate on the premium for the stand-alone benefit, the
rates should be cheaper than the stand-alone rates. Charging the same rates
would therefore provide some additional margins and would avoid product
bias. This is the usual pricing method adopted by insurers under this approach.
Charges are usually made
on current-cost basis
More often, though, charges for add-on insurance benefits are made on
a current-cost basis, applying risk premium rates to the sum at risk. To the
extent that the charges are greater than the expected claims amounts, this will
serve as an additional margin available to cover renewal expenses or to help
recoup initial expenses. There is no requirement to load these charges for
commission or expenses as commission is already considered in the
premium for the main unit-linked contract, and expenses can be recovered
from the main contract as well.
As the risk premium rates can usually be increased at any time (subject to
any premium rate guarantees), there is no requirement for any significant
contingency margin in the rates.
Add-on benefit charges
can help to reduce visible
charges
Unit statements to clients on policies which charge for add-on benefits using
a current-cost method, are quite complex, particularly if credits and debits are
shown on a monthly basis. From both the client and intermediary points of
view, it is difficult to tell whether the charges made for add-on benefits are
cheap or dear in comparison with competitors. Furthermore, the primary
purpose of the policy is often investment and the charges for add-on benefits
are rarely put under scrutiny. These charges are not subject to the same
competitive pressures as the premium rates under pure risk insurance and
insurers are therefore able to take some additional margins to help keep down
the levels of the more visible charges.
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6
PRICING AND PROFIT TESTING
6.1
OVERVIEW
Pricing and profitability of unit-linked insurance
Pricing and profit testing is the process of determining the charges that
will result in a profitable product.
This is done by choosing a charging structure and projecting the cash flows
(charges taken less costs incurred) over the life of a portfolio of business.
This requires a set of per policy expenses to go with the charging structure.
The objectives of the profit-testing process are:
• To produce a charging structure that is marketable, meets the insurer’s
financial targets, and can be supported by the administration system.
• To produce a charging structure that is fairly insensitive to the mix of
business written (in terms of age, sex, premium level, etc.). In this
connection, it is worth remembering that the better the incidence of
charges matches the incidence of incurred expenses, the more robust
the profitability of the product.
6.2
Objectives of profit testing
EXPENSES INCURRED
These are the costs associated with running the portfolio of unit-linked
business. Identifying these costs is a complex issue and must allow for
(amongst other things):
• One-off administration systems development costs
• Other product development costs
• A share of distribution overhead costs
• Administration costs (including overhead costs)
• Investment management costs
All costs need to be split up between acquisition costs and renewal costs.
For a start-up insurer, this is a fairly straightforward matter, but for an insurer
writing other lines of business, identifying and projecting these expenses is
much more difficult. For this reason, insurers often set up separate companies
to deal with their unit-linked business and expenses are recharged from the
existing company on a time and materials basis. As the unit-linked business
develops, formulae for the apportionment of expenses can be refined, but in
the early days they will of necessity be somewhat approximate.
The list of expense assumptions required is relatively simple, but derivation of
amounts is much more difficult. They must also allow for economies of scale in
the future.
Identifying and projecting
expenses is often complex
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6.3
CHOOSING THE CHARGING STRUCTURE
There will be certain constraints on the charging structure imposed
by the market. The key constraints will be in the areas of
• whether an initial charge or surrender penalty is acceptable.
• the maximum fund management charge that is acceptable.
• the maximum bid/offer spread that is acceptable.
The charging structure is
a delicate balance
Within these constraints, the insurer must choose a charging structure that
allows it to pay competitive levels of commission, meet its financial targets
and not be sensitive to small changes in the mix of business. To a certain
extent, this will be a matter of trial and error.
6.4
THE ASSUMPTIONS REQUIRED
EXPENSES
•
•
•
•
•
•
•
Initial expenses
Renewal expenses
Inflation of renewal expenses
Initial commission (and overriding commission)
Clawback rules
Renewal commission
Asset or trail commission
CHARGES
•
•
•
•
•
•
Initial charge
Renewal charges (bid/offer spread, policy administration charge, etc.)
Fund management charge
Allocation rates
Add-on benefit charges
Any other charges
OTHER
•
•
•
•
•
•
•
•
•
Profit testing should be
across a whole portfolio
Mix of business (age, sex, premium, add-on benefits)
Fund returns (gross and net of tax)
Mix of funds
Lapse rates
Claims experience under add-on benefits
Valuation and reserving methods (including solvency requirements)
Tax computation
New business volumes and projections
The discount rate to be used
It is important to profit test a portfolio of business rather than just one year’s
new business to allow for economies of scale to take effect. The portfolio profit
test will generate a present value of future profits (PVFP) at the discount rate
used. To decide whether the result is acceptable, the insurer will have a
financial target to meet. This can be expressed in one of the following ways:
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•
•
•
Pricing and profitability of unit-linked insurance
To generate a return of at least x% on capital. The minimum required rate
should be the risk free rate plus an allowance for future inflation plus the
insurer’s allowance for provision of capital. If the return on investment
(ROI) is equal to or greater than x%, the product would be considered
profitable (the ROI is by definition the rate which will discount the future
profit stream to zero and is the rate earned over the life of the policy on the
amount needed to cover the initial strain when a policy is sold).
To generate a present value of future profits of x% of new premiums based
on a discount rate of y%.
To generate a contribution to overhead of $x per policy based on a discount
rate of y%.
The setting of profit objectives is not an easy matter and should always take
into account the degree of risk of a product (in consideration of its guarantees
and options), the level of competition, and the insurer’s financial objectives.
Profit targets should be set such that an adequate return is earned on the
capital that is used to support the business (thus earning a rate that will satisfy
shareholders) and may be set even higher if the company wants to increase its
free surplus and improve its ratings and/or fund future growth.
Setting profit objectives
In addition to achieving certain levels of profit in the best estimate scenario,
there are usually constraints that the sensitivity of the results to changes in
the assumptions should lie within certain bounds and that the break-even point
should be before a certain time. The break-even point is the point in time at
which the accumulated value of profits and losses first becomes positive using
a specified accumulation rate.
This rate could be
• the accumulation rate applied to the unit-linked funds;
• the accumulation rate applied to non-unit reserves;
• the investment return on shareholders’ funds retained within the business;
• a fixed rate (say, 10%);
• the minimum required rate (x% above).
If the minimum required rate is exactly achieved, (assuming that the policy
generates an increasing profit stream over the policy term), the break-even
point will be at the end of the policy term.
Most commonly, insurers calculate the break-even point based on the return
they expect to earn on shareholders’ funds that are not used to finance new
business. This rate of return will often be that for a fairly conservative
investment portfolio and will often be similar to the projected rate of return on
the balanced unit-linked funds. The rate of return can therefore be viewed as
the rate of return that could be obtained by following a relatively conservative
investment strategy as opposed to investing in expanding the insurer’s
business.
The precise form of the targets will vary between insurers depending on the
requirements of the shareholders and the way in which the performance of the
company is measured.
Calculating the break-even
point
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6.5
VALUATION AND OTHER RESERVES
6.5.1
GENERAL CONSIDERATIONS
This section discusses in greater detail valuation reserves as they relate to unitlinked business.
Holding assets to support
the liabilities
The sale of a life insurance contract is not the same as the sale of a
manufactured good whereby profit is immediately and fully realized once the
transaction has been made. Under a portfolio of life insurance policies, there
are cash inflows and outflows over the duration of the portfolio and the profits
arising from a portfolio of business can only finally be determined when the
last policy has left the portfolio. During the term of the policies, the insurer
must ensure that, at any time, it holds sufficient assets to support the liabilities
under its policies and to cover any negative cash flows.
Different territories have different rules for the calculation of liabilities, but they
have a common objective of ensuring that the liabilities are not underestimated
and that the insurer will never become insolvent. This means that the insurer
should always be able to
• pay the claims (including surrenders and maturities) as they arise;
• meet the running expenses of the business;
• meet the cost of any guarantees that have been given.
Solvency margins are
often required
In some territories (for example in the countries of the European Union but also
in North America), there is an additional required margin of capital that the
insurer must provide. This is called a “solvency margin” (also sometimes
called a minimum or surplus requirement). In the European Union, this is made
up of two parts:
• A proportion of the mathematical reserves, plus
• A proportion, usually 0.3%, of the sum at risk. The sum at risk is the sum
insured, say, a death benefit minus the mathematical reserve for the policy.
In the European Union, the percentage related to mathematical reserves is
4% for policies with investment and expense guarantees. However, if there is
no investment (or maturity) guarantee, the amount can be reduced to 1.0% of
mathematical reserves. If there are also no expense or mortality guarantees,
the percentage is reduced to zero. The level of finance needed to write a unitlinked policy without guarantees can be much less than for a policy with
guarantees. Different territories have different rules, and the actuary must
ensure that such regulations are respected. If there are no explicit regulations,
the actuary should carefully consider an appropriation of free capital to support
unit-linked business, especially where guarantees are included.
In any case, in some countries, insurers will reflect in their pricing the use of
even more than the minimum solvency margin. They do this because insurers’
credit ratings depend on the amount of total surplus they maintain in relation
to the minimum required amount; and in order to achieve an overall desired
return on all surplus (or capital), they must allocate more than the minimum
capital required to support each policy.
Munich Re Group
6.5.2
Pricing and profitability of unit-linked insurance
MATHEMATICAL RESERVES FOR UNIT-LINKED POLICIES
In this section, only the rules for UK unit-linked or unbundled contracts will
be considered with respect to mathematical reserves.
One of the original problems regulators had with unit-linked contracts was the
difficulty of applying traditional reserving methods to unit-linked policies. This
may still be true in other territories where unit-linking is new.
In the UK, the calculation of the mathematical reserves has traditionally
followed the judgement of the “appointed actuary”. The UK actuarial
profession is continually devising new guidelines for valuations and these
become part of the legal requirements in due course or become universally
adopted good practice. Although this system gives the UK actuary some
freedom of judgement, the statutory reports that the actuary has to file with
regulatory authorities must fully describe the methods and assumptions that
have been used in valuing the unit-linked business.
Devising new guidelines
for valuation
The current guidelines for unit-linked business were largely developed during
the 1970s and 1980s, for example Brown1, Ford2 and Fine3. One of the main
guidelines is that the mathematical reserve should be separated into two parts:
• A unit-linked reserve and
• A “sterling” (or non-unit) reserve
Unit and non-unit reserves
are required
The first part should reflect the value of the units that have so far been
allocated to the policy according to the policy conditions.
The second part is to ensure that future premiums can be allocated as
promised and that claims and expenses can continue to be met without the
need for further finance (i.e. that there are no negative cash flows during the
policy term apart from the initial negative cash flow). It is usually not needed
for a policy that has no guarantees because the policy charges can be
increased to the level necessary to reflect these costs (but care has to be
taken if there are practical problems in implementing this, including delays).
The calculated sterling reserve on a policy can be negative (e.g. if the future
charges more than cover the future mortality and expense costs). In this
situation, reducing the total reserve by the amount of the negative non-unit
reserve effectively capitalizes future profits. Alternatively, the negative nonunit reserve could be regarded as an asset. If such a policy lapsed, the insurer
would have to pay a surrender value in excess of the total reserve it held for
the policy (or alternatively if the negative reserve was treated as an asset, that
asset would become worthless). To avoid this, negative non-unit reserves are
either eliminated (i.e. set to zero) or restricted such that the total reserve is
equal to the surrender value. However, a positive reserve is often needed for
a policy that has expense and mortality guarantees and has been in force for
some time. Again, different countries have different regulations, and negative
non-unit reserves may not be allowed.
1 Brown and others, “Valuation of Individual Investment Linked Policies”, in: Journal of the Institute of Actuaries, 1978.
2 Ford and others, “Report of the Maturity Guarentees Working Party”, in: Journal of the Institute of Actuaries, 1980.
3 Fine and others, “Proposals for the Statutory Basis of Valuation of the Liabilities of linked long term insurance
business”, in: Journal of the Institute of Actuaries, 1988.
Negative non-unit
reserves are eliminated
15
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Pricing and profitability of unit-linked insurance
Munich Re Group
The non-unit reserve is calculated on a policy by policy basis using discounted
cash flow methods. The actuary must ensure that the reserves are sufficient to
meet the liabilities as they arise. The actuary must carefully investigate the cost
and impact of product guarantees and options. In flexible premium plans this is
made even more difficult since future premium patterns and levels are
uncertain and much testing will be needed to make sure that an adequate
reserve is held.
Additional reserves for
guarantees are required
If the policy has a maturity (or surrender) value guarantee, a special type of
non-unit reserve may be needed. This is called a “maturity guarantee reserve”.
A “Monte Carlo” method is often used to derive this figure. This involves using
a computer to simulate a large number (5,000 or more) of random investment
outcomes and setting reserves such that the probability that the reserves are
insufficient is acceptably low (e.g. less than 1%).
Mismatching reserves may
be required
Other types of sterling reserve may also be needed, for example a mismatch
reserve if the unit-linked assets are smaller than the unit-linked liabilities (or are
not invested in the assets from which the unit price is determined).
Munich Re Group
7
PRICING A UNIT-LINKED POLICY
7.1
EXAMPLE OF PRICING
Pricing and profitability of unit-linked insurance
The method for pricing unit-linked policies follows from the preceding sections.
Given profit requirements and the best estimates of future factors, the objective
is to find an acceptable set of charges. The details are best shown by an example.
Consider a simple 10-year unit-linked policy for a man aged 40 paying £100 per
month. The minimum death benefit is the greater of £9,000 or the bid value of
the units (the £9,000 figure is 75% of the total premiums payable throughout
the policy term to comply with UK tax rules). For the sake of simplicity, the
example ignores the flexibility of the plan for both the client and the insurer.
Also, taxation will be excluded from the calculations, even though a prudent
pricing exercise would reflect its impact.
Appendix 1 lists the product design and pricing assumptions. The design of
this product consists mainly of a front-end load (there is only a 50% premium
allocation in the first year) with a small back-end load (the surrender penalty
is 100% of units during the first year but 0% afterwards). It is possible to find
more than one set of appropriate charges, but the most robust set is the one
that most closely matches the expected costs. However, it may not always be
possible to have a perfect match between charges and expense factors, for
marketing as well as for other reasons. For example, there is a fixed initial
cost of £75 for writing each policy, but the product design does not allow for
a fixed initial charge.
The most efficient charging
structure matches the
expected costs
Other items to note are:
• The mortality charge will be applied to the amount at risk (the sum insured
less the reserve). The mortality charge is 100% of the central mortality rate,
whereas the expected mortality is only 90% of the central mortality rate.
This effectively means that there is an 11% loading on the mortality
charges which can be used to cover expenses and contribute to
profitability.
• The unit interest rate is the rate of return that the units will earn before the
application of the management charge. The non-unit interest rate is the rate
earned by the insurer on its cash flows.
• The allocation rate increases to 101.5% after the first policy year. This may
seem to imply that more than the full premium is used to purchase units,
but since there is a bid/offer spread of 5%, it is equivalent to having a 100%
allocation rate and a 3.575% bid/offer spread.
The approach used is to project the cash flows from a block of identical policies
as described in Appendix 1 that are issued at exactly the same time. Using the
computer power available today, it is best to look at results for each month in
the future.
Appendix 1 also shows the profit measures for the block of policies.
Cash flows are projected
17
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Pricing and profitability of unit-linked insurance
Munich Re Group
Projection of the
policyholder account
Appendix 2 projects the unit-linked fund value of a policy assuming it is still
in force at the end of each future month. To show ten years of results easily,
only the year-end figures after the first are printed. The final column shows
the expected percentage of clients still paying premiums at the end of each
month. Appendix 2 gives the full movement (in money amounts) of all items
that affect the client’s unit holdings. A similar statement can be prepared using
units instead of money. A unit statement produced yearly (with perhaps a little
less detail) is the best way to make the policy transparent to the client. The
example shows that the policy’s surrender value eventually exceeds the sum
insured.
Projection of the insurance
profits
Appendix 3 lists the cash-flow projections that the insurer can expect from the
block of policies (unless it has been expressed in terms of a “block” of just one
policy). Amounts of expected outgo are shown in brackets. Most of the items of
the cash flow are quite straightforward. Appendix 3 allows for reserves and
solvency margins before arriving at the profit. The stream of profit figures
shown in the last column of Appendix 3 is called the profit signature of the
contract. There is a very heavy loss at the start of the contract due to the large
initial expenses and commissions. This is followed by some rapid repayment for
the rest of the first year and then a smaller stream of figures afterwards.
Projection of cash flows
to shareholders
Appendix 4 expresses profit from the shareholder’s perspective. Of course,
this profit is the same as found in Appendix 3, but its derivation is somewhat
different. The approach is particularly relevant for unit-linked products. This
appendix can be regarded as an income and outgo statement. Income to
the shareholders comes from the various product charges (i.e. unallocated
premiums, including the bid/offer spread, as well as expense, management,
surrender, and mortality charges). Outgoings are death benefit payments in
excess of the policy’s fund value, expenses and commissions, and the funding
of the solvency margin. Of course, there is also the need to allow for interest
on these items.
7.2
PROFIT TESTING RESULTS
This method provides a good indication as to how well matched charges and
outgoings are and which loadings account for most of the profit. It assists in
understanding how sensitive the product is to changes in basic assumptions.
Profitability measures
The profit testing results in the example are considered below:
•
•
•
•
The return on investment (ROI) is close to 20%.
The present value of future profits (PVFP) expressed as a percentage of the
present value of premiums payable is a commonly used measure for
profitability, as it corresponds to the profit margin of a manufactured good.
In the example, the “profit margin” is 1.18%.
A variation of this measure is to consider only the premium payable in the
first year (i.e. to consider PVFP as a percentage of the new annualized
premium). In the example, this measure is 5.33%
The PVFP expressed as a percentage of the present value of charges (i.e. all
policy charges including unallocated premiums and the bid/offer spread) is
Munich Re Group
•
•
Pricing and profitability of unit-linked insurance
another measure often used in pricing unit-linked plans. In the example, this
measure is 5.22%.
The break-even point is the time at which profits accumulated at the nonunit interest rate first become positive. In the example, the break-even point
is nearly five years. The accumulation rate here is the non-unit interest rate
under the simplified assumption that this is the rate earned on the insurer’s
free capital. If a higher rate had been used, the break-even point would have
been further delayed. The break-even time is so long because the charging
structure fails to recoup all expenses in the first year, leaving a small
negative accumulated profit balance at that time.
There is also a measure of PVFP as a percentage of the first-year commission.
This may be used as a pricing target – for example that PVFP is at least
15% of the first-year commission. In this way, if the product is successful,
the insurer and the intermediary both gain. In the example, this measure is
17.77%.
The example uses a risk discount rate of 11% to compute the present value
figures. The risk discount rate is the minimum rate of return that is needed
to satisfy the expectation of the providers of capital (e.g. shareholders) and
reward them for the risk of supporting the selling of insurance. The risk
discount rate used generally reflects the available supply of capital and the
demand for it.
Satisfying the shareholder
The product in this example has an even higher expected profit since the ROI
exceeds the risk discount rate (assuming it is still marketable despite
competition). If the company does not vary its risk discount rate according to
different classes of business, the profit targets of a particular class of business
(e.g. unit-linked insurance) may exceed the risk discount rate in order to reflect
the risk and potential rewards available from selling this type of business.
Having the same risk discount rate for all plans facilitates comparisons of
present values between different classes of business.
However, another reason to set pricing at a target that exceeds the risk discount
rate is to simply increase profit, and therefore capital, so as to be able to
support future company growth. Also, there may be a need to strengthen the
capital base and improve claims-paying ability or other ratings. If the extra
capital is not provided by the shareholders of the company, it needs to come
from an extra margin in the current pricing. If the ROI is exactly equal to the
risk rate (i.e. the present value of future profits is zero), this means that the
expectations of the shareholders are met. If the insurance company were to pay
dividends representing the full return on the business issued, no money would
be left with the insurer to fund future growth or enhance ratings. Thus, the
insurer may want to have an ROI greater than the risk rate (or, alternatively, a
positive present value of future profits). Only if the company does not want to
grow or enhance ratings would an ROI equal to the risk rate be acceptable. In
practice, the market will demand a risk rate which will be determined in part by
the supply and demand of capital as well as returns available from alternative
investments.
Supporting future growth
19
20
Pricing and profitability of unit-linked insurance
Munich Re Group
7.3
EFFICIENT PRODUCT DESIGNS
As has been explained in Section 2.3, the rapid repayment of the initial loss is
best for the shareholders as it means the capital is tied up for the shortest time.
This is because the risk discount rate is greater than what the unit funds can
earn. Small charges early in the policy life are equivalent to larger charges later
on, and such larger charges have the effect of creating a smaller unit fund at
the end of the contract.
Most clients will not appreciate this and in the past it was thought necessary
to disguise a front-end load (or high initial charges) by using methods such as
capital units. However, other things being equal, a comparison of long duration
surrender values and maturity values would demonstrate the superiority of
using high initial charges.
Combining charging
structures
More recently, the UK industry has been realizing that some clients prefer a
combination of level charges and back-end loads even if they ultimately create
smaller long duration surrender values and maturity values (although perhaps
not in the earlier policy years). This is in part because modern life-styles are
less certain than they were twenty years ago and early surrenders are more
unpredictable at the client level. Also, level charges and back-end charges are
better marketable in the sense that clients often do not tolerante high front-end
loads.
7.4
COMMISSION STRATEGIES
Front-end loads are one way to obtain an efficient design but other ways can
also be found. For example, the initial commission could be spread over the
first 12 or 24 months of the policy. This would reduce the burden on the insurer
of finding the immediate capital for the sale. If the premiums stopped, there
would be no more initial commission payments and this would shift a
significant part of the lapse risk from the insurer to the intermediary. However,
it should be noted that level (or levellized) commissions introduce the problem
of initially reduced income flows to intermediaries, and the difficulties posed
by the introduction of such a structure should not be underestimated.
Commission clawbacks
In the UK, it is standard practice for initial commissions to have an element
of clawback in case of lapse. This means that the initial commission is paid in
month 1 but, if the policy lapses early on, the intermediary will have to pay
some of it back to the insurer. Commission clawbacks usually apply for the first
one to four years of a policy and are on a sliding scale. This usually means that
the insurer’s lapse risk is partly converted into a credit risk with the intermediary.
The example in the appendices does not include a clawback mechanism.
Munich Re Group
7.5
Pricing and profitability of unit-linked insurance
SENSITIVITY TESTING
The pricing exercise should attempt to determine which changes in assumptions
have the greatest effect on profitability and whether the insurance company
can accept such variations. Sensitivity tests can be made by adjustments to
each of the assumptions to see the effect on the profit measures. If necessary,
the product design can then be slightly adjusted to reduce its sensitivity. The
most sensitive adjustments will be those where the future assumptions do not
correspond with the features of the product design. The following table lists the
effect of changing a few of the parameters listed in Appendix 1.
(1)
Base
ROI (annualized %)
Break-even month
PVFP (£)
PVFP (% of PV premiums)
PVFP (% PV of charges)
PVFP (% of initial commission)
19.86
(2)
(3)
£200
£50 premium
premium £4,500 SI
£18,000 SI
29.84
6.35
(4)
33 1/3%
higher
lapses
(5)
33 1/3%
lower
lapses
18.83
20.85
(6)
(7)
(8)
(9)
(10)
10% higher 10% lower +2% of the -2% of the +100% of
expenses expenses unit interest unit interest central
rate
rate
mortality
13.38
27.68
20.46
19.27
19.54
59
12
112
59
59
83
26
58
60
60
63.96
234.37
-21.24
53.40
75.62
18.75
109.16
69.95
58.27
61.77
1.18
5.22
2.17
10.01
-0.79
-3.19
1.09
4.59
1.26
5.82
0.35
1.53
2.02
8.91
1.30
5.63
1.08
4.82
1.14
5.04
17.77
32.55
-11.80
14.83
21.00
5.21
30.32
19.43
16.19
17.16
The assumed average size is important because most of the charges are related
to it, but there are large assumed costs that are not. Testing shows that a £200
monthly premium (£18,000 sum insured) or a £50 premium (£4,500 sum
insured) produces profits that vary significantly from the base scenario. This
may be accepted as a cross-subsidy from larger to smaller policies (assuming
confidence in the average of £100) or, more likely in this case, the product
could be redesigned and priced according to premium size (e.g. relate
allocations to premiums).
Another parameter that needs to be tested, but which is not included in the
example, is the effect of taxation.
It is important to consider the lapse rate. The example above shows that a
constant percentage increase or decrease of 33 1⁄3% in lapses only has a
relatively small effect on profitability. However, more detailed testing would
normally be performed, such as increasing lapses in the early years and
decreasing them in later years.
Policy size and expenses
significantly affect
profitability
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Pricing and profitability of unit-linked insurance
Munich Re Group
Other important variables are expenses. A difference of 10% higher or lower
would affect profitability dramatically. Expense differences between actual
expenses and those assumed are often due to inaccurate forecasts of business
volumes, and business volumes are the driving force behind unit costs.
Business volumes are therefore a key assumption for pricing purposes.
Profitability is not
sensitive to lapses or
investment returns
On the other hand, the effect of the average investment return on the units is
not big. Note that the investment return can vary greatly during the term of the
contract. If there is a prolonged market downturn, this could be serious for the
PVFP of plans written just beforehand. On the other hand, the PVFP of plans
written during a strong market can be enhanced. This makes it important to
test various unit-return scenarios and patterns, perhaps also using stochastic
processes, especially if much of the insurance company’s income comes from
charges on the fund value.
Different assumptions
apply to different product
designs
Different product designs would be sensitive to different assumptions. For
example, a product with a high death benefit would be sensitive to the entry
age and the mortality experience. If there were a wide choice of death benefits,
the product would be sensitive to the assumed average death benefit. Our
example is not sensitive to changes in mortality since it has little amount at risk
and is only for a 10-year duration.
In the end, the actuary must recognize the factors that affect the profitability
and by how much. There must also be an understanding of the options and the
guarantees that are provided to clients and how much they cost or may cost
the insurer when examining the best estimate scenario and deviations from it.
Thorough testing may involve changes to multiple parameters and even
stochastic modelling.
Munich Re Group
Pricing and profitability of unit-linked insurance
APPENDIX 1:
PRODUCT DESIGN AND PRICING ASSUMPTIONS
FOR A SIMPLE UNIT-LINKED PLAN
Product design
Economic assumptions
Monthly premium paid:
£100
Unit interest rate (p.a.):
7.0%
Sum insured (SI):
£9,000
Non-unit interest rate (p.a.):
4.5%
Policyholder age:
40
Inflation rate (p.a.):
3.0%
Policyholder sex (M/F):
M
Smoker status (NS/SM):
NS
Charging structure
Allocation rate in reduced allocation period: 50.0%
Allocation rate in subsequent periods:
101.5%
Reduced allocation period (in months):
12
Allocation price (BID/OFFER):
OFFER
Annual management charge
Lapse assumptions
First-year lapse rate:
15.0%
Second-year lapse rate:
10.0%
Subsequent years’ lapse rate:
5.0%
Mortality assumptions
Mortality table:
AM80(2)
Experience mortality (central rate):
90.0%
(deducted monthly):
0.75%
Non-smoker loading:
75.0%
Bid/offer spread:
5.0%
Smoker loading:
150.0%
Expense charge (p.m. inflating):
£2.00
Mortality charge (central rate):
100.0%
Nil surrender value period (in months):
12
Expense and commission assumptions
Initial commission (IC)
(% of first-year premium):
Solvency margin
Percentage of reserves:
1.0%
Percentage of sum at risk:
0.3%
Results (computed from monthly figures)
30.0%
Initial expense (IE) (% of IC):
50.0%
Risk discount rate:
11%
Initial expense (IE) (fixed amount):
£75
Break-even month:
59
Renewal commission (RC) (% of premium):
2.5%
Month in which renewal commission
PVFP (£):
£63.96
PVFP (% of PV premium):
1.18%
PVFP (% of new annual premium):
5.33%
13
PVFP (% of IC):
17.77%
Renewal expense (RE) (p.a. inflating):
£2.50
ROI (annualized):
19.86%
Renewal expense (RE) (% of premium):
1.0%
Spread (ROI – non-unit interest rate): 15.36%
commences:
PV of charges:
£1,225.41
PVFP (% of PV charges):
5.22%
23
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Pricing and profitability of unit-linked insurance
Munich Re Group
APPENDIX 2:
PROJECTION OF A POLICYHOLDER’S ACCOUNT
Month
1
Unit fund
at start
of month
0.00
Allocated
premium
Expense
charge
Mortality
charge
Management
charge
Unit fund at
end of month
(0.48)
Unit
investment
return
0.25
(0.03)
45.25
Proportion of
policies still
in force at end
0.987452
47.50
(2.00)
2
45.25
47.50
(2.00)
(0.48)
0.51
(0.06)
90.73
0.975061
3
4
90.73
136.43
47.50
47.50
(2.00)
(2.00)
(0.47)
(0.47)
0.77
1.03
(0.09)
(0.11)
136.43
182.37
0.962826
0.950744
5
182.37
47.50
(2.00)
(0.47)
1.29
(0.14)
228.55
0.938814
6
7
228.55
274.96
47.50
47.50
(2.00)
(2.00)
(0.47)
(0.46)
1.55
1.81
(0.17)
(0.20)
274.96
321.60
0.927034
0.915402
8
321.60
47.50
(2.00)
(0.46)
2.07
(0.23)
368.48
0.903915
9
368.48
47.50
(2.00)
(0.46)
2.34
(0.26)
415.60
0.892573
10
415.60
47.50
(2.00)
(0.46)
2.60
(0.29)
462.96
0.881373
11
12
462.96
510.56
47.50
47.50
(2.00)
(2.00)
(0.45)
(0.45)
2.87
3.14
(0.32)
(0.35)
510.56
558.40
0.870313
0.859392
1-12
0.00
570.00
(24.00)
(5.58)
20.23
(2.25)
558.40
0.859392
Year
Allocated
premium
Expense
charge
Mortality
charge
Unit fund at
end of year
1,157.10
(24.72)
(6.84)
Unit
investment
return
81.08
Management
charge
2
Unit fund
at start
of year
558.40
(9.01)
1,756.02
Proportion of
policies still
in force at end
0.776667
3
1,756.02
1,157.10
(25.46)
(7.13)
164.59
(18.30)
3,026.81
0.737987
4
3,026.81
1,157.10
(26.23)
(6.45)
253.23
(28.15)
4,376.32
0.701146
5
6
4,376.32
5,809.80
1,157.10
1,157.10
(27.01)
(27.82)
(5.37)
(3.76)
347.37
447.40
(38.62)
(49.73)
5,809.80
7,332.98
0.666048
0.632604
7
7,332.98
1,157.10
(28.66)
(1.48)
553.70
(61.55)
8,952.09
0.600729
8
8,952.09
1,157.10
(29.52)
0.00
666.68
(74.11)
10,672.25
0.570342
9
10,672.25
1,157.10
(30.40)
0.00
786.64
(87.45)
12,498.14
0.541366
10
12,498.14
1,157.10
(31.31)
0.00
913.98
(101.60)
14,436.31
0.513729
Munich Re Group
Pricing and profitability of unit-linked insurance
APPENDIX 3:
PROJECTED INSURANCE REVENUE ACCOUNT
Month
Premiums
Investment
income
Commission Management
expenses
Deaths
Surrenders
Change in
unit reserve
Net profit
(44.68)
Change in
solvency
margin
(27.32)
1
100.00
(1.71)
(360.00)
(255.00)
(0.43)
0.00
2
98.75
0.79
3
97.51
1.03
0.00
(3.46)
(0.43)
0.00
(3.41)
(0.42)
0.00
(43.78)
0.03
51.90
0.00
(42.90)
0.03
4
5
96.28
95.07
1.27
1.50
0.00
0.00
(3.37)
(3.33)
51.83
(0.42)
(0.41)
0.00
0.00
(42.03)
(41.17)
0.03
0.04
51.77
51.70
6
93.88
1.73
0.00
(3.29)
(0.41)
0.00
(40.33)
0.04
51.62
7
92.70
1.95
8
9
91.54
90.39
2.17
2.38
0.00
(3.24)
(0.40)
0.00
(39.50)
0.04
51.55
0.00
0.00
(3.20)
(3.16)
(0.40)
(0.39)
0.00
0.00
(38.68)
(37.88)
0.04
0.04
51.47
51.38
10
89.26
11
88.14
2.59
0.00
(3.12)
(0.39)
0.00
(37.09)
0.04
51.30
2.79
0.00
(3.08)
(0.38)
0.00
(36.31)
0.05
51.21
12
87.03
2.99
0.00
(3.05)
(0.38)
0.00
(35.54)
0.05
51.11
1-12
1,120.55
19.48
(360.00)
(290.72)
(4.85)
0.00
(479.89)
(26.88)
(22.31)
Year
Premiums
Investment
income
Deaths
Surrenders
Change in
unit reserve
Net profit
2
984.94
67.29
(24.62)
(35.21)
(5.82)
(97.51)
(883.95)
Change in
solvency
margin
(3.84)
3
910.53
126.30
(22.76)
(33.25)
(6.67)
(92.06)
(869.91)
(4.91)
7.27
4
865.13
184.27
(21.63)
(32.29)
(7.15)
(134.67)
(834.69)
(4.84)
14.15
5
821.89
239.94
(20.55)
(31.35)
(7.67)
(175.56)
(801.17)
(4.65)
20.89
6
780.69
293.43
(19.52)
(30.43)
(8.24)
(214.82)
(769.27)
(4.47)
27.38
7
8
741.43
704.01
344.85
394.39
(18.54)
(17.60)
(29.55)
(28.69)
(8.84)
(10.37)
(252.53)
(288.74)
(738.91)
(709.05)
(4.31)
(6.92)
33.62
37.03
9
10
668.32
634.30
442.05
487.78
(16.71)
(15.86)
(27.85)
(27.03)
(13.11)
(16.30)
(323.45)
(356.69)
(679.24)
(650.28)
(6.79)
(6.50)
43.23
49.42
Commission Management
expenses
(589.13)
1.26
25
26
Pricing and profitability of unit-linked insurance
Munich Re Group
APPENDIX 4:
SHAREHOLDER’S ACCOUNT
Month
Unallocated
premium
Non-unit
interest
IC
IE
RC
RE
1
2
3
4
5
1
52.50
(1.96)
(360.00)
(255.00)
0.00
0.00
2
51.84
0.29
0.00
0.00
0.00
(3.46)
3
51.19
0.29
0.00
0.00
0.00
(3.41)
4
50.55
0.29
0.00
0.00
0.00
(3.37)
5
49.91
0.28
0.00
0.00
0.00
(3.33)
6
49.29
0.28
0.00
0.00
0.00
(3.29)
7
48.67
0.28
0.00
0.00
0.00
(3.24)
8
48.06
0.28
0.00
0.00
0.00
(3.20)
6
9
47.46
0.28
0.00
0.00
0.00
(3.16)
10
46.86
0.28
0.00
0.00
0.00
(3.12)
11
46.27
0.28
0.00
0.00
0.00
(3.08)
12
45.69
0.28
0.00
0.00
0.00
(3.05)
1-12
588.29
1.15
(360.00)
(255.00)
0.00
(35.72)
Year
Unallocated
premium
Non-unit
interest
IC
IE
RC
RE
2
35.21
1.57
0.00
0.00
(24.62)
(35.21)
3
32.55
1.96
0.00
0.00
(22.76)
(33.25)
4
30.93
2.37
0.00
0.00
(21.63)
(32.29)
5
29.38
2.81
0.00
0.00
(20.55)
(31.35)
6
27.91
3.28
0.00
0.00
(19.52)
(30.43)
7
26.51
3.77
0.00
0.00
(18.54)
(29.55)
8
25.17
4.40
0.00
0.00
(17.60)
(28.69)
9
23.89
5.19
0.00
0.00
(16.71)
(27.85)
10
22.68
6.03
0.00
0.00
(15.86)
(27.03)
Munich Re Group
Pricing and profitability of unit-linked insurance
Expense
charge
Mortality
cost
Mortality
charge
Management
charge
Surrender
charge
Change in
solvency
margin
Net profit
7
8
9
10
11
16
17
2.00
(0.43)
0.48
0.03
0.56
(27.32)
(589.13)
1.97
(0.42)
0.47
0.06
1.12
0.03
51.90
1.95
(0.42)
0.46
0.08
1.66
0.03
51.83
1.93
(0.41)
0.45
0.11
2.19
0.03
51.77
1.90
(0.40)
0.45
0.14
2.71
0.04
51.70
1.88
(0.39)
0.44
0.16
3.22
0.04
51.62
1.85
(0.39)
0.43
0.19
3.72
0.04
51.55
1.83
(0.38)
0.42
0.21
4.21
0.04
51.47
1.81
(0.37)
0.41
0.23
4.68
0.04
51.38
1.79
(0.37)
0.41
0.26
5.15
0.04
51.30
1.76
(0.36)
0.40
0.28
5.61
0.05
51.21
1.74
(0.35)
0.39
0.30
6.06
0.05
51.11
22.41
(4.69)
5.21
2.04
40.89
(26.88)
(22.31)
Expense
charge
Mortality
cost
Mortality
charge
Management
charge
Surrender
charge
Net profit
20.29
(5.06)
5.62
7.31
0.00
Change in
solvency
margin
(3.84)
19.32
(4.87)
5.41
13.82
0.00
(4.91)
7.27
18.91
(4.18)
4.65
20.22
0.00
(4.84)
14.15
18.50
(3.30)
3.68
26.36
0.00
(4.65)
20.89
18.10
(2.19)
2.45
32.25
0.00
(4.47)
27.38
17.71
(0.81)
0.92
37.92
0.00
(4.31)
33.62
17.32
0.00
0.00
43.35
0.00
(6.92)
37.03
16.93
0.00
0.00
48.56
0.00
(6.79)
43.23
16.55
0.00
0.00
53.55
0.00
(6.50)
49.42
1.26
27
28
Pricing and profitability of unit-linked insurance
Munich Re Group
BIBLIOGRAPHY
1
2
3
4
5
6
7
Goford. “The control cycle: Financial control of a life assurance company”.
SS, 1984.
Laker and Squires. “Unit pricing and provision for tax on capital gains in
linked life assurance business”. JIA, 1985.
Lee. “A prophet of profits”. SS, 1984.
Mehta and Instance. “Taxation in the assessment of profitability of life
assurance products and of life office appraisal values”. SIAS, 1990.
Mehta and others. “The financial management of unit-trust and investment
companies”. BAJ, 1996.
Smart. “Pricing and profitability in a life office”. JIA, 1977.
The Society of Actuaries in Ireland – Unit pricing and equity in the
management of life assurance unit funds.
Abbreviations used:
JIA Journal of the Institute
of Actuaries
BAJ British Actuarial Journal
SS Institute of Actuaries
Students’ Society paper
SIAS Staple Inn Actuarial
Society paper
© 2000
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