Reinsurance and the
Homeowners Indication
CAS Ratemaking Seminar
March 10-11, 2005
Agenda







Brief Review of the Basics
Catastrophe Excess Reinsurance
Justification for Including Cost in Rates
Components of the Reinsurance Premium
Two Methods to Include the Cost of
Reinsurance into the Rate
An Example of the “Net Cost of Reinsurance
Method”
Miscellaneous/Related Topics
The Basics of Reinsurance


Reinsurance is simply insurance for insurance
companies
In exchange for a premium, the reinsurer
agrees to assume all or part of some risk that
had previously been assumed by the primary
insurer.
The Basics of Reinsurance

Primary insurers purchase reinsurance
for a variety of reasons, including:




To
To
To
To
increase capacity
stabilize underwriting results
provide catastrophe protection
obtain surplus relief
Catastrophe Excess
Reinsurance



Under a catastrophe excess agreement, the
reinsurer indemnifies the primary insurer for
aggregate losses in excess of a given
amount, called the retention, arising from a
catastrophic event
The reinsurer’s risk is generally limited to
some amount
A reinsurer may only indemnity the primary
company for a percentage of loss in excess of
the retention
Catastrophe Excess
Reinsurance - Example


Assume a reinsurance contract provides
coverage for 50% of $600MM of loss in
excess of $400MM per catastrophic event
If no event causes loss in excess of $400MM,
the reinsurer pays nothing
Catastrophe Excess
Reinsurance - Example


Assume a reinsurance contract provides
coverage for 50% of $600MM of loss in
excess of $400MM per catastrophic event
If an event causes loss in excess of $1 billion,
the reinsurer pays $300MM (= $600MM limit
x 50%)
Catastrophe Excess
Reinsurance - Example


Assume a reinsurance contract provides
coverage for 50% of $600MM of loss in
excess of $400MM per catastrophic event
If an event causes loss between $400MM and
$1 billion, the reinsurer pays 50% of the
amount in excess of $400MM.
Catastrophe Excess
Reinsurance - Example
Amount of Loss
Primary Insurer
$1 Billion
Retention + Limit
Primary Insurer
Reinsurer
$400 Million
Retention
Primary Insurer
Catastrophe Excess
Reinsurance

Reasons to purchase catastrophe excess
reinsurance


Catastrophic events may cause an
unacceptable drain on company surplus
Company is unable to achieve the required
return on the capital it must hold because
of the risk of catastrophic events
Alternatives to Catastrophe
Excess Reinsurance

Possible Alternatives to Catastrophe
Excess Reinsurance


Non-renewal of existing policies
Restrictions on new business
Justifying Including
Reinsurance in the Rate

Catastrophe Excess Reinsurance


contributes to the availability of insurance
is a legitimate business expense that
benefits both the insurer, and the market
as a whole
Catastrophe Excess
Reinsurance


A rate should provide for “all costs associated
with the transfer of risk”
“Consideration should be given to the effect
of reinsurance agreements in the
development of the rate”
- Statement of Principles Regarding Property
and Casualty Ratemaking
Components of the
Reinsurance Premium



Expected Loss and Loss Adjustment
Expenses
Reinsurer Expenses
Reinsurer Profit
Components of the
Reinsurance Premium



Expected Loss and Loss Adjustment
Expenses – “Reinsurance Benefit”
Reinsurer Expenses
“Transaction Costs”
Reinsurer Profit

Terminology from Reflecting Reinsurance Costs in Rate
Indications for Homeowners by Mark J. Homan
Components of the
Reinsurance Premium

Only the transaction costs represent
incremental, or “net,” costs to the
primary insurer

This is because the premium for the
reinsurance benefit is offset by a
corresponding reduction in the primary
company’s losses
Including the Cost of
Reinsurance in the Indication

Two possible methods


Distinct, but theoretically equivalent
Arise from the separation of the
reinsurance premium into its transaction
cost on reinsurance benefit components
Including the Cost of
Reinsurance in the Indication

First Possible Method

“Net Cost of Reinsurance” method


Include only the transaction costs, or net cost,
of the contract as an expense
Leave expected losses unadjusted
Including the Cost of
Reinsurance in the Indication

Second Possible Method

“Net Loss Plus Reinsurance” method


Include the entire reinsurance premium as an
expense
Reduce expected losses by the amount of the
expected reinsurance benefit
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance

Which is preferable?

Theoretically, they are identical


Reduction in losses under the Net Loss Plus
Reinsurance method is offset exactly by the
inclusion of the additional portion of the
reinsurance premium as an expense
No preference on theoretical grounds
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance

Which is preferable?


Preference given to the method that best
conveys the pertinent information within.
If the total effect of the reinsurance
agreement on the indication is of interest,
the Net Cost of Reinsurance method is
preferred.
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance

An example….

Reference Exhibit 1
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance
A. Indicated Rate - Pre-Reinsurance
(1) Expected Losses:
$100
(2) Variable Expense and Profit:
20%
(3) Indicated Premium (1) / [1 - (2)]:
$125
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance
B. Reinsurance Contract Information
(1) Reinsurance Premium:
$30
(2) Expected Losses covered by contract (Reinsurance Benefit):
$10
(3) Net cost of reinsurance (Transaction Costs): (1) - (2)
$20
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance
C. Indicated Rate Including the Cost of Reinsurance
Net Loss Plus Reinsurance Method
(1) Net Expected Losses:
$90
(2) Reinsurance Expense:
$30
(3) Variable Expense and Profit:
20%
(4) Indicated Premium: [(1) + (2)] / [1 - (3)]
$150
Net Cost of Reinsurance vs.
Net Loss Plus Reinsurance
D. Indicated Rate Including the Cost of Reinsurance
Net Cost of Reinsurance Method
(1) Expected Losses:
$100
(2) Net Reinsurance Expense:
$20
(3) Variable Expense and Profit:
20%
(4) Indicated Premium: [(1) + (2)] / [1 - (3)]
$150
A Complete Example



Flannel Insurance Company (FIC)
State of Armstrongland
Current rates appear to be perfectly
adequate

Reference Exhibit 2
A Complete Example
Armstrongland
Development of Indicated Rate Level Change
(1)
Projected Average Earned Premium at Current Rate Level:
$500.00
(2)
Indicated Provision for Non-Catastrophe Losses and LAE:
$150.00
(3)
Indicated Provision for Catastrophe Losses and LAE:
$200.00
(4)
Indicated Provision for General and Other Acquisition Expense:
$50.00
(5)
Commissions, Taxes, Profit, and Contingency Provision:
20%
(6)
Indicated Average Premium: [(2) + (3) + (4)] / [1.00 - (5)]
$500.00
(7)
Indicated Rate Level Change: [(6) / (1)] - 1.00
0.0%
A Complete Example

Subsequently, FIC enters into the
following reinsurance agreement

Reference Exhibit 3
A Complete Example
Exhibit 3
Reinsurance Contract Terms for FIC
Type of Contract:
States Covered:
Lines Covered:
Perils Covered:
Time Period:
Placement, Retention, and Limit:
Reinstatement Terms:
Reinsurance Premium:
1. Including all loss adjustment expenses.
Excess Catastrophe
Armstrongland
Homeowners
All, although only hurricane events are expected to
exceed retention
January 1, 2006 to December 31, 2008, with terms
renegotiable at the end of each calendar year
50% of the first $400 million in loss 1, excess of $100
million, per catastrophic event
Reinstatement is automatic, and without additional
premium
$11 million for the first year
A Complete Example

A few assumptions:



The exposure base for the development of the
hurricane catastrophe provision is the AIY, where
1 AIY = $1000 of Dwelling Coverage insured for 1
year
A model is used to simulate a sufficient number of
years of experience from which to develop an
expected hurricane loss per AIY
Only hurricane events will trigger a reinsurance
recovery
Quantifying the Reinsurance
Benefit

Quantifying the Reinsurance Benefit


Reinsurer’s Estimate
Internal Estimate
Quantifying the Reinsurance
Benefit

The Reinsurer’s Estimate

Advantages


Saves the primary company the work of
developing its own estimate
Disadvantages


May be difficult to obtain
May not be compatible with the primary
company’s estimate of expected hurricane
losses
Quantifying the Reinsurance
Benefit

Problems with using the Reinsurer’s
Estimate:




Insurer expects $10 million in hurricane
loss/year
Cedes all hurricane risk to reinsurer
Reinsurer estimates loss at $12 million/year
This implies negative net losses!
Quantifying the Reinsurance
Benefit

Problems with using the Reinsurer’s
Estimate:


Same may arise within any individual layer
or portion of loss that might be reinsured
When possible, internally generated
estimate should be used
Quantifying the Reinsurance
Benefit

Developing an Internal Estimate






Obtain modeled loss for each simulated event, and
the AIYs underlying those losses
Determine AIYs to be insured during the
reinsurance contract period
Adjusted modeled losses to future exposure level
Apply contract terms to each adjusted modeled
loss
Determine average annual reinsurance benefit as
average annual simulated reinsured loss
Reference Exhibits 4 and 5
Quantifying the Reinsurance
Benefit

Consider Event 4 from Year 5



Model simulates $97,275,005 in loss
Model assumes 13,248,231 AIYs
We expect 15,891,785 AIYs will actually be
insured over the reinsurance contract
period.
Quantifying the Reinsurance
Benefit

Consider Event 4 from Year 5 cont.


Adjust the expected loss by multiplying it
by the ratio of expected AIYs to modeled
AIYs
$97,275,005 x (15,891,785 / 13,248,231)
= $116,685,274
Quantifying the Reinsurance
Benefit

Consider Event 4 from Year 5 cont..


We then apply the contract terms to the
$116,685,274 loss
8,342,637 of the loss is reinsured
Quantifying the Reinsurance
Benefit

We follow this process for each
modeled loss



Losses under $100 million do not trigger
coverage
Losses over $500 million trigger maximum
coverage of $200 million
Losses between $100 million and $500
million trigger coverage of 50% of the loss
excess of $100 million
Quantifying the Reinsurance
Benefit

Then sum up the reinsured losses and
divide by 100,000 years (or however
many have been modeled) to determine
an expected annual reinsurance benefit
of $4,767,536
Determining the Net Cost of
Reinsurance

The net cost of reinsurance equals:
$11,000,000 reinsurance premium
- $ 4,767,536 reinsurance benefit
$ 6,232,464 net cost of reinsurance
Incorporating the Net Cost of
Reinsurance into the Indication

Now must adjust for difference in reinsurance
period and ratemaking period
Incorporating the Net Cost of
Reinsurance into the Indication

If the company believes the terms of the
contract will be similar in the remaining years,
it may be easiest to relate the net cost to
some base, and assume a constant net cost
relative to that base over time
Incorporating the Net Cost of
Reinsurance into the Indication

In this instance we’ll assume the net
cost of reinsurance is proportional to
AIYs.


This assumption is not quite true, since
expected losses within a layer are not
exactly proportional to exposure, even if
total losses are
However, it is a reasonable, and easy to
calculate, approximation
Incorporating the Net Cost of
Reinsurance into the Indication


Net cost of reinsurance per AIY =
$6,232,464 / 15,891,785 = $.39/AIY
Reference Exhibit 6
Incorporating the Net Cost of
Reinsurance into the Indication


Once net cost per AIY is determined,
incorporate it as an expense into the
indication
(Reference Exhibit 7)
Incorporating the Net Cost of
Reinsurance into the Indication
Armstrongland
Development of Indicated Provision for Net Cost of Reinsurance 1
(1)
Projected Average AIYs Per Policy:
(2)
Net Cost of Reinsurance Per AIY:
(3)
Indicated Provision for Net Cost of Reinsurance: (1) x (2)
1. All figures are for the policy year January 1, 2006 to December 31, 2006
125.00
$0.39
$48.75
Incorporating the Net Cost of
Reinsurance into the Indication
Armstrongland
Development of Indicated Rate Level Change
(1)
Projected Average Earned Premium at Current Rate Level:
$500.00
(2)
Indicated Provision for Non-Catastrophe Losses and LAE:
$150.00
(3)
Indicated Provision for Catastrophe Losses and LAE:
$200.00
(4)
Indicated Provision for Net Cost of Reinsurance:
$48.75
(5)
Indicated Provision for General and Other Acquisition Expense:
$50.00
(6)
Commissions, Taxes, Profit, and Contingency Provision:
(7)
Indicated Average Premium: [(2) + (3) + (4) = (5)] / [1.00 - (6)]
(8)
Indicated Rate Level Change: [(6) / (1)] - 1.00
20%
$560.94
12.2%
Incorporating the Net Cost of
Reinsurance into the Indication



Indication increased 12.2%
Indicated premium increased $60.94
In return for the additional premium,
policyholders are more assured that coverage
will remain available, both before and after a
catastrophic event, and, in the case of such
an event, that their own losses will be paid.
Recapping the process




Determine the expected reinsurance benefit
Determine the net cost of reinsurance
If reinsurance and ratemaking periods do not
correspond, relate net cost to some base
Incorporate the net cost of reinsurance into
the indication using the selected base
Multi-State/Company/Line
Reinsurance Contracts





Adjust losses for each state/company/line to the
expected level of exposure during the reinsurance
period
Apply contract terms to the total expected loss from
each event
Allocate reinsured losses back to each
state/company/line in proportion to total loss for the
particular event
Allocate reinsurance premium in proportion to total
expected reinsured loss
Continue process as before
Territorial Ratemaking


Theoretically, territories can be treated just as
states/companies/lines are
However, this can get messy, particularly if
losses aren’t modeled by territory, but instead
by zip code

This is because zip code data must be combined
into territorial data, but there may be 500 zip
codes in a state x 100,000 years of modeled
events
Territorial Ratemaking

While theoretically less ideal, it may be
necessary to simply allocate the net cost of
reinsurance to territories in proportion to
expected annual loss, or some other base