INSURANCE (Social Science)

Risk is ubiquitous in the world and is generally considered a burden. Risk management, the art of coping with this onus, takes several forms: (1) doing nothing, or bearing the burden; (2) avoiding the risk, which includes reducing or quitting the risky activity; (3) spending resources to reduce the risk’s implication or probability, such as self-insurance; (4) hedging; and (5) transferring the burden to someone else, which is insurance. Some risks, like individual and group extinction, are so important that one could study history as the theme of risk management or view culture and social institutions like marriage and state, as evolving in response to the challenge of risks. Risk management is not special to humans—for example, ants spend effort and hoard excessive food, a form of self-insurance that humans parallel by precautionary saving—but insurance is a human invention.

Insurance is a transaction that transfers a specified risk to another party for a fee, called a "premium." In return the insurer provides the insured with a promise of indemnification (insurance company payment for damages) should the specified event occur. The specified events vary widely and comprise the different lines of the insurance industry: marine, property, vehicle, liability, life, and health, but the basic structure is the same. The amount of indemnification may be event-dependent (small or large fire) or fixed (life). In life insurance the event specified is either death or longevity. Insurance is both a consumption good consumed by households and an intermediate input purchased by firms. In property insurance the business is split about equally between households and firms. As can be gleaned from a cross-section as in Table 1, insurance is growing faster than national product, suggesting that it is a luxury good (income elasticity larger than one) and a "super normal" input. It may imply that adequate development of the insurance industry is vital for economic development and growth. By providing assets whose value is contingent on a given random state of nature, insurance helps make the market more complete and therefore more efficient. Without insurance availability some useful transactions and investments would be curtailed or thwarted.

Table 1

The demand for insurance is theoretically explained by risk aversion. A risk-averse person faced with a probability p of loss D, like a house that may burn, is willing to insure against that risk even at a premium higher than the mean damage pD. Firms demand insurance to placate their risk-averse owners and other parties, like customers, suppliers, employees, and lenders, thereby securing better contract terms with them.

Insurance differs from gambling by some of its fundamentals designed to restrain devious incentives. The purchaser must have "insurable interest," that is interest in the well-being of the insured asset (owner, mortgage lender). Other than in the case of life insurance, indemnification must be bounded by the value of the asset, including by double coverage. In return for indemnification, the insured surrenders to the insurer subrogation of all his relevant legal rights to claim from other parties. Still, the insurance market is burdened by fraud and by imperfections like adverse selection, where the firm cannot completely ascertain the risk of each customer thereby charging a premium that attracts the bad risks more than the good, and by moral hazard, where after the insurance transaction the insured may wish to increase his or her risk.

The supply side raises two puzzles. First, what is the relative advantage of the insurer in bearing risks over its clients? Second, if indeed it has some such relative advantage, why does it seek to insure itself by purchasing reinsurance? Reinsurance is a transaction where an insurer buys insurance from another insurer thereby transferring, or ceding, some of its risks and business to others. The remainder is called retention. Reinsurance is a global industry with some large specialized firms.

The production of insurance can be done in two distinct modes: mutual and capital-backed. A mutual is an association of members-customers who barter in insurance and pledge to indemnify each other if damaged. This insurance is backed by members’ commitments and capital. It must be a natural and intuitive arrangement since it goes back to antiquity. Second-century CE agreements among boat or donkey owners are legally analyzed in the Talmud.

Even a two-person mutual is advantageous. If each one has total property W and faces an independent risk of losing value D (like a house by fire) with probability p the advantage of such a mutual is:

The first line in (1) is the expected utility of each person in the 2-member fire-mutual, while the second line is his expected utility bearing the risk alone. The inequality follows from the concavity of the utility function that is implied by risk aversion.

The agreement improves with any additional member. The attractiveness of an n-member mutual may be explained by the expediency of (risky) portfolio diversification. Instead of holding one risky asset valued D, the agreement affords the member to hold the risk of n small assets, each valued D /n, which is always better for a risk-averse. In (1) the two fire events were assumed independent. Partial positive dependence leaves the inequality intact but reduces the advantage. Most mutuals collect a provisionary premium upfront and reassess members after risks’ realization, collecting more or refunding some.

However the main mode of insurance provision nowadays is by a stock company where insurance is backed by equity capital. Such production dates to the fourteenth-century marine transaction that combined banking and insurance. In such maritime loans the lender would finance a trade transaction but waive the loan if the vessel is lost. It appeared in two variants regarding the collateral: bottomry (the vessel) and respondentia (the cargo). While in a mutual the number of owners-partners must vary jointly with that of the insureds, in the stock firm the two are independent.

OPERATION

Assume schematically an insurance firm that sells only one type of policy against the risk of, say, fire, which occurs independently with the same known probability p of total loss D for each customer. Let V be the firm’s capital before any insurance transaction, serving as a cushion to enhance the value of its policies-promises. Suppose n such policies are sold at price s + c where cn covers the cost of running the business. Usually s would exceed pD, the expected loss (and indemnification), and the balance is a safety factor that goes to profit and tax. The revenue ns is called unearned reserve because it is designated for probable coming claims. As time elapses the uncertainty regarding the year’s fires is gradually cleared, more and more of the reserve becomes earned reserve, owned by the firm and part of its annual profit and of V. The firm’s funds V + ns are meanwhile invested and bear a random rate of return r thereby generating a major part of its profits. The number of fires that occur is a random variable k. If the two random variables happen to have realizations R and K then the firm’s net worth at the year end is (V + ns )(1 + R) – KD. If it is negative, the firm’s future promises are worthless so it is declared insolvent and ceases operation.

The risk of failure is real and troubling. In the United States during the 1990s approximately 70 firms, or 0.8 percent of all insurance firms, failed within a year. The condition (V + ns )(1 + r) – KD < 0 points out the reasons for failure: low V; low premia s; low R; large K. The dependence of the ex-ante probability of failure Prob(( V+ ns )(1 + r) — KD < 0) on the magnitude of n is less clear-cut. Conventional wisdom attributes the relative advantage of the stock insurance firm in bearing risk to the multitude of clients and the law of large numbers. However, whether the numbers (n) in insurance are large enough to warrant this explanation is an empirical question. According to the 1963 work of Paul A. Samuelson, the advantage of the insurance firm lies in the multitude of its owners. Spreading a given risk over many bearing shoulders (stockholders) tends to evaporate its burden. In 1970 Kenneth J. Arrow and Robert C. Lind analyzed a large risky public project, where the risk was spread over the population, and demonstrated it for a single risk. This result explains the advantage that governments may have in insuring against catastrophic losses. It does not address the issue faced by the insurance industry of insuring against multiple risks. In this light, reinsurance is a handy mechanism to spread risks.

BUSINESS CYCLE

The insurance industry manifests a peculiar business cycle of its own. In times of hard market, prices are high and yet insurance is hard to get as firms offer only constrained extent of coverage and carefully select the clients. The result is high profits and rise in surpluses. That by itself may lead to the opposite, soft market, as the high surplus warrants more business and risk taking so prices go down to attract more and necessarily lower-grade customers. Profits go down, equities are depleted, and the cycle repeats itself.

INNOVATIONS

Since the 1990s a rise in world catastrophes like earthquakes, hurricanes, and terrorist activities drained world insurance surplus and constrained the industry’s production capacity. In response financial innovations were introduced as substitutes for equity capital. The simplest is catastrophe bonds. An insurer issues such a bond, and the repayment of the interest and/or the principal is made contingent on a specified event like the catastrophe cost (for the insurer, for the region, or for the world) not exceeding a predetermined number. It shifts some of the risk from shareholders to bond holders and is a modern resurrection of the Middle Ages’ maritime loan-cum-insurance. More complicated instruments are call and put options whose strike price is some catastrophe number.

REGULATION

All over the world, insurance industries are regulated. The raison d’etre of regulation is the risk of insurers’ insolvency. Such occurrence would disrupt the economy, prevent gains from trade in risk-bearing, and cause personal loss and suffering to consumers. Although insurers themselves would suffer in case of insolvency, they can not be fully counted on to take steps to avoid it because of several market imperfections. First, because of the limited liability of a stock company, stockholders would not have to bear, in case of insolvency, its full cost but lose at most their equity. That weakens stockholders’ incentives to avoid excessive risk. Second, moral hazard and agency problems develop. After issuing policies purchased under presentation of a certain risk level, the insurer may wish to assume more risk because part of its cost is borne by the insured policyholders. Regulators issue guidelines regarding the extent of underwriting, prices, and investment policy. They monitor the business and upon detecting signs of trouble intervene by issuing various directives.