Chapter 6 Flashcards
Nature and Purpose of reserves
Nature: Insurance reserves are the means by which life insurance companies determine the liabilities that must be established to assure that future policy benefits such as death claims can be paid.
Purpose: These reserves are required both by law and by actuarial theory to ensure fulfillment of commitments guaranteed to policyholders and their beneficiaries, even though the obligations may not be due for many years.
Individual Life Insurance Reserves
These premiums or gross premiums, consist of several elements, e.g., interest, mortality, expenses, taxes, voluntary terminations, and contingency margins (if the insurer is a mutual company), and profit margins (if the insurer is a stock company).
- Net Premium: For purposes of reserving, only a portion of the gross premium is used involving interest and mortality.
Loading: The difference between the gross premium and the net premium
level premium method
This approach provides that the insured can continue insurance protection from year to year by the payment of a premium that does not change.
Under the level premium approach, the insured is paying excess premiums during the early years (compared to a one-year term policy) of the policy and inadequate premiums during the later years. The insurance company accumulates a reserve that is built up from these excess premiums in the early years and interest thereon to supplement the later premiums. It is from this concept that the reserve is developed.
Reserve Valuation
To assure this conservatism, insurance laws and regulations specify what assumptions will be acceptable in the valuation of a company’s minimum reserve liability.
- These assumptions concern interest and mortality only.
- Statutory reserve requirements do not allow discounting of benefits or premiums for voluntary terminations, such as surrenders or lapses.
- The NAIC model law also provides that the maximum interest rate for any year will not be changed from that of the prior year if the newly calculated rate varies less than one-half of one percent (or 0.50%) from the prior year’s rate.
Net Level Reserves
Reserves can be calculated by either a prospective method or an equivalent retrospective method.
- It is very important to note that the two methods produce exactly the same reserve for any duration of the policy.
Net Level Reserves
Prosprospective method or retrospective method
(that the two methods produce exactly the same reserve for any duration of the policy)
- Prosprospective method:
> Formula: PV of its Future Benefits minus PV of Its Future Net Premiums.
Retrospective method: reserve may be calculated by looking backwards at what has occurred in the past
> Formula: Accumulated Value of the Past Net Premiums minus Accumulated Value of Past Benefits
Net Level Reserves
David Parks Fackler (Successive reserves)
- Derived from the retrospective formula for calculating reserves.
- The Fackler formula is the basis of a convenient method for preparing reserve tables for a particular policy, at a given age at issue, for consecutive durations.
- The formula can be programmed for computers.
- It is also very efficient for calculating reserves for policies that have changing net premiums or changing benefits throughout their coverage periods.
* Formula: Reserve at End of Year (t+l) = [Reserve at End of Previous Year (t) + The Net Premium] x [Accumulation Factor for One Year Using Interest and Mortality] - [The Cost of That Year’s Benefits]
Mean Reserves
Valuations are commonly done using “mean reserves.” * A mean reserve is the reserve as of the middle of a policy year and is simply the average of the initial reserve and the terminal reserve. *The mean reserve is 50% of the initial reserve plus 50% of the terminal reserve.This assumes that a full annual net premium has been paid.
mean reserves are commonly used for individual life insurance reserves.
Minimum Level: common insurance department requirement and a common actuarial practice to set the mean reserve to be not less than 50% of the net cost of one year’s term insurance for the benefit that year.
This is the same as 50 percent of the net premium for a one-year term insurance policy at the insured’s attained age.
Modified Reserves
Full Preliminary Term Method.
- This method allows the entire first year gross premium, less the first year mortality cost, to be used for expenses.
Thus, the first year net premium is set equal to one year’s mortality cost.
Modification of Assumptions
Interest?
Mortality?
Timing of Premiums and Death Claims?
Interest:
an increase in the rate of interest produces a decrease in reserves, and a decrease in the rate of interest produces an increase in reserves, provided that the reserves increase with duration.
Mortality :
constant increase in the rate of mortality produces a decrease in reserves, and a constant decrease in the rate of mortality produces an increase in reserves, provided that the reserves increase with duration.
Timing of Premiums and Death Claims:
* > Curtate assumption: assumptions that the annual premium is paid at the beginning of a policy year, and that death claims are paid at the end of the policy year.
Adjustments:
Curtate assumption
+ Reserve for Immediate Payment of Claims (claims paid immediately)
+ Reserve for Nondeduction of Deferred Fractional Premiums on Death (for premiums not paid annually)
+ Reserve for Refund of Premium Paid Beyond the Date of Death (Return of unearned premium beyond death)
Premium Adjustments
These adjustments are primarily a function of the valuation method of using mean reserves.
The mean reserve was shown to be 50% of the initial reserve plus 50% of the terminal reserve. This assumes that a full annual net premium has been paid.
- However, that is not the case if a policy is on a mode of premium payment other than annual and the full annual premium for the policy year has not been paid.
• Since a liability has been set up for 50% of the net premium, an adjustment then has to be made to give credit back to the insurance company for any unpaid portion of the annual premium.
• This adjustment is accomplished by setting up an asset account for deferred and uncollected premiums
Methods of Calculating the Policy Reserve
Five methods by which reserves are commonly calculated?
1 namely 2 seriatim 3 group 4 attained age 5 retrospective 6 approximate
Methods of Calculating the Policy Reserve
Seriatim
• High-speed computers have generally allowed the seriatim method to be the method of choice
* • Applies the reserve factors on a policy-by-policy basis. The total reserve liability for the company then
becomes the summation of the individual calculations
Advantages:
- It is a simple method not requiring complicated records.
- Accuracy is easily checked by checking individual policies to see if the appropriate factor has been applied.
- It is easily adaptable to electronic equipment, specially where the in force business is recorded on a master file from which the valuation indicative data can be gathered.
- If the company is small and there are a number of different plans being issued, a grouping method may not save much time.
Disadvantages:
- The size of the in force file may make it prohibitive.
- It can cause a peak load on calculation equipment at the time valuation is done.
- The accuracy of the valuation depends upon the correctness of the reserve factors, which have been placed in some type of machine-readable form. Any errors in those reserve factors would be hard to detect on an individual basis.
- To obtain any type of grouping, various sorts and summations would have to be performed.
Methods of Calculating the Policy Reserve
Group.
- The group method utilizes a summarization of records within each valuation cell.Once the valuation cells have been summarized and grouped together, the method becomes exactly like the seriatim method, with individual factors being applied to each cell.
The advantages of the group method are similar to those for the seriatim method with the added advantage that the number of calculations is lessened by grouping of policies.
Methods of Calculating the Policy Reserve
Attained Age
It is a form of group method, which minimizes the number of valuation cells.
This method eliminates the use of durations as used in the seriatim and group methods, and utilizes reserve factors only varying by attained age.
Disadvantages:
- It is a complicated method that is not easily understood by those not technically trained in it, thereby increasing error potential.
- It is difficult to prepare reports with fine breakdowns, which might be needed, for management information.
- It is not suitable if the valuation bases involve dual interest rates or if the policies have varying amounts of insurance and varying premium levels.
Methods of Calculating the Policy Reserve
Retrospective.
reserves are calculated as the excess of the accumulation of the net premiums over the accumulated costs of insurance.
Advantage
• it reduces the number of valuation cells and the number of calculations.
Disadvantage (outweigh advantages)
• it has no breakdown by plan of insurance, which otherwise provides valuable management information;
- there are difficulties if there are modified premiums or changing levels of amount of insurance;
- it is difficult to use for paid-up policies.
Methods of Calculating the Policy Reserve
Approximate
is not a method unto itself but is a name applied to several methods that are not exact calculations.
Indeterminate Premium Plans
A plan of insurance that provides a maximum guaranteed premium but permits the insurance company to charge a premium less than or equal to that guaranteed premium.
Based on policy experience evaluated (expenses, mortality, interest, and lapses), a gross premium will be determined that does not exceed the maximum guarantee. This gross premium may be guaranteed for one or more policy years.
reserves under such plans must be
a. appropriate in relation to the benefits and the pattern of premiums for that plan, and
b. computed by a method, which is consistent with the principles of the Standard Valuation Law, as determined by regulations promulgated by the commissioner.
Deposit Term Plans
- a typical plan is where the 1 yr premium exceeds the renewal premiums for the 9 yrs.
At the end of the 10th yr the policy provides an endowment equal to a multiple (such as 250 percent) of the excess first year premium.
The actual reserve to be used is the greater of the regular CRVM reserve or the alternative reserve.
Multiple Life Policies
Joint life: policy that paid the death benefit when the first of two insured lives died was among the first of these types of policies.
Second to die or last to die policy: pays a death benefit when the last of two named insureds dies.
Valuation of Life Insurance Policies Model Regulation /
A.K.A. Regulation XXX
Select and ultimate adjustment factors for 20 years are applied to the valuation mortality table. These dramatically lower the valuation mortality rates in the early durations.
Furthermore, the company’s appointed actuary can determine “X” factors to apply to these select and ultimate factors based upon actual company experience. If X is less than 100 percent, the actuary must annually give a professional opinion on the appropriateness of X.
Variable Insurance Products
- These products are a hybrid of insurance and investments where the owner is taking most or all of the investment risk. The insurance company assumes the mortality and expense risk.
The reserves are based upon the values of the investments. The values fluctuate up or down based upon the performance of the assets.
