Chapter 2 The risk and its contractual coverage
2.1 Risk
2.1.1 Did you say risk?
The vast majority of human activities involve risk, which is what makes life so exciting. If you’re planning a family barbecue on a summer’s Sunday, you’re in for a rainstorm. If you’ve booked a plane ticket to an island paradise, your flight may be cancelled. If you invite a beautiful woman (or a handsome man, as the case may be) to dinner, your invitation may be politely declined. While the three examples above will at most only result in a wasted Sunday, an extra wait before hitting the white sandy beaches or a (big?) disappointment, many of the risks we face on a daily basis can have dramatic consequences (the death of a loved one, a traffic accident, a fire, …).
In addition to the grief and suffering caused to the victim and his or her family, these adverse events, which we will henceforth refer to as risks, often have economic consequences that can be objectively assessed (using the services of a specialist, for example). For example, if your house were to go up in smoke, an expert could determine how much it would cost to rebuild it, and hence how much you would lose.
Risk is therefore born of uncertainty: risk exists when the individual is unable to predict with certainty the future state of his or her assets. In practice, the term “risk” is often used to designate the cause of the risk, the object of the risk or the consequences of the loss. For example, the risk of fire is the reason for insurance, and a fire risk represents both the building that could fall prey to the flames, and the expense to which the company would be exposed if it granted cover to the owner. Sometimes, the term peril is used to designate the cause of the risk, as in the case of fire peril. Technically, therefore, risk is often confused with the insurer’s benefit.
In the case of economic consequences that can be expressed in monetary terms, these may be covered by a third-party organization, such as a mutual or commercial company. Over the centuries, mechanisms have been developed to transfer the economic consequences of risks to individuals. A new sector of activity has emerged: insurance.
2.1.2 The reason for insurance: risquophobia
All economic agents (individuals and companies alike) are subject to hazards (fire, accident, death, illness, bankruptcy, unemployment, etc.), the financial consequences of which could threaten their assets. In some cases, their personal fortunes (or equity) may not even be sufficient to cope. Some economic agents are aware of these risks, and seek to protect themselves by transferring some or all of them to other agents. This spontaneous fear of risk is known as risk aversion, or risquophobia. It is the very reason for insurance.
Roughly speaking, any decision by a risquophobic agent will involve two considerations: return and risk. For a comparable return, he will always prefer the least risky solution. He will only accept to run a high risk if, in compensation, this choice provides him with sufficient profit. Of course, risk-averse behavior depends on many criteria: a risk-averse agent may well buy a lottery ticket if the financial loss (the price of the ticket) is insignificant, and the pleasure derived from taking part in the draw more than compensates.
It is interesting to distinguish between the insured’s view of risk, which is often subjective and polluted by their degree of aversion to danger, and the insurer’s more objective view of risk. We will not make this distinction in the remainder of this book, and will assume that both parties have accurate knowledge of the transferred risk}) that there is no need to protect themselves against it. Third parties concerned by their financial situation, such as a lender for example, may nevertheless require them to provide guarantees of solvency, obliging them to transfer all or part of the risks to which they are subject. The State may also consider that social unrest resulting from the insolvency of certain citizens would be so damaging to the community that a guarantee obligation should be introduced. The best-known example is the requirement for motorists to have third-party liability insurance. In this way, any damage they may cause to other road users is covered by a solvent organization.
2.2 Risk management methods
Risquophobia, which combines a desire for safety with a fear of hazards, seems to be a characteristic widely shared by human beings. As a result, there are numerous risk management systems, which have varied according to time and region. The main risk management mechanisms are as follows:
2.2.1 Caution and self-insurance
This is, of course, the most obvious way of reducing risk: it’s “enough” to be cautious. In a nutshell, agents will adopt attitudes aimed at reducing the risks they run. This explains, for example, the decline in household consumption and the consequent increase in the volume of savings in times of economic recession.
Among the techniques applicable to individual management, there is one that is characteristic of risquophobia: diversification. A risquophobic agent will always prefer to carry several small independent risks rather than a single very large one. This is the technical transcription of the popular saying that “you shouldn’t put all your eggs in one basket”.
2.2.1.1 Risk mutualization
Many perils (accidents, theft, illness, etc.) threaten a large number of people, but ultimately affect only a small number. In this case, the risks are said to be sufficiently dispersed. What’s more, there is often a degree of independence between these risks: the fact that my neighbor causes a road accident generally doesn’t affect the risk of me causing one myself. This distinguishes the risks in question from natural disasters, which affect a large number of people at the same time.
These two properties (dispersion and independence) form the basis of a fundamental risk management technique: mutualization. This consists in grouping a large number of independent risks within a common structure. We’ll see in detail in the following chapters that, in the words of Maurice Allais, winner of the Nobel Prize in Economics, risk is “globally eliminable” under these conditions: it is significant at the individual level, but dissolves at the collective level.
Mutualization often acts as a substitute for self-insurance: the more an individual is covered externally, the less he or she will need to err on the side of caution when making choices. Collective risk management therefore reduces constraints at the individual level, enabling agents to take advantage of interesting opportunities without being paralyzed by minimum risk imperatives. The absence of coverage for certain risks would slow down innovation.
The danger of over-coverage is that external coverage no longer encourages prudence, discouraging prevention and ultimately increasing overall risk. This is the phenomenon of moral hazard, which we’ll discuss below.
2.2.1.2 Risk sharing
Pooling considerably reduces individual risks, provided they are small, numerous and sufficiently independent. However, not all hazards meet these conditions - far from it. Some risks are, by their very nature, of major importance (think of industrial risk coverage). Others, even if they result in moderate individual damage, affect a large number of individuals, rendering illusory any idea of compensating for individual hazards through collective management (think of natural disasters, such as floods, earthquakes, tornadoes, etc.).
Faced with such risks, the solution lies in division (rather than aggregation). The idea is to spread the burden of claims over a large number of agents, so that each bears only a small share of the initial risk. Large risks (catastrophes of all kinds, satellite launches, industrial complexes, etc.) are covered by pools of insurers, themselves covered by reinsurers.
An extreme form of risk distribution involves spreading risk over a few tens of millions of agents, the taxpayers. In this way, governments can cover major risks.
Another recent form of risk sharing involves securitizing risks and selling them on the financial markets. Catastrophe insurance, for example, can borrow from this type of vehicle (cat-bonds).
2.2.1.3 Transfer of risk between agents
It is often possible to transfer risk between agents, in a mutually beneficial way. In addition to the transfer organized in the insurance contract between an individual and a company, many other contracts also include a risk transfer dimension. An employment contract, for example, specifies the conditions under which a hazard suffered by the employer (a drop in orders, for example) can be passed on to employees (lower wages, economic unemployment, etc.). Financial instruments also provide excellent examples of such transfers, as we shall see later.
Remark. Before going any further, it’s worth noting that the principles detailed above are by no means exclusive, but rather complementary. For example, an insurance company may use both
- self-insurance by diversifying its portfolio and building up substantial technical reserves
- mutualization, by covering a large number of individual risks
- sharing by transferring part of its risks to reinsurers.
This enables it to have a low level of risk-phobia, and therefore to accept the risks that individuals wish to transfer to it.
2.2.2 Risk management vehicles
The various risk management principles outlined above have been implemented by a wide range of more or less specific institutions, including
2.2.2.1 The family
The oldest forms of risk-sharing have taken place within the family, whether nuclear or extended. Today, in many cases, the family is still the key to effective risk management.
It is only recently that certain risks (unemployment, illness, old age, etc.) have been covered by the governments of industrialized countries. Today, these risks are still almost exclusively the responsibility of the family unit in most developing countries.
2.2.2.2 Financial markets
Financial markets are a simple, yet robust and often highly effective risk-sharing mechanism. They are first and foremost a meeting place for agents who are exposed to different risks, and have different aversions to these risks. Their purpose is to enable the transfer of mutually beneficial risks. To illustrate this point, let’s take a simple example: a European contractor concludes a major contract with an American counterpart. Payment will be made on delivery, say in 6 months’ time, for an amount specified at the time of the order, in US dollars. If the US currency devalues in the meantime, the European contractor will have lost a good part of his profit. To cover this risk, he can enter into a sales contract on the dollar futures market, under which he undertakes to exchange his dollars for a fixed sum in euros on that date. In this way, he eliminates all risk, since he already knows the profit he will make. Of course, the feasibility of the operation is questionable: the counterparty could simply be an American exporter who needs to be paid in euros, or any other economic agent who assumes the risk of a rising dollar.
2.2.2.3 Insurance companies
Traditionally, risk for the general public is handled by insurance companies. These companies can be either commercial or mutual. These two forms share many characteristics, but are distinguished by the following basic features:
- contributions (called premiums for mutual companies) are variable for mutuals, which may issue a reminder in the event of a particularly unfavorable claims experience or, on the contrary, pay back part of the sums collected in the event of an advantageous claims experience. Commercial companies, on the other hand, work with fixed premiums.
- The mutual is jointly owned by its policyholders, called mutualists, and therefore has no shareholders to remunerate (unlike a commercial company). This may explain why mutuals are often driven by more social considerations.
The mechanisms used by insurance companies to manage risk are described in detail later in this book.
2.2.2.4 The Government
Within the European Union, the most important insurer remains the State, either directly or via specialized bodies (e.g. social security). It is the State that covers the most basic risks, such as sickness, old age and unemployment, with the private sector playing only a complementary role. To a large extent, the rationale behind the management of these public schemes is solidarity and income redistribution.
The remainder of this book is devoted to the mechanisms of risk management through mutualization by insurance companies.
2.2.3 Risks assumed by insurers
2.2.3.1 Responsibility
Over much of the world, the liability system prevails. Very briefly, if an individual commits a fault and a third party suffers damage as a result, he or she is held liable and must compensate the injured third party for the damage incurred. The liability system therefore requires three conditions to be met simultaneously: a fault, a prejudice and a causal link between the fault and the prejudice. This system seems socially desirable: it is designed to ensure that everyone behaves prudently, avoiding causing harm to others for fear of incurring liability.
In liability insurance, the insurer undertakes to compensate the third party injured by the insured’s fault. In this way, the insurer protects the insured’s assets against liability claims brought against him by the third party. In addition to the actual indemnification, the insurer assists the insured, for example, by organizing the insured’s defense before the courts.
In a society where liability prevails, insurance has become a discreet but omnipresent daily companion. The plane takes off, so it’s insured. The patient undergoes surgery, so the surgeon and hospital are insured. The motorist takes to the road, so he and the other drivers are insured.
2.2.3.2 Property
In addition to his liability, the insured can also cover his property against perils that threaten it. You can insure your vehicle against theft, your home against fire, your luggage against loss, and so on. This is often referred to as property and casualty insurance, as it is used to compensate for the loss resulting from damage to the insured’s property.
Property and casualty insurance has profoundly transformed our relationship with misfortune and adversity. In the past, the destruction of the family home by fire was synonymous with disaster for the farmer and his family. Today, the pater familias is certainly annoyed, even saddened, to see the destruction of the building that has sheltered his family for so many years, but he is freed from all economic fear, knowing that the insurer will take care of the material consequences of the tragedy. Insurance thus enables modern man to concentrate on the human aspects of the risks he runs, by transferring to insurers the task of repairing the economic consequences.
2.2.3.3 Persons
Finally, the insured can cover human capital: his or her health and that of his or her loved ones. In this case, the insurer undertakes to contribute financially to the cost of hospitalization, doctors’ fees, medication, etc. The insurer may also undertake to guarantee a replacement income for the insured. The insurer may also undertake to guarantee a replacement income in the event of the insured being unable to work. It can also cover the cost of assistance from a third party if the insured is no longer able to carry out daily activities himself/herself (long-term care insurance). This is personal insurance, which we won’t cover in this book, any more than we will life insurance.
To give an idea of the relative importance of the various lines, the table @ref{tab:AssFrance2002} shows the benefits paid out and allocations to claims reserves for property and liability insurance, in France (in 2021).
| Line of Business | Billions of Euros |
|---|---|
| Automobile | 24.1 |
| Private property | 12.1 |
| Professional and agricultural property | 8.7 |
| General liability | 4.3 |
| Construction | 2.6 |
| Transport | 1.3 |
| Natural disasters | 1.8 |
| Personal legal protection | 1.7 |
| Credit guarantee | 1.6 |
| Assistance | 2.6 |
| Financial loss | 2.5 |
2.2.3.4 Uninsurable risks
Certain risks are excluded from coverage. For example, the risk of receiving a financial penalty cannot be covered by insurance, otherwise the penalty would lack the deterrent effect expected of it. The same applies to insurance on the life of young children, as a benefit in the event of death could give rise to speculation on the part of unworthy parents or unscrupulous persons who, through lack of care, would cause the death of the child in order to collect the insured capital.
2.2.5 Transfer of risks
The effect of an insurance transaction is to transfer all or part of the financial consequences of the risk borne by the insured to an insurance company, under the conditions and circumstances specified in a contract. The expenses borne by the company may correspond either to indemnities to be paid to third parties in respect of the insured’s liability (civil, professional or other), or to compensation for damage suffered by the insured.
Insurance is often presented as a means of substituting a deterministic amount (the insurance premium) for a random financial loss (the damage suffered by the insured, or a third party injured by the insured). In reality, the situation is far more complex. For reasons we’ll explain later, the insurer usually provides only partial cover, limiting its intervention through clauses such as deductibles, indemnity ceilings, compulsory overdrafts and so on. Insurance therefore enables the insured to significantly reduce the impact of risk on his assets, but not to eliminate it completely. In practice, the insurance operation consists of substituting an initial risk with another, more advantageous for the insured, in return for the payment of a premium.
The insured also bears the risk of the insurer’s default: if the company that has guaranteed the insured goes bankrupt, it will no longer be in a position to compensate for the damage suffered. To limit the risk of default as much as possible, governments have instituted supervision of insurance companies. You can’t just become an insurer! Only specialized companies offering sufficient guarantees and approved by the authorities may engage in this activity. This clearly distinguishes insurance operations from bets between two individuals or occasional financial speculation.
2.2.5.1 Risk compensation
How can an insurer manage the risks it underwrites? Risk compensation, the basis of classical actuarial techniques, consists in compensating claims by means of all the premiums collected for the same risk. This is easy to understand intuitively. If the company were to issue a single policy (covering fire, for example), it would make a modest profit with a high probability (if fire does not destroy the insured property), but would be exposed to a considerable loss if a claim were to occur. In this case, the company’s situation is identical to that of the insured. If, on the other hand, the company takes out a large number of policies covering similar buildings against fire, and if a loss affecting one of the policies has no influence on the other risks in the portfolio, it is intuitive that the company should be able to offset the risks, i.e. compensate losses affecting a small number of policies using the premiums for all the policies. The insurer therefore proceeds by offsetting: by grouping a large number of similar, non-mutually-influential risks within its portfolio, it will be able to use the premiums relating to the contracts to compensate claims affecting unlucky policyholders. For readers unfamiliar with this mythical player in the insurance industry, the story begins in 1687, in Edward Lloyd’s tavern in Tower Street, London. This establishment, frequented by shipowners, seafarers and merchants, gradually became a kind of insurance exchange, eventually becoming the world center for ship and cargo insurance. A royal charter in 1720 recognized Lloyd’s as an insurance corporation}.
Natural disasters, such as earthquakes, are risks that are not sufficiently dispersed and escape the principle of compensation. Traditionally, catastrophic risks were excluded from insurance, but today, the insurability of such risks is increasingly accepted. Coinsurance and reinsurance, in particular, can be used to cover catastrophic risks, ensuring that risks are dispersed on a larger scale. The securitization of risks (which enables insurance companies to call on the financial market to cover the risks they have underwritten) and, more generally, so-called Alternative Risk Transfer} techniques should enable significant progress to be made in this respect, by pushing back the boundaries of insurability.
2.2.5.2 The calculation of probabilities
When it comes to uncertain events, insurance is the offspring of the calculation of probabilities, and was only really able to develop when mathematical tools became available. The notion of probability dates back to Antiquity. But it wasn’t until the Chevalier de Méré presented Blaise Pascal with the problem of distributing bets between two players during a game that we saw the emergence of decision theory in an uncertain universe. For insurance as we know it today to come into being, the scientific basis for risk management by insurance companies had to be developed, and this became actuarial science. The foundations of actuarial science were laid in the first treatise on actuarial science, written by Richard Price in the mid-18th century.
2.2.7 Common point: risk
Insurance contracts are not alone in offering conditional compensation for certain events. Many financial instruments also have a risk-transfer dimension. By issuing shares to finance his investments, the owner of a company effectively transfers a share of his risks to prorata the new shareholders’ capital outlay. The holder of a share can in turn protect himself against a fall in the share price by acquiring a put option (a security giving him the right to sell the share at a set price and at a set time).
2.2.7.1 The difference: how risk is managed
There is, however, an essential difference between insurance and financial risks. To illustrate this, let’s take the example of a put option, which gives the holder the right to sell the security at a set price (whatever the actual market price). The put option writer cannot reduce his risk by selling more shares. On the contrary, if the share price falls, the issuer is exposed to more losses the more options he has sold. In other words, all “losses” occur simultaneously for the option writer, since all a company’s shares move in the same way.
Whereas an insurance company manages its risks by compensation after aggregation within large portfolios, a financier works by replication (insofar as the market allows). The principle of replication consists in building up a portfolio of assets whose value will be identical at all times to that of the financial instrument in question. This strategy is hard to imagine for an insurer: no conventional financial portfolio could replicate the cost of an automobile claim, for example.
2.2.7.2 Trend towards integration
There is currently a trend towards unifying the approaches of financiers and actuaries. This is undoubtedly the actuarial revolution of the third millennium. This is essentially due to two major trends observed in industrialized countries:
- firstly, the integration of insurance companies and banks into holding companies providing financial services, and the emergence of insurance products with a strong savings component, sometimes linked to investment funds.
- then changed the nature of damage risks. We have moved on from the world of accidents to that of catastrophes (natural, technological, environmental, terrorist, etc.), which lend themselves less well to the principle of compensation and exhaust the capacities of reinsurers, forcing insurers to turn to the financial markets.
2.2.7.3 Titrization of insurance risks
Catastrophes are risks whose probability of occurrence is very low, but whose financial consequences are very significant. The California earthquakes are a perfect illustration. A new form of risk transfer has emerged to cover such events, no longer using the traditional vehicle of the insurance company: the securitization of risk on the financial markets. For example, bonds indexed to the occurrence of natural disasters have been issued on the American market (cat-bonds). These bonds are characterized by the fact that their coupons and/or principal may disappear if a natural disaster of a certain magnitude occurs. A high yield is provided to compensate the lender for the possible loss of cash flow linked to its loan. The lender thus plays the role of an insurance company: it insures the borrower against the damage caused by the occurrence of a natural disaster.
The financial markets’ interest in this type of instrument is justified by their low correlation, or even negative dependence, on the returns provided by other available securities (equities, bonds, etc.).
2.3 Alea iacta est…
2.3.1 Insolvency of the insurer
Let’s assume that the insurer has crossed the Rubicon: he has underwritten a series of insurance contracts. The task now is to manage them as well as possible. The insurer’s commitments to its customers are uncertain and conditional, since they depend on the random occurrence of claims. Consequently, by accumulating the risks it has underwritten, the insurance company itself runs the risk of insolvency.
To avoid the risk of bankruptcy, which would have unfortunate social consequences (for third-party accident victims and policyholders alike), most countries have set up bodies to supervise the activities of insurance companies operating on their territory. In order to carry on an insurance business, you must first obtain an administrative authorization issued by the public authorities (known as “agrément”). A government-appointed body verifies that insurance companies are able to honor the commitments they have made to policyholders. These checks focus on the adequacy of technical reserves (accounting valuation of commitments to policyholders), the quality of the assets (investments) that represent them, and the existence of a solvency margin to cover any future losses. Approval may be withdrawn if the company’s financial situation is likely to deteriorate in the future.
2.3.2 Settlements
While many minor claims can be settled within a few months, more serious claims often take much longer to resolve. Take, for example, a road accident resulting in bodily injury: it will be necessary to wait until the victim’s condition has stabilized before being able to assess the damage he or she has suffered. Liability insurance has a reputation for long claims settlement periods, while property insurance is often settled more quickly. In motor insurance, claims are paid on average two to three years after they are incurred. To get a fairly accurate idea of the average claims settlement rate in a particular line of business, all you have to do is calculate the ratio between the total amount of reserves set aside by the companies operating in a given market and the total annual premium income of these insurers}. To give you an idea of the length of these delays, we can cite the example of compensation for victims of the pollution caused by the sinking of the Amoco Cadiz in 1978, for which the final judgement was handed down in 1992!
In some lines of liability insurance, claims settlement times can be very long, so it is often necessary to distinguish between the year in which a claim is made (the year in which the claim occurred), the year in which the claim is reported (the year in which the insured notified the insurer of the existence of the claim), and the year in which the claim is settled (the year in which the insurer finally settled the claim). The years between the year of occurrence and the year of settlement are referred to as development years.
2.3.3 Necessity of reserving
Insurance companies operate in a competitive environment. As a result, companies’ portfolios are open: some policyholders leave the company by cancelling their policies, while new business comes in. As a result, the insurer cannot rely on future premiums to meet its current commitments. It therefore operates on a capitalization basis: the premiums collected in a given year must be sufficient to pay the claims incurred in that year. The current system is based on the occurrence year: the insurer covering the risk at the time of the claim must bear the cost, even if the insured has changed company in the meantime.
Since the year in which claims are paid may differ by several years from the year in which premiums are received, companies are obliged to build up reserves or technical provisions using premiums for a given year, in order to settle claims occurring during that year once their amounts are known. At any given moment, the insurer must have sufficient reserves to enable it, assuming underwriting ceases at that moment, to fully compensate claims that have affected or will affect contracts underwritten to date, including management expenses.
Pure capitalization is one of the differences between private insurers and Social Security organizations. The latter can operate on a pay-as-you-go basis, i.e., use premiums collected during the year, or even the month, to settle claims to be paid during the same period, even if these claims relate to previous policy periods. The continuity of these systems is guaranteed by compulsory membership of the population.
2.3.4 Inversion of production cycle
2.3.4.1 Principle
The financial burden caused by a policy in the portfolio is unknown at the start of the insurance period, even though the premium has already been claimed. The premium itself is determined on the basis of historical statistics, and there is no guarantee that it is appropriate for the business to which it is applied. There is therefore real uncertainty as to whether the premium is appropriate to the risk represented by the policy.
This simple observation prompts a few comments. In industry, when a new product is launched on the market, we know exactly how much was spent on developing it, and hence its cost price. On the other hand, the company’s turnover is a priori unknown, as it depends on the company’s ability to sell its products. On the other hand, when the insurer sets the premium, he doesn’t know the amount of claims or the management costs incurred. The insurer’s situation is therefore quite different from that of other industries, since he knows a priori his turnover (the volume of premiums collected), but not the cost price of the products he markets (i.e. his future expenses).
This is the principle of the inversion of the production cycle. It can take many years before a company is able to accurately assess the profit generated by an insurance product, due to the very slow claims settlement rates in some lines of business. This fundamental principle underpins most actuarial techniques.
2.3.4.2 The annuality trap
Premiums paid {priori} should not blind insurers to the “annuality trap”. The “annuality trap” is the temptation to make figures and carry the loss experience forward to future years (by underestimating the technical reserves to be built up). In some cases, high sales figures can conceal a virtual bankruptcy when premiums have been underestimated. The issue of each policy is then synonymous with a future loss.
2.3.6 Liabilities of an insurance company
Liabilities comprise seven major headings:
- shareholders’ equity;
- subordinated liabilities: this heading concerns rights attached to debts, represented or not by securities which, in the event of liquidation or bankruptcy, must be exercised only after those of other creditors;
- Technical provisions: these are provisions relating to the insurance business, recorded gross of reinsurance;
- Provisions for risks and charges;
- item debts for cash deposits received from assignees;
- item other liabilities: these include other financial liabilities (negotiable debt securities issued by the company, loan for start-up funds), and third-party accounts (personnel, government, social security bodies, miscellaneous creditors);
- accruals: these are income items to be spread over several years (e.g. amortization of differences in bond redemption prices).
2.3.7 The assets of an insurance company
Assets also comprise seven major headings:
- uncalled subscribed capital;
- intangible assets: start-up costs and acquisition value of goodwill;
- investments: all investments, including land and buildings, investments in affiliated or participating companies, other (financial) investments and cash receivables deposited with ceding companies;
- reinsurers’ share of technical provisions: this represents the reinsurers’ share of technical provisions;
- receivables;
- assets: these include tangible operating assets, bank balances and treasury shares;
- accruals and deferrals: these include deferred expenses, accrued interest and rent not yet due, and deferred acquisition costs.
2.3.7.1 Impact of the inversion of the production cycle on the balance sheet of insurance companies
The principle of inversion of the production cycle has a major impact on the balance sheet of an insurance company. The balance sheet shows that premiums are collected before the corresponding benefits are paid out. It explains how liabilities to policyholders (represented by technical reserves) are covered by investments made by the insurer.
Insurance company accounting operates on an accruals basis: it must record commitments given as soon as they arise, and even anticipate the late declaration of claims occurring during the financial year. The total cost of a claim is recorded in the year in which it occurs, even if this total cost is only estimated and the claim is settled over several subsequent years.
In most companies, the bulk of the activity is found on the assets side of the balance sheet, in inventories, factory buildings, patents, etc. The balance sheet can therefore be read from left to right: it shows how the assets have been financed by the liabilities. In an insurance company, on the other hand, business leads to liabilities representing the company’s commitments to policyholders. The company’s activity is illustrated above all by its liabilities, and the balance sheet is read from right to left: it shows how the liabilities have been invested.
2.3.7.2 Technical reserves
In exchange for the premiums it collects, the insurer records a liability on its balance sheet. The technical provisions shown on the liabilities side of the balance sheet represent the risk-bearing company’s commitments to policyholders or injured third parties. A distinction is made between
- the unearned premium reserve calculated pro rata temporis, covering the portion of written premiums relating to the following accounting period. This provision arises from the fact that most non-life insurance contracts provide for a one-year guarantee period, and the premium is paid in advance. Each premium is therefore allocated between the accounting periods in which it gives rise to coverage. A policyholder who pays his annual premium on March 1 will have 2/12 of the premium deferred to the following year, in the form of an unearned premium reserve Only the portion of premiums relating to the current year is included in earned premiums.
- The provision for current risks is designed to offset any shortfall in rates. The aim here is to protect against model risk: if the model used by the actuary proves to be erroneous, or if it transpires that risks unknown at the time of pricing fall within the scope of the guarantee, the insurer is exposed to systematic losses, which it reflects in its balance sheet in the form of a provision for current risks, is the claims-payable reserve, which relates to claims that have already occurred (or incurred) at the inventory date but which have not yet been settled. A distinction must be made between two types of claims-payable reserve: those relating to current cover for which claims have not yet been revealed, and the provision corresponding to claims that have been incurred but not yet paid. A distinction is thus made between
- claims settled but not yet paid: the amount of the claim has been determined, but the corresponding payment has not yet been (fully) made;
- claims not yet settled:
- either the claim has been reported and the final amount has yet to be assessed;
- or it has occurred but has not yet been reported, and we need to estimate the number and cost of such claims (declared late or IBNR). A typical IBNR claim is a fire in a hotel on New Year’s Eve. If the fire occurs before the stroke of midnight, it must be attributed to the year just ended, even if it is not reported until the beginning of the following year.
The random nature of the insurer’s commitments and the sometimes very long settlement periods make accounting valuations difficult: while it’s easy to record a payment made, it’s much harder to forecast future payments, the amounts of which are random. In some cases, estimating provisions is more of an art than an exact science. It goes without saying that these provisions may subsequently be revised upwards or downwards to take account of additional information. Payments made will be charged to the provisions set aside for this purpose.
2.3.9 Insurers, institutional investors
Since the Second World War, rising living standards, the increase in the value of traditional insured assets (buildings, automobiles, etc.) and, even more so, the rise in the price of human life (obtained by discounting the average income lost in the event of permanent disability or death) have largely contributed to the growth of the insurance market. At the same time, governments have made it compulsory for certain categories of the population (e.g. motorists) to have insurance covering their liability. This explains why insurance is becoming an increasingly important part of the economy.
The capitalization mechanism to which insurance companies are subject explains why they are institutional investors: the large amounts set aside to cover the future settlement of claims arising during each financial year are invested in a variety of ways (loans to individuals or companies, bonds, shares, real estate, etc.). Financial management is therefore at the heart of the insurer’s business.
For the insurer, it means investing the colossal sums constituted by technical reserves in the best possible way, while respecting the imperatives of prudence. The insurer’s investments are the guarantee that he will be able to keep his promises. This is why they are subject to strict prudential rules. What’s more, public authorities often require insurance companies to invest in the public interest and in economic development (while at the same time complying with prudential imperatives).
2.3.10 Asset and liability management
The dynamic management of assets and liabilities has also helped bring actuarial science and finance closer together. The assets accumulated to meet future claims are of such importance that their management and performance are becoming an essential element in determining the results of insurance companies. As a result, it is not uncommon for an underwriting deficit (i.e. premiums insufficient to cover claims) to be offset by sufficient financial returns.
A strategic aspect of non-life insurance company management is to invest technical reserves appropriately, while complying with legal and regulatory requirements. Since these reserves are used to pay claims, the investments representing them must mature when the claims are due to be paid. This dynamic management of the company’s assets and liabilities using ALM (Asset and Liability Management) techniques maximizes the financial returns generated by the technical reserves, and reduces premiums accordingly. Very briefly, ALM techniques tend to match the maturities of assets and liabilities. As the strategy of keeping all premiums collected in liquid form is far from optimal, the aim is to select investments with maturities that will enable future obligations to be met. Note that since the most costly claims generally require long settlement times, non-life insurers also make long-term investments.
2.4 The insurance contract
2.4.1 The origins: the marine insurance contract
Since the dawn of time, people have sailed the world’s seas. Navigation was perilous in its early days, which explains why insurance was born of the sea. The first insurance contracts were found in the archives of the great ports of Catalonia and Italy: Barcelona, Genoa and Venice. The roots of insurance therefore lie in maritime trade, which explains why this branch of insurance has had a considerable influence on the development of the sector.
Marine insurance was not really practiced until the 14th century. Prior to that, other forms of insurance were used to protect against the dangers of shipping. The Greeks and Romans, for example, used the “contrat à la grosse aventure”. This was a loan pledged against a consignment of goods to be shipped far away. If the goods failed to arrive at their destination, the lender lost all rights to repayment of the loan. On the other hand, if the ship returned safely to port, the lender was reimbursed his advance plus substantial interest. When transporting goods by sea, the merchant thus mitigated the risks of the voyage by being lent all or part of the value of the cargo. It was a financial transaction in which the lender “ventured” his money across the seas. The borrower paid a high rate of interest (known as “grosse interest”) to compensate for the permanent insecurity of sea travel (the price of risk), but this interest was only paid, and the capital returned, if the ship arrived safely.
A closer look at the “grosse aventure” contract reveals that it is in fact a credit transaction, involving a special risk for the lender of total loss of the sum loaned. Unlike the premium, the interest stipulated was not related to the chances of the risk being realized (i.e., it was not proportionate to the risk). Nonetheless, the adventure contract is a conscious formula for protection and transfer against the risks of navigation.
The often very high interest rates set arbitrarily by the lender, taking into account the high profits expected by the merchant, incurred the wrath of canon law. In 1234, following Pope Gregory IX’s prohibition of usury and all high-interest loans conditional on transfers by sea or land, the use of the contract à la grosse aventure was virtually abolished. The papal decree of 1234 may well have been justified by the fact that the “contrat à la grosse aventure” took the form of a wager. Indeed, in many places, it had become possible to receive money on the sole chance that a particular ship would reach port. In this case, the loan was repaid, with comfortable interest. If not, all was lost for the lender. It was, in fact, an ordinary gamble.
In order to remove the papal ban on the contract à la grosse aventure, the intellectuals of the day set about analyzing and breaking it down. They proposed to distinguish two distinct conventions in the contract for big adventure:
- one consisting of a loan, under which the giver remitted a sum of money
- the other, known as susceptio periculi, whereby the giver, in return for an agreed sum, took upon himself the risks likely to reach the sum loaned. \end{enumerate} In this way, they cleverly removed the loan part of the “contrat à la grosse aventure”, retaining only the agreement relating to the perils of navigation. The marine insurance contract was born!
2.4.2 The birth of terrestrial insurance: the great fire of London
In the Middle Ages, towns were made up of wooden buildings (with the exception of a few important edifices, such as the church, the keep or the stone houses housing the notables). Because of the lack of space, the streets were narrow and the houses, built side by side and often two or three storeys high, were an ideal prey for the flames.
Fire insurance was born in Great Britain, after the Great Fire of London in 1666. On September 2 of that year, at around 1 a.m., the fire that had started in a bakery spread so rapidly that it took 7 days to bring it under control. The population of London was forced to leave the city by road and river. Some 13,000 houses and 90 churches (including St. Paul’s Cathedral) were totally destroyed.
Struck by this national disaster, the English government encouraged the creation of fire insurance companies. They organized their own fire brigades, instructing them to give priority in the event of fire to buildings whose owners were insured with them (they were identifiable by “fire marks”, metal plates affixed to the facade and bearing the name of the company covering the building).
2.4.3 From informal solidarity to insurance
Solidarity means a group of people taking responsibility for the losses suffered by some of its members. The durability of such an organization requires a coherent social group, where reciprocity applies: by helping today’s victims, everyone knows that they can count on a similar contribution from others in the future, should the need arise.
Insurance is the worthy heir to the informal solidarity that binds all social groups together. Primitive forms of risk transfer can be distinguished by two features:
- the beneficiaries of the guarantees have a social bond between them, making contractual formalism unnecessary;
- there is no prior payment of a premium to finance the repair of losses, but solidarity manifests itself through the payment a posteriori of a sum to repair the damage caused by the loss.
These informal systems have proved their worth over the centuries. However, with the development of human activities (industry and commerce) and the creation of cities, the need for a more elaborate system, accompanied by greater formalism, became apparent. With rapid urbanization, the communities of yesteryear fell apart. As a result, it became unthinkable to rely solely on solidarity to counter the bad blows of fate. The solidarity of yesteryear naturally gave way to mutual insurance, then to commercial insurance: risk pooling is organized by companies, and the community of yesteryear gives way to a group of policyholders who no longer have any particular social ties with one another.
2.4.4 Contract and policy
An insurance contract is an agreement between an insurance company and a subscriber or policyholder, fixing financial exchanges in advance and for a specified period, based on a well-defined set of random events.
The policy (from the Latin polliceor meaning promise) is the written document evidencing the formation of an insurance contract. The insurance policy includes non-personalized general terms and conditions and special terms and conditions, which specify the effective date of the contract, the duration of coverage, the characteristics of the insured risk, the amount of payments to be made by the policyholder, and the method of determining the insurer’s benefits.
It should be noted that the insurance contract is characterized by the fact that not all the parties’ commitments are set out in the policy. As far as the policyholder is concerned, only the method of calculating the premium may be described in the contract (which may include a bonus-malus mechanism, for example). The insurer’s benefit is obviously unknown at the beginning of the period, but the policy must specify how it is to be determined. In this sense, the insurance contract is a random contract.
2.4.5 Insured, policyholder and beneficiary
The insured is often confused with the policyholder, who pays the premiums, but can be distinct. In property insurance, the policyholder is the owner of the insured property; in liability insurance, the policyholder is the person whose liability is covered; and in life and accident insurance, the policyholder is the person whose future fate generates the risk. Finally, the insurance contract can be stipulated for a third party. The beneficiary is a person entitled to the cover provided by the insurer under the policy taken out by the policyholder. Henceforth, we will only refer to the insured, this term designating the person whose fate generates the risk.
2.4.6 What about technology?
As points out, a risk can be covered even if no statistics are available about it, or even if no theoretical analysis seems to apply to it, as the following anecdote illustrates. In 1971, the Cutty Sark whisky distillery offered a reward of £1 million to anyone who could capture Nessie, the famous monster supposedly haunting the waters of Loch Ness in Scotland. Apparently, the company’s directors, like good fathers (albeit a tad gullible), were a little frightened by the idea of having to pay out such a sum. So they contacted the famous Lloyd’s of London. As always, Lloyd’s agreed to cover the risk of having to pay the promised reward, in return for a premium of £2,500. A formal policy was even drawn up, stipulating that the risk would only be covered if the monster was captured alive between January 1, 1971 and April 30, 1972, provided it exceeded 20 feet in length (around seven meters) and was recognized as Nessie by the curators of London’s Natural History Museum. Lloyd’s did not omit to specify, as is customary in marine insurance, that the monster would become their property if they paid the reward (which made the contract risk-free for them, given the considerable revenue generated by the exhibition of a hypothetical monster such as Nessie).
In another field, atypical insurance contracts are occasionally used by the entertainment world, which hopes to benefit from the publicity effect they will cause. For example, a famous London theater scheduling a vaudeville show for the festive season took out a policy (again with Lloyd’s) to cover the risk of an audience member dying as a result of laughter.
On a more serious note, satellites sent into space are covered against a whole range of risks, yet claims statistics are virtually non-existent in this field. Clearly, expert opinion plays a key role here.
The principles described in this book are relatively general in scope, and can be adapted to more exotic policies (Lloyd’s area of expertise), where the actuary often has only his common sense and the more or less informed opinion of experts at his disposal.
2.4.7 Party representations
2.4.7.1 Insured
The sums paid by the policyholder in order to be entitled to the are called premiums (or sometimes contributions). This term, enshrined in legislation, corresponds to the English “premium”, which recalls the anticipatory payment: the policyholder pays the premium at the start of the contract in order to be entitled to the insurer’s cover once the claim has occurred during the guarantee period.
The policyholder is also expected to take all reasonable precautions to avoid claims, and once a claim has occurred, to take all necessary steps to mitigate its consequences.
2.4.7.2 Insurer
The insurer’s service is primarily a sum of money, but it can also consist of a service to be provided. Monetary benefits do not call for any particular comment. In damage or liability insurance, the starting point is an assessment of the damage suffered in the event of a claim, or of the claims of third parties who have suffered loss, after an adversarial phase that ends with an out-of-court settlement or a judgment. The insurer’s final settlement (the amount of the claim) will be equal to the estimate referred to above, possibly reduced by the application of an upper limit of coverage or by the deduction of an excess.
Increasingly, companies are offering policyholders advantageous claims settlement terms (e.g. direct payment by the company to repairers), provided the policyholder complies with their instructions. Typically, the policyholder is required to choose a repairer from a network approved by the company. This enables insurers to keep repair costs under control by hiring honest, conscientious craftsmen.
When the service does not involve a sum of money, the insurer may promise personal services. In liability insurance, the insurer reserves the right to take legal action against the injured party. In legal expenses insurance, the insurer promises to advise the insured in specific cases. In assistance contracts, the insurer can arrange for a family member to travel to the insured’s bedside. In assistance contracts, the insurer can arrange for a family member to travel to the insured’s bedside. Most motor insurance policies now provide for a replacement vehicle to be made available, should the covered vehicle be immobilized following an insured loss.
2.4.7.3 Compensatory or lump-sum repair
When compensation consists of a sum of money, a distinction is usually made between indemnity compensation and lump-sum compensation: in the event of a claim, the insurer will, depending on the case, pay out
- an indemnity to compensate for the loss suffered by the insured or the injured third party (who can in no way benefit from the loss). In the case of indemnity compensation, the amount paid by the insurer is therefore unknown a priori. Most policies also specify how the loss is to be assessed. In property insurance, a distinction is made between compensation for replacement value, compensation for value in use, and so on.
- The amount of the lump sum is specified in the policy. The extent of the loss and the damage suffered by the insured are not taken into account when determining the amount paid. In the case of lump-sum compensation, there is therefore no uncertainty as to what the insurer will spend in the event of a claim. This is the case, for example, with certain policies covering loss or theft of luggage, or insurance covering the insured’s loss of income.
Some forms of insurance include both a lump-sum and an indemnity component. This is the case, for example, with health insurance that covers hospital fees, drug purchases, etc. (indemnity component) and includes a lump sum per day of hospitalization.
2.4.7.4 Limitation of the insurer’s intervention
More often than not, the risk borne by the insured is only partially covered by the insurer, even in the case of compensation. This is because the insurer frequently stipulates deductible clauses, compulsory overdraft, coverage limits (intervention ceiling), etc. in the policy.
Deductibles and compulsory overdrafts mean that the insured must pay a portion of the claim. The aim is to ensure the sound financial management of the mutual society: small claims are eliminated from coverage in order to reduce overheads. In addition, the policyholder is encouraged to be vigilant in avoiding claims.
In most cases, the company will provide for a maximum amount of intervention (except where prohibited by law), per claim or per period. The portion of claims exceeding this limit will be borne by the insured.
Finally, in cases where the insured’s behavior can influence the amount of claims, it is sometimes useful to provide for a compulsory overdraft expressed as a percentage of the indemnity paid by the company.
2.4.7.5 Sum insured
The sum insured is of considerable importance in the actuary’s calculations. Under no circumstances can the indemnities paid by the company under the contract exceed the sum insured. This is either the value assigned to the insured property, or the amount up to which the insured intends to protect his or her assets against a liability claim. In accordance with the principle of indemnity, the insurer’s benefit depends on the sum insured and the loss suffered by the insured or the beneficiary of the insurance following the occurrence of the risk.
2.4.7.6 Proportional rule
The premium must be proportionate to the risk and the sum insured, not only when the contract is concluded, but throughout its duration. Legislation applies this principle in a number of ways, including the proportional rule.
If the premium has been calculated on the basis of a value lower than the actual value of the insured property, the indemnity must, in the event of a claim, be reduced by the proportion existing between the insured value and the insurable value (this is the famous proportional rule). Thus, if \(v_d\) is the declared value of the property and \(v_r\) its actual value, underinsurance occurs when \(v_d<v_r\). In most cases, underinsurance is only detected when a claim is made (as it would be too costly to systematically check policyholders’ declarations when they take out the policy). In this case, if \(x\) is the amount of the claim, the indemnity is reduced to \(x\times v_d/v_r\) in application of the proportional rule. This rule protects the insurer from under-pricing due to misrepresentation by the insured.
To protect consumers, insurance companies offer various mechanisms to avoid the application of the proportional rule. In fire insurance, for example, most companies provide the prospective policyholder with a property appraisal form. If the latter completes the form in good faith, the premium will be determined on the basis of the value deducted from the answers to the various questions (such as number of bedrooms, building materials, etc.), and the company will not be able to invoke the proportional rule clause even if it discovers after the loss that the value of the property has been undervalued.
There is one important exception to the proportional rule: first risk insurance. With this type of insurance, the insurer undertakes to cover the portion of the loss not exceeding a specified threshold, regardless of the value of the property. Few insurers, however, still offer this type of cover.
2.5 Bibliographical notes
This chapter is based essentially on (Chiappori 1997), (Eeckhoudt and Kimball 1992), (Lambert 1996) and (Tosetti et al. 2000). For more cultural and historical references on risk and insurance, readers can consult (Bernstein and Bernstein 1996) and (Ewald 1996).
(Gallix 1985)’s book contains numerous reproductions of old policies, which are well worth a look. On the other hand, (Haberman 1996) and the 10-volume (Haberman and Sibbett 1995a, 1995b, 1995c, 1995d, 1995e, 1995f, 1995g, 1995h, 1995i, 1995j) are packed with details on the origins of the profession.