Chances Are Read online

  Profit—you will notice that there is nothing about that in Bernoulli or Laplace. Theoretically, insurance distributes loss but shouldn’t add to it. All other businesses attach themselves somehow to the productive element of human life: their profits derive, however tortuously, from the increase in value of all the world’s goods. Insurance, though, is simply a reassignment of responsibility—and where’s the productive element in that?

  We could say that Barbon’s profits were fortuitous, as there happened to be no more great fires; or that the small base of observations from which he worked made it necessary to calculate conservatively. We could say his investors deserved a reward for tying up their funds. Moreover, an average loss is not the actual loss; some years could require far more capital to cover pay-outs. We must say, though, that Barbon’s conspicuous revenues changed insurance at its outset from a pure exercise in probability to the complex, devious institution it is today.

  Two competitors arose almost immediately, each embodying a rival principle. The first was the government: within a year, London’s Common Council had voted itself the right to issue insurance at rates slightly lower than Barbon’s company. The courts speedily decided it had no power to do so, but the idea that our misfortune is properly the responsibility of the State (like our security, our employment, our health and our old age) remains a powerful one, countered in practice principally by arguments about the incompetence or untrustworthiness of governments.

  The other new-sprung rival to the Fire Office was the Friendly Society, established in 1684 and followed twelve years later by the “Contributorship for Insuring Houses, Chambers, or Rooms from Loss by Fire by Amicable Contributions” (which is still in business, although now under the fashionably mock-Latin name of Aviva). These followed the mutual principle, which, in purist terms, has much to recommend it: there are no shareholders anxious for profit; the risk to be covered, moreover, is that of the actual members of the Society, not a haphazard selection of society at large. Just as, nowadays, women drivers constitute a lower accident risk than men and therefore can find lower-cost insurance, self-constituted groups—Quakers, Masons, Rechabites (organized teetotalers; also still in business)—could exploit the specific risk implications of their own peculiarities to offer themselves better terms. In Bernoullian terms, a self-selecting group needs a smaller N to bring its difference |X/N - p| within the degree of accuracy ɛ than does a random sample of humanity.

  Supporters of profit-making joint-stock companies could counter that mutual societies cannot make speedy decisions and are always tempted to keep too little capital tied up; and indeed these and other arguments came to a head very quickly in 1687, when the Fire Office and the Friendly Society each petitioned James II for a monopoly on fire business. Typically, James came up with an arrangement that pleased nobody—alternate three-month exclusivity periods—but an afterthought to his decision added a new, complicating variable: he required the Fire Office to fund London’s firefighting effort. The Fire Brigade was not to return to State responsibility until 1865.

  The idea seems plain common sense: it is in an insurance company’s interest to reduce its losses, so paying for firefighters is really just the company’s own insurance policy. But it greatly complicates the issues of probability involved. First, each overall fire risk now constitutes two separate but related gambles: the chance a fire will start, and the chance it can be stopped before a total loss of the insured property. The chance of the first one is determined by probability, but its cost is variable and paid for directly by the policyholder; the chance of the second is variable, but its cost is determined, and is the company’s, to be paid out of income. Moreover, the responsibility for putting out fires is very hard to restrict to insured risks: in the world’s biggest city, it would have been foolish as well as immoral to wait until a blazing uninsured house had ignited the insured one next door before manning the pumps. Ultimately, the policyholders ended up paying for their neighbors’ peace of mind as well as their own.

  Returning to Laplace’s principles, this almost off-hand royal decision had complex ramifications, all of which tended to increase moral fear. Compounding simple risk by associating it with prevention increased uncertainty, adding the fixed cost for fire prevention but an unknown return from that prevention. Giving the Fire Office a vague but undeniable responsibility for the security of the uninsured increased expense without reducing hazard. The only way to bring the moral impact of this uncertainty within mathematically acceptable bounds would be to increase capital—following the 10th Principle—and this soon became the great imperative of the industry.

  The basic equations of insurance offer a measure of control over three ratios. The first is the ratio of observed cases to moral certainty—how many past events you need to know to be willing to bet on the future— which suggests that greater specialization can be more profitable. The second is the ratio of actual loss to insured loss—how much you can save from the wreck—which suggests that prevention is worth the expense. And the third is the ratio of potential loss to total capital—how hard any one misfortune will hit your reserves—which implies that bigger capital is always better. The manipulation of all three ratios has shaped the industry over the past three hundred years—and the abuse of each has brought its own particular disasters.

  The success of fire and life insurance in the seventeenth century quickly spawned a multitude of specialist policies; and the increasing complication of life over the next two centuries encouraged the invention of many more. In the mid-nineteenth century, heyday of projector and prospectus, you could buy insurance “against bad debts or for bonds and securities in transit, against railway accidents, boiler explosions, earthquakes, failure of issue, loss on investment, leasehold redemption, non-renewal of licenses, loss of or damage to luggage in transit, damage to pictures, breakage of plate glass, loss of profits through fire, imperfect sanitation, birth of twins” . . . and famously, some time later, against damage to Betty Grable’s legs. Each line of business required its own specialist expertise and its own collection of statistics to price the bet properly. Insurance against contract or bond default, for instance, became an industry on its own, particularly in the United States—the reason so many American financial companies have the word “fidelity” in their names.

  The basic problem with specialist insurance is its very small N. Where specialization has an intrinsic advantage (insuring, say, Eskimos against sunstroke or Orthodox Jews against shellfish poisoning) the small number of observed cases is immaterial; but what about complex, important, expensive things that just don’t happen very often? How do you price those?

  Lloyd’s of London learned a costly lesson about the dangers of a small N, when it first entered the satellite insurance business. From the 1960s to the early ’80s, it had only one customer: the U.S. government, covering its commitment to the Intelsat consortium for satellite communications. Every launch was controlled by NASA, and every launch was different—in its technology, in its costs, in its inherent risk. High fluctuation, low correlation: the parallel with Marine insurance was obvious . . . so Lloyd’s took the business.

  In 1984, Westar VI and the Indonesian Palapa B-2 became stranded in low earth orbit, triggering a loss of $180 million—a loss so large that it was actually worth the syndicate’s while to pay $5.5 million toward a shuttle mission to recover the satellite, repair, and relaunch it—all under the Marine insurer’s age-old right of salvage. It also gave the early days of space commerce one of its odder images: a stout, pink, pinstriped underwriter at Mission Control in Houston, uncomfortably alone in a sea of crew-cuts, pocket protectors, and white drip-dry short-sleeved shirts.

  Nor were Westar and Palapa the only payouts: between 1965 and 1985, total losses were $882 million, against a premium income of $585 million. Then came 1986, the annus horribilis in which the Challenger disaster was followed by successive failures of the Delta, Titan, Ariane, and Atlas launchers. As the industry lost, though, it learned:
N and X were growing larger as each rocket left the pad. Bolstered by experience, satellite insurers are now much more confident in the pricing of launch insurance and are therefore free to worry about the parts of their business that still have a small N: solar storms, space junk, and dwindling orbital space.

  Specialization begets expertise and expertise begets prevention: a company that must pay for disaster gains both incentive and opportunity to forestall it. The Fire Office may have had the responsibility to put out fires, but it was with the beginning of the Industrial Revolution that insurance companies actually began to shape the world into a less risky place.

  Only by tiny, easily missed details of design and maintenance can a steam boiler be distinguished from a bomb. Locomotion, the very first successful railway engine, blew up and killed its driver—an ominous beginning. Steam had lurched suddenly and awkwardly from large, low-pressure installations like pumping water to small, high-pressure applications like transportation. The comfortable laissez-faire philosophy of early-nineteenth-century government made travel horribly dangerous—to the point where the Reverend Sydney Smith suggested that a minor bishop ought to give his life in a railway accident to draw attention to the problem.

  As no bishop stepped forward, it was left to the insurance companies to deal with steam safety: money was a more efficient agent of social change than human life. The companies hired investigators to inspect and approve steam boilers; it was they who checked that the riveting was sound, that the tubes were clear, that no speed-hungry engineer had tied down the safety valve. Without certification, an engine could not be insured; and without insurance, it could not run—and could not kill.

  The principle quickly extended throughout the new, dangerous fields opened by fast-expanding trade and industry. Lloyd’s began to certify ships, giving the world the by-word “A1” for “best.” Samuel Plimsoll, outraged at the insurance scams of unscrupulous ship-owners, earned the thanks of thousands of sailors through his plimsoll lines, painted on the outside of ships’ hulls to prevent overloading (as well as his rubber-soled shoes to prevent slipping on the new steel decks). Buildings, especially after the great Chicago and Boston fires of the 1870s, were built to “insurance code” rather than to the sloppier requirements of local government.

  This certification came to mean that the insurers, rather than the State or the trade, increasingly determined the standards to which the physical and legal world should be held. In late-nineteenth-century America, even the validity of land title came to depend on whether it could be insured—insurance became a stamp of approval rather than a stop against ruin.

  A practice like this was clearly too attractive to keep within the bounds where it makes most sense. After all, if insurance can offer you sound title to your land, a house worth owning, and the confidence you won’t be blown to atoms on the train to work, why can’t it bring the same security to the rest of life—to, for instance, your ability to make a living? Loss of livelihood was a pressing issue in a world with no welfare and hideous working conditions. The earliest mutual societies, the medieval guilds, acknowledged the probability of a member’s losing the ability to work through sickness or injury and the need to do something. Hatters do go mad, tailors blind—these were predictable risks that club dues could cover, since all the members had a clear if unmathematical sense of the frequency and severity of loss.

  The Industrial Revolution changed all that: mass employment not only increased the danger of work but destroyed the mutual principle, removing the onus from fellow workers without putting it on the employers. Miners choked, cotton-spinners coughed—the risk was still concrete and quantifiable, but no one was obliged to take it on.

  Not until 1880 did a British government, having dealt with the religious instruction, drinking habits, and drains of the laboring classes, address the question of injury at work with the Employers’ Liability Act. The employers, forced at last to acknowledge some responsibility, were quick to pass it on: the first workmen’s compensation insurance companies appeared almost immediately.

  The ground plan of this business shows slight but significant deviations from simple probability. For one thing, the person insured, the employer, is not really the person who has borne the loss: the mill girl loses her finger, but the mill owner loses only in the sense that the State has assigned the fault and the cost to him. He, in turn, passes on this cost—in the further hope that the insurance company’s trained investigators will find ways to adjust the loss and haggle with the State. The finger—the thing of value—is too easily lost again in this complex machinery of transferred responsibility.

  This is not to say, however, that everyone in the industry is shifty: Vince Marinelli is a site inspector in Manhattan for a large workmen’s compensation insurer. To walk the streets with him is to see a different city. In place of the horizontal torrent of strangers there is a vertical forest of friends, calling and whistling down greetings from scaffolding on every block. Priestly in dress and manner, Vince is a celebrity: although he’s an insurance employee, he is known and loved in every trade and on every site from one end of the island to the other—because he saves lives.

  “No workmen’s comp, no work—so sure, I can shut a job down if I have to. But who wants to do that?” Two weeks before, Vince had dropped in on a West Side job, an office building with an impressive eight-story atrium. “The steel just topped out. New trades were going to be coming on, maybe not so familiar with the site. Now, atriums—I don’t like them: you’re working on a building, you don’t expect a big hole in the floor. So I went to the general contractor and said: ‘Look. For me: rig a net across that, OK?’ And thank God he did—three men dropped in that net the first week. If you can do something like that occasionally, guys don’t mind so much you hassling them about wearing their hard hats. It’s like they know they got someone looking out for them.” In medieval times, Vince would deserve at least beatification and a statue, carrying his attributes of clipboard and cellphone.

  The fact that insurance companies have taken, however indirectly, a moral responsibility for preventing misfortune has opened them to the charge of moral (and legal) responsibility whenever it happens. Nowhere has this been clearer than in the American asbestosis story of the past thirty years, where hundreds of thousands of people have claimed compensation for the effects of something that was not even classed as a risk when the relevant insurance contract was written. Nothing about asbestosis relates to the Law of Large Numbers; loss and premium are entirely unconnected.

  “Once our grace we have forgot, nothing goes right: we would—and we would not.” By entering, or being drawn into, the arena of workmen’s compensation, insurers abandoned their own guiding principles and now find themselves ruled instead by the twin tenets of American personal-injury law: Somebody Is Responsible and Go Where the Money Is. These, you must know, have nothing to do with probability; they are inevitability.

  “Consider the sequence of independent events a1, a2 . . . an”: as basic a phrase in probability as “Construct triangle ABC ” is in geometry. As with all the best magic tricks and confidence games, the hook has been cast and swallowed in the first sentence. “Independent events”—how difficult they are to imagine, let alone consider! Nothing in real life seems independent: you met your soul mate because you went to a Christmas party; your neighbor lost his job because of Mexican wages; your aunt won’t travel by plane because of Arab politics. Industries like insurance that work by probability have first to establish what is and isn’t independent—like sexing day-old chicks, it’s a job that requires both experience and instinct.

  The desire to free up capital, balance portfolios, and limit loss prompts insurers to pass on risk to others—just as bookmakers “lay off” liabilities by betting with other bookmakers. Sometimes this can be a disastrous process: During the 1980s, the London market in excess-of-loss reinsurance—the “LMX spiral”—saw the same risks circulating through Lloyd’s again and again, with syndicates effect
ively, unwittingly, paying themselves to insure themselves against ruin. These policies seemed to be independent risks, but were in fact the same great risk—total market insolvency—in different guises; as a result, when one syndicate made a loss that triggered its excess-of-loss policy, the liability would bounce back and forth between syndicates, amplified at each bounce like a pinball trapped between spring-loaded bumpers. It left many Names destitute and nearly destroyed Lloyd’s.

  The simpler method for an insurance company to lay off risk is to secure it to one of the great cold, serene lakes of capital that lie beneath the Alps: Swiss Re, Munich Re—the reinsurers. Although reinsurers do redistribute some risk back into the market, this is essentially where the music stops. Your house, your car—even your life, is ultimately secured by one or another of these vast companies. For them, sitting in the last of the chairs, there can be no laying off, no pooling and sharing of risk—so what is left? The same technique used by the Chinese merchants on their way down river, five thousand years ago: diversification.

  Thomas Hess occupies a large top-floor office in Zurich. “OK, nobody wants to insure against something that won’t happen. So of course, we will pay out—a lot—every year. We have to know when these payouts are independent and when they are cumulative. We could assume, for instance, that earthquake insurance in Japan and motor insurance in Germany are independent; but earthquake in Japan and motor in Japan could be cumulative if, say, a highway collapses. See?

  “It’s also information arbitrage; we know more about risk, so the clients don’t have to. They can sleep at night. We sleep at night because we can say no if the risk doesn’t suit our appetite. I tell you, I feel a lot more secure running an insurance portfolio than I would running an airline. An airline has all its risks bunched together—and if it doesn’t take those risks, it’s out of business.”