Question

Mr. Y said, “Everyone should buy medical insurance for the whole family. Especially for new born babies, you will only need to pay premium for the first 18 years, after that, you don’t have to pay anymore, and the protection will continue for the rest of your children’s lives. So, these plans provide good protection for your children. At the same time, these plans are cheap and they save you a lot of money.”

Comment on Mr. Y statement.                                                                                                                                         

Answer 1

Mr. Y statement covers several actuarial parameters listed below; The actuarial math of each is beyond the scope of the question and only the broad effect of protection and risk are discussed.

Parts of this answers are from public actuarial records and Assurance Institute.

Insurers parameters

1. Morbidity of the Population
2. Mortality rates based on GINI ratios
3. Inflation
4. Interest
5. Pooling of many exposures into a group,
6. Accumulating a fund through contributions (premiums) from the members of the group, i.e. life insurance involves the group sharing (pooling) of individual losses.
7. Paying from this fund for the losses of those who die each year.
8. Expenses of the Insurer/carrier (inflationary)
9. Protection and Risk

On Mortality/Morbidity rates

The major argument given by insurers for taking a life insurance policy at an early age (say 18) is that it charges a very low premium – in contrast if one had to insure oneself in latter years.

The mortality rate for youth are obviously lower than an older person. [This is fact and no empirical study is required]

Ergo, the mortality curve will always show that yearly renewable term life insurance, where premiums increase each year as mortality increases, becomes prohibitively expensive at advanced ages.

This is the economic tension between cost of providing Protection (risk) and Cash Value of the carrier.

Example: Assume the Insurer promises to pay $100,000 at the death of each insured who dies during the year, it must collect enough money to pay the claims.

If experience indicates that 0.1 percent of a 18year olds will die during the year, and we expect 0.1 death may be expected for every 1,000 persons in the group. If a group of 100,000 18 years olds are insured, 100 claims (100,000 × .001) are expected. Because each contract is for $100,000, the total expected amount of death claims is $10 million (100 claims × $100,000). To collect enough premiums to cover mortality costs (the cost of claims), the insurer must collect $100 per policyowner ($10 million in claims / 100,000.

If the morality rate was 2x, 3x, 10x of the 18 year olds, it erodes the cash value of the insurer or destroy it completely.

[A table of morality rates for a give population can be sourced from your location]

Source: AIA

However, the premium for Life Terms is normally charged Flat Rate or a Level Rate and does not increase with age

An 18-year-old will pay the same rate in year 60 as he had paid when he was 18.

Benefits of a Flat Premium

A flat premium or usually called a level premium remains constant throughout the premium-paying period, instead of rising from year to year.

This level premium is the amount of the constant periodic payment over a specified period (ending before the insured event , like death); it is equivalent to a single premium that will be paid at the beginning of the contract, discounting for interest and mortality.

Effects of Flat Premium

From an economic perspective, the level premium plan does two things.

1. the insurer offers an instalment payment plan with equal payments over time.
2. the level premium policies are made up of two elements: protection and investment.

Although the periodic premium payments exceed death/health crisis benefits and other expenses for an insured group during the early years of the policy, they fall short during later years consequently, the insurer accumulates a reserve to offset this deficiency.

Mathematically, the insurer’s reserve should be great than in amount, but not identical, to the sum of cash values for the insured group. If the reserves fall below the cash value, the insurers can raise the premiums to a subsequent new population to cover the shortfall in its reserve

This reserve is a liability on the insurer’s balance sheet, representing the insurer’s obligation and reflecting the extent to which future premiums and the insurer’s assumed investment income will not be enough to cover the present value of future claims on a policy. At any point, the present value of the reserve fund, future investment earnings, and future premiums are enough to pay the present value of all future death claims for a group of insureds.

The difference between the reserve at any point in time and the face amount of the policy is known as the net amount at risk for the insurer and as the protection element for the insured.

Source: AIA

As this graph illustrates, this element of risk declines each year because the reserve (investment or cash value) increases. The protection/net-amount-at-risk element is analogous to decreasing term insurance. All level premium life policies have a combination of cash value and protection.

The amount at risk for the insurer (that is, the protection element) decreases as the cash value element increases with age; thus, less true insurance (protection) is purchased each year.

This decreasing amount of insurance is one of the reasons why the annual cost of pure insurance (that is, the protection element) to the insurer is less than the sum of the level premium plus investment earnings, even at advanced ages when mortality rates significantly exceed the premium per $1,000 of death benefit.

Over time, the growing amount of investment earnings (due to increasing cash value) more than offsets the inadequacy of the level premium.

This accumulation of funds, combined with a decreasing amount of true insurance protection (which is the net amount at risk to the insurance mechanism), makes possible a premium that remains level even though the probability of death rises as the insured grows older.

In summary, the level premium is higher than necessary to pay claims and other expenses during the early years of the contract, but less than the cost of protection equal to the total death benefit during the later years.

If the policy includes disease and health events the total premium paid will be less than the pay-out of the medical benefits and can be inflationary defeating.

Hence Mr. Y statement is correct.

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