Choosing Reinsurance Retention Limits is often more
art than science. A careful study of the risks can help us make better business
decisions.Such decisions make a
trade-off between

lower profits with greater certainty, and

higher
but more volatile profits.

In this discussion:

The term “Claims” means direct claims
ignoring reinsurance.

“Claim
Cost” means direct claims, minus reinsurance reimbursements, plus
reinsurance costs.

The methods discussed below work
well for all lines of insurance.However, Life Insurance claims are relatively large and rare.This can mean more severe fluctuations in
claims.So, consider a block of 10,000
newly-issued Life Insurance policies with a total Face Amount of about $5
billion, priced for a 10% pre-tax profit margin.

Table 1 — 10,000 newly-issued Life Insurance
policies

Breakdown

One year’s
Issues

10-year

Expected Claims

Policy Count

Face Amount

Average Size

Issue Age

0 – 30

1,661

$861 m

16.6%

$518 K

$3,301 K

31 – 40

3,472

$1,798 m

34.7%

$518 K

$10,436 K

41 – 50

3,376

$1,731 m

33.4%

$513 K

$23,841 K

51 – 60

1,287

$681 m

13.1%

$529 K

$20,762 K

61+

204

$115 m

2.2%

$561 K

$8,210 K

Total

10,000

$5,186 m

100.0%

$519 K

$66,551 K

Face Amount

0 – 100 K

491

$40 m

0.8%

$81 K

$461 K

100 – 200 K

1,259

$207 m

4.0%

$165 K

$2,542 K

200 – 500 K

4,092

$1,459 m

28.1%

$357 K

$18,019 K

500 – 750 K

2,152

$1,344 m

25.9%

$625 K

$16,977 K

750 – 1,000 K

1,094

$960 m

18.5%

$878 K

$12,689 K

1,000 K +

912

$1,176 m

22.7%

$1,289 K

$15,863 K

Total

10,000

$5,186 m

100.0%

$519 K

$66,551 K

Sex

F

4,447

$2,287 m

44.1%

$514 K

$23,757 K

M

5,553

$2,899 m

55.9%

$522 K

$42,793 K

Total

10,000

$5,186 m

100.0%

$519 K

$66,551 K

Because this is a small block, we
may expect a great deal of uncertainty.Even over 10 years, that implies significant deviations from our
expected $66.5 million of claims.

Reinsurance can reduce this
uncertainty.Imagine a reinsurance
treaty that imposes a 10% load on expected claims, covering the reinsurer’s
profit and expenses.That is, if we
reinsure the entire risk, the reinsurance cost is exactly 110% of expected
claims.Instead of $66.5 million of
expected claims (± a random deviation) we incur $73.2 million of
reinsurance cost (with no deviation).For
less than full reinsurance, the actual claim cost is some combination of actual
claims and fixed reinsurance cost.

The 10% load sounds modest[1].But if the expected loss ratio is 60%, then full
reinsurance increases total costs to 66%.Our expected 10% pre-tax profit margin drops to 4%.The trade-off is clear enough: do we prefer
an uncertain 10% profit margin or a guaranteed 4% margin?Or do we prefer something in between?

To see what really happens, I did
5,000 random trials, assuming a range of retention limits.The results appear in Table 2,
Figure 1,
and Table 3.

Table 2
and Figure 1
show the trials individually.Adding
reinsurance

decreases the standard deviation,

but increases
the expected cost.

In
the “full reinsurance” case, all 5,000 trials weigh in at a uniform $72.5
million.Because the entire risk is
transferred to the reinsurer, the claim cost is just the cost of
reinsurance.Figure 1 shows this case as a vertical yellow line.

Table 3
summarizes our findings.

Without
reinsurance,

There’s an 0.6% chance that claims exceed 130% of expected,
resulting in a pre-tax profit margin of -8.0% or worse.

There’s a 9.1% chance that claims will exceed 115% of expected.Here, the profit margin is 1.0% or
less.

And 54.0% (100.0% minus 46.0%) of the time, the
profit margin exceeds 10%.

Full Reinsurance costs 10% of expected claims.But without reinsurance, actual claims
exceed the reinsurance cost only 17.4% of the time.In other words, over a 10-year period,
there’s an 82.6% probability of a “loss” from reinsurance.

In
this example, we have analyzed a volatile block of Life Insurance.The 10-year study period is long enough to
mitigate this somewhat.Most companies
have a much larger policy count, further stabilizing the results.

Often, the
reinsurance decision is based on a reluctance to be caught in a “worst case”
situation (however improbable it may be), in which claims greatly exceed
expectations. But if we have a good
handle on the claim rates, we have shown that the risks can be quantified.

Most lines of insurance are much
less volatile and may not need much reinsurance.

Compared
to our Life insurance Example, Health Insurance claims are much more frequent
and generally much smaller.

Similar
considerations apply to Group LTD and Individual Disability Income, but
perhaps to a lesser extent.

Long
Term Care is a hybrid.In its
early policy years, it resembles Life Insurance.Claims are rare but large.Subsequently, claims become much more
frequent.

Some factors are not covered in
the above analysis.

When
the risk is not fully understood, we may well benefit from the reinsurer’s
underwriting expertise.

Epidemics
and major disasters are not included in the above analysis.But in extreme situations, a deluge of
claims may render the reinsurers unable to pay.