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Chapter 7 REINSURANCE GARY S. PATRIK
INTRODUCTION
What is Reinsurance?
Reinsurance is a form of insurance. A reinsurance contract is legally an insurance contract. The reinsurer agrees to indemnify the cedant insurer for a specified share of specified types of in- surance claims paid by the cedant for a single insurance policy or for a specified set of policies. The terminology used is that the reinsurer assumes the liability ceded on the subject policies. The cession , or share of claims to be paid by the reinsurer, may be defined on a proportional share basis (a specified percentage of each claim) or on an excess basis (the part of each claim, or aggregation of claims, above some specified dollar amount).
The nature and purpose of insurance is to reduce the finan- cial cost to individuals, corporations, and other entities arising from the potential occurrence of specified contingent events. An insurance company sells insurance policies guarantying that the insurer will indemnify the policyholders for part of the financial losses stemming from these contingent events. The pooling of liabilities by the insurer makes the total losses more predictable than is the case for each individual insured, thereby reducing the risk relative to the whole. Insurance enables individuals, cor- porations and other entities to perform riskier operations. This increases innovation, competition, and efficiency in a capitalistic marketplace.
The nature and purpose of reinsurance is to reduce the fi- nancial cost to insurance companies arising from the potential occurrence of specified insurance claims, thus further enhancing innovation, competition, and efficiency in the marketplace. The cession of shares of liability spreads risk further throughout the
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insurance system. Just as an individual or company purchases an insurance policy from an insurer, an insurance company may pur- chase fairly comprehensive reinsurance from one or more rein- surers. A reinsurer may also reduce its assumed reinsurance risk by purchasing reinsurance coverage from other reinsurers, both domestic and international; such a cession is called a retroces- sion.
Reinsurance companies are of two basic types: direct writers , which have their own employed account executives who produce business, and broker companies or brokers , which receive busi- ness through reinsurance intermediaries. Some direct writers do receive a part of their business through brokers, and likewise, some broker reinsurers assume some business directly from the ceding companies. It is estimated that more than half of U.S. reinsurance is placed via intermediaries.
The form and wording of reinsurance contracts are not as closely regulated as are insurance contracts, and there is no rate regulation of reinsurance between private companies. A rein- surance contract is often a manuscript contract setting forth the unique agreement between the two parties. Because of the many special cases and exceptions, it is difficult to make correct gen- eralizations about reinsurance. Consequently, as you read this chapter, you should often supply for yourself the phrases “It is generally true that:::” and “Usually:::” whenever they are not explicitly stated.
This heterogeneity of contract wordings also means that whenever you are accumulating, analyzing, and comparing var- ious reinsurance data, you must be careful that the reinsurance coverages producing the data are reasonably similar. We will be encountering this problem throughout this chapter.
The Functions of Reinsurance
Reinsurance does not change the basic nature of an insurance coverage. On a long-term basis, it cannot be expected to make
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reinsurer to the cedant until the cedant’s surplus is large enough to support the new business. We will see other ways that rein- surance can be used to alter a cedant’s financial numbers. As you might expect in a free market, this aspect of reinsurance has led to some abuses in its use. As we discuss the various forms of reinsurance coverage, we will note their financial ef- fects.
Management Advice Many professional reinsurers have the knowledge and ability to provide an informal consulting service for their cedants. This service can include advice and assistance on underwriting, mar- keting, pricing, loss prevention, claims handling, reserving, actu- arial, investment, and personnel issues. Enlightened self-interest induces the reinsurer to critically review the cedant’s operation, and thus be in a position to offer advice. The reinsurer typically has more experience in the pricing of high limits policies and in the handling of large and rare claims. Also, through contact with many similar cedant companies, the reinsurer may be able to provide an overview of general issues and trends. Reinsurance intermediaries may also provide some of these same services for their clients.
The Forms of Reinsurance
Facultative Certificates A facultative certificate reinsures just one primary policy. Its main function is to provide additional capacity. It is used to cover part of specified large, especially hazardous or unusual exposures to limit their potential impact upon the cedant’s net results or to protect the cedant’s ongoing ceded treaty results in order to keep treaty costs down. The reinsurer underwrites and accepts each certificate individually; the situation is very simi- lar to primary insurance individual risk underwriting. Because facultative reinsurance usually covers the more hazardous or un- usual exposures, the reinsurer must be aware of the potential for antiselection within and among classes of insureds.
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Property certificate coverage is sometimes written on a pro- portional basis; the reinsurer reimburses a fixed percentage of each claim on the subject policy. Most casualty certificate cover- age is written on an excess basis; the reinsurer reimburses a share (up to some specified dollar limit) of the part of each claim on the subject policy that lies above some fixed dollar attachment point (net retention).
Facultative Automatic Agreements or Programs
A facultative automatic agreement reinsures many primary policies of a specified type. These policies are usually very sim- ilar, so the exposure is very homogeneous. Its main function is to provide additional capacity, but since it covers many policies, it also provides some degree of stabilization. It may be thought of as a collection of facultative certificates underwritten simulta- neously. It may cover on either a proportional or excess basis. It is usually written to cover new or special programs marketed by the cedant, and the reinsurer may work closely with the cedant to design the primary underwriting and pricing guidelines. For example, a facultative automatic agreement may cover a 90% share of the cedant’s personal umbrella business, in which case the reinsurer will almost certainly provide expert advice and will monitor the cedant’s underwriting and pricing very closely.
Facultative automatic agreements are usually written on a fixed cost basis, without the retrospective premium adjustments or variable ceding commissions sometimes used for treaties (as we shall see below).
There are also non-obligatory agreements where either the cedant may not be required to cede or the reinsurer may not be required to assume every single policy of the specified type.
Treaties
A treaty reinsures a specified part of the loss exposure for a set of insurance policies for a specified coverage period. For ongoing treaty coverage, the claims covered may be either those
INTRODUCTION 349
A surplus-share treaty also reinsures a fixed percentage of each subject policy, but the percentage varies by policy accord- ing to the relationship between the policy limit and the treaty’s specified net line retention. Its main function is capacity, but it also provides some stabilization. A surplus-share treaty may also assume in-force exposure at inception, which together with a ceding commission provides some management of financial results. This is typically a property cover; it is rarely used for casualty business.
Treaty Excess Covers An excess treaty reinsures, up to a limit, a share of the part of each claim that is in excess of some specified attachment point (cedant’s retention ). Its main functions are capacity and stabiliza- tion. An excess treaty typically covers exposure earned during its term on either a losses-occurring or claims-made basis, but run-off exposure may be added in. The definition of “subject loss” is important.
For a per-risk excess treaty, a subject loss is defined to be the sum of all claims arising from one covered loss event or occur- rence for a single subject policy. Per-risk excess is mainly used for property exposures. It often provides protection net of facul- tative coverage, and sometimes also net of proportional treaties. It is used for casualty less often than per-occurrence coverage.
For a per-occurrence excess treaty, a subject loss is defined to be the sum of all claims arising from one covered loss event or occurrence for all subject policies. Per-occurrence excess is used for casualty exposures to provide protection all the way up from working cover layers through clash layers.
A working cover excess treaty reinsures an excess layer for which claims activity is expected each year. The significant ex- pected claims frequency creates some stability of the aggregate reinsured loss. So working covers are often retrospectively rated , with the final reinsurance premium partially determined by the treaty’s loss experience.
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A higher exposed layer excess treaty attaches above the work- ing cover(s), but within policy limits. Thus there is direct single- policy exposure to the treaty.
A clash treaty is a casualty treaty that attaches above all policy limits. Thus it may be only exposed by:
- extra-contractual-obligations (i.e., bad faith claims)
- excess-of-policy-limit damages (an obligation on the part of the insurer to cover losses above an insurance con- tract’s stated policy limit)
- catastrophic workers compensation accidents
- the “clash” of claims arising from one or more loss events involving multiple coverages or policies. Both higher exposed layers and clash are almost always priced on a fixed cost basis, with no variable commission or additional premium provision.
Catastrophe Covers A catastrophe cover is a per-occurrence treaty used for prop- erty exposure. It is used to protect the net position of the cedant against the accumulation of claims arising from one or more large events. It is usually stipulated that two or more insureds must be involved before coverage attaches. The coverage is typically of the form of a 90% or 95% share of one or more layers (separate treaties) in excess of the maximum retention within which the cedant can comfortably absorb a loss, or for which the cedant can afford the reinsurance prices.
Aggregate Excess, or Stop Loss Covers For an aggregate excess treaty, also sometimes called a stop loss cover, a loss is the accumulation of all subject losses during a specified time period, usually one year. It usually covers all or part of the net retention of the cedant and protects net results, providing very strong stabilization. Claims arising from natural
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discussion has sufficient risk transfer to pass FAS 113 require- ments.
The first typical form for finite reinsurance is a financial pro- portional cover. As noted above, proportional treaties quite often have a ceding commission that varies inversely with the losses; this limits the risk transfer. The degree of variation can be in- creased to further limit the risk transfer. Also, the loss share may be defined to decrease somewhat if the losses exceed some maximum. Quite often, these treaties may also have some kind of funding mechanism, wherein the aggregate limit of cover- age is based upon the fund (net cash position less the reinsurer’s margin) together with some remote risk layer. Whatever the risk- limiting structure, the contract must be checked with the cedant’s accountants to assure that they will approve the risk transfer for FAS 113 guidelines.
A loss portfolio transfer is also a very prevalent form for finite reinsurance. This is a retrospective cover, a cession of part of the cedant’s loss liabilities as of a specified accounting date. It may be a cession of the total liability or, more often, a cession of some aggregate excess layer of the liability. An aggregate excess cover attaching at the cedant’s carried loss reserve is often called an adverse development cover. It is clear that a loss portfolio transfer could be a pure risk non-finite cover. To make the risk transfer finite, it has an aggregate limit and may have sublimits for various types of claims, and it is priced to be essentially a present-value funding of liabilities with a substantial upfront provisional margin for the reinsurer. Part of this margin will be paid back to the cedant in the form of a profit commission if the loss experience is favorable.
A funded aggregate excess cover is, as you might expect, an aggregate excess treaty in which the premium is high enough to fund the loss payments except in extraordinary circumstances. It is analogous to a funded loss portfolio transfer except that it covers future occurring claims. In addition to financial results
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management, it may provide strong stabilization of the cedant’s net results.
A Typical Reinsurance Program
There is no such thing as a typical reinsurance program. Every insurance company is in a unique situation with regard to loss exposure, financial solidity, management culture, future plans, and marketing opportunities. Thus each company needs a unique reinsurance program, a combination of ceded reinsurance covers tailor-made for that company.
Nevertheless, Table 7.1 displays what we might regard as a “typical” reinsurance program for a medium-sized insurance company.
If the company writes surety, fidelity, marine, medical mal- practice, or other special business, other similar reinsurance cov- ers would be purchased. If the company were entering a new market (e.g., a new territory or a new type of business), it might purchase a quota-share treaty to lessen the risk of the new busi- ness and the financial impact of the new premium volume, and to obtain the reinsurer’s assistance. Or it might purchase a propor- tional facultative automatic agreement for an even closer work- ing relationship with a reinsurer. If the company were exiting a market, it might purchase a loss portfolio transfer, especially an adverse development cover, to cover part of the run-off claims payments.
The Cost of Reinsurance to the Cedant
The Reinsurer’s Margin
In pricing a reinsurance cover, the reinsurer charges a margin over and above the ceded loss expectation, commission, and bro- kerage fee (if any). The margin is usually stated as a percentage of the reinsurance premium. It is theoretically based upon the reinsurer’s expenses, the degree of risk transfer, and the magni-
INTRODUCTION 355
ance premium and is paid by the reinsurer. Offsetting this cost is the fact that broker reinsurers usually have lower internal ex- penses because they don’t maintain separate marketing staffs. The brokerage fee is usually a fixed percentage of the reinsur- ance premium, but on occasion may be defined as either a fixed dollar or as some other variable amount.
Lost Investment Income For most reinsurance contracts, the premium funds (net of ceding commission) are paid to the broker, if any, who then passes them on (also net of brokerage fee) to the reinsurer. The cedant thus loses the use of those funds, and the reinsurer gains the investment income earned on those funds until returned as loss payments, ceding commission adjustments or other premium adjustments. The price of the reinsurance cover accounts for this investment income.
Some contracts incorporate a funds withheld provision, where the cedant pays only a specified margin to the reinsurer, from which the broker, if any, deducts the brokerage fee. The remain- ing reinsurance premium is “withheld” by the cedant. The cedant then pays reinsurance losses out of the funds withheld until they are exhausted, at which time payments are made directly by the reinsurer. The reinsurance contract may define a mechanism for crediting investment income to the funds withheld. The reinsurer will want a higher profit margin for a funds withheld contract because of the added risk (the credit worthiness of the cedant) and the lost investment income.
Additional Cedant Expenses The cedant incurs various expenses for ceding reinsurance. These include the cost of negotiation, the cost of a financial analysis of the reinsurer, accounting, and reporting costs, etc. If a broker is involved, the brokerage fee covers some of these services to the cedant. In general, facultative coverage is more expensive than treaty because of individual policy negotiation, accounting, and loss cessions.
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Reciprocity In some cases, in order to cede reinsurance, the cedant may be required to assume some reinsurance from the reinsurer, in this case usually another primary company. If this reciprocal reinsur- ance assumption is unprofitable, the loss should be considered as part of the cost of reinsurance. Reciprocity is not prevalent in the United States.
Balancing Costs and Benefits
In balancing the costs and benefits of a reinsurance cover or of a whole reinsurance program, the cedant should consider more than just the direct costs versus the benefits of the loss cov- erage and reinsurance functions discussed previously. A major consideration should be the reinsurer’s financial solidity—Will the reinsurer be able to quickly pay claims arising from a natu- ral catastrophe? Will the reinsurer be around to pay late-settled claims many years from now? Also important is the reinsurer’s reputation: does the reinsurer pay reasonably presented claims in a reasonable time? Another consideration may be the reinsurer’s or broker’s services, including possibly underwriting, marketing, pricing, loss prevention, claims handling, reserving, actuarial, in- vestment, and personnel advice and assistance.
Reinsurance Introduction: Final Comments
This introduction is only a brief review of basic reinsurance concepts and terminology. The interested reader will find more extensive discussions in the general reinsurance texts listed in the references.
REINSURANCE PRICING
General Considerations
In general, reinsurance pricing is more uncertain than pri- mary pricing. Coverage terms can be highly individualized, es- pecially for treaties. These terms determine the coverage period,
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will discuss a few actuarially sound methods. In general, the exposition of pricing methods will begin simply and become more complex as the situation demands and as we ask more questions. In many real situations, you might want to get a quick first evaluation via the simplest methods. Indeed, if you judge the situation to be either fairly predictable by these methods, or if you judge the risk to be small, you may decide to stop there. If not, you may want to pursue your analysis and pricing along the lines presented here. As in most actuarial work, you should try as many reasonable methods as time permits (and also reconcile the answers, if possible).
In this spirit, please note that the simple flat rate pricing for- mula and the use of the Pareto and Gamma distributions in this chapter are for illustrative purposes. The pricing formula a rein- surance actuary would use depends upon the reinsurer’s pric- ing philosophy, information availability, and complexity of the coverage. The probability models should be selected to describe the actual situation as best as possible given all the real statisti- cal and analytical cost constraints preventing you from obtaining more information. Klugman, Panjer, and Willmot [12], Hogg and Klugman [11], and Patrik [18] all discuss model selection and parameter estimation.
A Flat Rate Reinsurance Pricing Formula
As we get into the formulas, there will be a lot of notation. For clarity, we will preface variables with PC for “primary company” and R for “reinsurer” or “reinsurance.” PV will be used in the traditional sense to mean “present value.”
A discussion of the pricing formula to be used in this chapter will illustrate certain differences from primary pricing. We will often use the word “technical” to distinguish the actuarially cal- culated premium, rate, etc. from the actual final premium, rate, etc., agreed to by the cedant and reinsurer. Formula 7.2 calculates the technical reinsurance premium in terms of reinsurance loss cost, external expenses, internal expenses, and target economic
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return in the simple case where there are no later commission or premium adjustments based upon the actual loss experience. You can see that 7.2 is an “actuarial” formula, based explicitly upon costs.^1
Formula 7.2: A Flat Rate Reinsurance Pricing Formula
RP =
PVRELC
(1! RCR! RBF ) " (1! RIXL ) " (1! RTER )
where
RP = reinsurance premium PVRELC = PV of RELC = RDF " RELC RELC = reinsurer’s estimate of the reinsurance expected loss cost, E [ RL ] RL = reinsurance loss E [ RL ] = reinsurance aggregate loss expectation RDF = reinsurance loss payment discount factor RCR = reinsurance ceding commission rate (as a percent of RP ) RBF = reinsurance brokerage fee (as a percent of RP ) RIXL = reinsurer’s internal expense loading (as a percent of RP net of RCR and RBF ) RTER = reinsurer’s target economic return (as a percent of reinsurance pure premium, RP net of RCR , RBF and RIXL )
(^1) Formulas traditionally used by reinsurance underwriters have more often been of the form: undiscounted loss estimate divided by a judgmental loading factor such as 0.85. Of course the problem with this type of formula is that all the information about the expenses, discounting and profit loading are buried in one impenetrable number.
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underwriting and claims handling effort, and thus inter- nal expenses, should be similar for each contract, varying only by claims and “risk” volume.
- Internal expenses by contract should be independent (or almost independent) of commissions or brokerage ex- penses. Thus the loading should be independent of these expenses.
Together, RTER and RIXL determine the reinsurer’s desired pricing margin for internal expenses and profit (economic re- turn).
Finally, the reinsurance ceding commission rate and broker- age fee are specified in each particular contract; they are almost always stated as percentages of the total reinsurance premium RP. There is often no ceding commission on excess coverage; this is very different from primary coverage where commissions almost always exist. Of course, the existence of a reinsurance brokerage fee also depends upon the existence of a reinsurance intermediary for the contract.
An example will help clarify this.
Example 7.4:
PVRELC = $100,000 (calculated by actuarial analysis and formulas)
RTER = 20% (The reinsurer believes this is appropriate to compensate for the uncertainty and risk level of the coverage.)
RIXL = 10% (The reinsurer’s allocation for this type of business.)
RCR = 25% (specified in the contract)
RBF = 5% (specified in the contract)
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Then
RPP =
RP =
Please note that the reinsurance premium less external ex- penses is
RPP 1! RIXL
= (1! RCR! RBF ) " RP
Also, the reinsurer’s desired margin for internal expenses and profit is
$138,889! $100,000 = $38,
= $13,889 + $25,000:
Very often the reinsurance premium is not a fixed dollar amount, but is calculated as a rate times a rating basis, quite often PCP, the primary company (subject) premium. In our ex- ample, if PCP was expected to be $5,000,000, the reinsurance rate would most likely be rounded to 0.04 or 4%. Then the expected reinsurance premium would be $200,000 and the ex- pected reinsurance premium less external expenses would be 0 : 7 " $200,000 = $140,000, and the expected reinsurance mar- gin would be $140,000! $100,000 = $40,000, greater than the desired margin. So, if the reinsurer’s internal expenses were still $13,889, then the reinsurer’s expected economic return (profit) would be $40,000! $13,889 = $26,111, greater than the target of $25,000.
