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  This method, too, is an essential component of insurance, particularly insuring credit. Whether a given person or company is a good or bad credit risk involves just this sort of winnowing of favorable from unfavorable aspects and gauging the probability of each. “The good news is he drives a Rolls-Royce; the bad news is he doesn’t own it.” As the recent spectacular failures among large corporations reveal, it’s a process that requires a fine hand on the calculator. This is something we will see again and again: each time probability leaves its cozy study full of urns and dice and descends to the marketplace of human affairs, it reveals its dependence on human capabilities—on judgment and definition. As powerful a device as it is, it remains a hand tool, not a machine.

  Laplace’s last Principle of mathematical hope is the most elusive, but also the most profound:10th Principle: The relative value of an infinitely small sum is equal to its absolute value divided by the total benefit of the person interested. This supposes that everyone has a certain benefit whose value can never be estimated as zero. Indeed even that one who possesses nothing always gives to the product of his labor and to his hopes a value at least equal to that which is absolutely necessary to sustain him.

  There are three linked parts at work here. The first—relative value—recognizes the essential difference that underlying wealth makes to particular hazard: J. P. Morgan could take huge risks, snapping up ailing railroads with a flourish of his pen, because the absolute value of any potential loss was small compared to his total fortune.

  The second part of the Principle is, typically for Laplace, a moral conclusion drawn from a mathematical source. The Principle states that the relative value of the amount risked is its absolute value divided by the total benefit or fortune of the person concerned, like this: risk ÷ fortune. So, as fortune grows smaller, the relative value of the amount risked grows greater. But what if you have no fortune at all? The relative value of your risk would then seem to be risk ÷ 0 . . . which is a mathematical absurdity, since dividing by zero has no meaning. Laplace’s interpretation, however, is that nobody is completely without value. Even the penniless man has the value of his labor and his hope. The essential worth of humanity is revealed—through a proof by contradiction.

  The third part of the Principle follows from the other two: that mathematical hope in itself is insufficient to describe how we should act in cases of uncertainty. We must modify our calculation of what we might win or lose by considering how it compares with our current fortune. If our pockets were infinitely deep, we could take each risk on its merits; but as our fortune diminishes, we lose the ability to bear loss, which in turn reduces our chance to gain—the most bitter, most familiar truth of poverty. This modified calculation is called “moral hope” and represents mathematical hope reinterpreted in light of the relative value of risk.

  Bernoulli’s “moral certainty” determines whether you should expect something to happen; Laplace’s “moral hope” determines the implications if it happens to you. It explains why our disaster is worse than another’s—because we are constrained to see it in relative terms, contrasting our happy past and doubtful future. It makes insurance necessary—because only through joining a great, collective fortune can we bring the moral fear of misfortune down to its mathematical value.

  The deepest implication of the 10th Principle is one that Job himself would have welcomed in his effort to accept God’s apparent capriciousness. It is this: life can never be fair. Since our resources are not infinite, even straightforward 50-50 odds make for a loss that will always be morally greater than the gain. The world is fundamentally different for the observer and the participant: the effective probability of an event changes the moment we take part in it, venturing our goods on an uncertain result. No wonder Damon Runyon’s Sam the Gonoph said: “I long ago come to the conclusion that all life is six to five against.”

  The earliest form of insurance needed no money, only the immutable laws of probability. There is a record of Chinese merchants, five thousand years ago, separating their cargoes and dispersing them among several ships, so that each bottom would carry only a portion of each trader’s capital. If you divided your bales of silk among five boats and shipped them down to Xian on the spring flood, intending to sell them at a 100 percent mark-up (not an unlikely figure in the more venturesome days of commerce), you could lose two vessels to rapids or piracy and still make a profit.

  Ship insurance springs naturally from the necessity of trade, the existence of sophisticated entrepôts, and the rapacity of barbarians—all long-familiar facts of life on the Mediterranean. Its ancient Greek form, as described by Demosthenes, was what is now called by the splendid name of “bottomry.” It was not a direct transfer of risk, but rather a conditional loan: The insurer staked the merchant to a sum of money in advance of the voyage, which was to be repaid with (considerable) interest if the voyage succeeded—but forgiven if the vessel was lost.

  It is an arrangement that is easy to describe but difficult to characterize: not a pure loan, because the lender accepts part of the risk; not a partnership, because the money to be repaid is specified; not true insurance, because it does not specifically secure the risk to the merchant’s goods. It is perhaps best considered as a futures contract: the insurer has bought an option on the venture’s final value.

  As trade picked up again after the Dark Ages, confusion about the exact nature of bottomry was further compounded by religious qualms. The classical contract clearly fell foul of the Christian (and Muslim) ban on usury—that is, taking interest on a loan rather than a share of anticipated profit. At the same time, there was a general worry about what seemed like betting on the will of God.

  And yet, clearly, something was needed. By the thirteenth century, Genoese merchants were trading with Tartars in the Crimea and Moors in the Barbary states. Spanish wool was being shipped to the Balearics; then to Italy to be carded, spun, dyed, woven, and finished; then back to the Balearics and Spain to be sold as cloth. Cargoes like spices, silks, porcelain, dried fruit, precious stones, and works of art concentrated lifetimes of value into a single, vulnerable point on the ever-treacherous sea. Reputable merchants—men who had prayed and fasted with conspicuous rigor, endowed chapels, and entertained bishops—were still finding themselves ruined by an unexpected tempest. Surely there could be an acceptable way to avert financial disaster without courting divine retribution?

  Surprisingly, the problem was solved, not through probability, but through the very Aristotelian tradition of quotation, comparison, and precise distinction that probability was later to replace—the splendid, tottering edifice that Bacon so mistrusted. Burrowing through Justinian’s Digest of Roman law, scholars unearthed two separate ideas which, when combined, made the modern insurance contract possible. The first was the casus fortuitus, the chance disaster no human could foresee: God moves in such mysterious ways that the law may treat at least some of them as random. Theologically, this could be questionable—but the Digest was compiled under a Christian emperor and rediscovered by agents of the greatest medieval pope. Authority combined with necessity to finesse this qualm.

  The other essential donation from the Digest was the idea that every contract or agreement is an exchange: we must be swapping, buying, or selling something—or else we would not need to agree. Adding this concept to that of the casus fortuitus created, out of nothing, an entirely new commodity—yet more valuable to trade than Javanese pepper or Turkish carpets: risk. If risk could be bought and sold, the whole theological nature of insurance changed. The insurer did not lend money but instead sold (or, more accurately, rented out) a risk-taking capacity. The merchant did not borrow but instead traded a hazard for a security. Making such a contract was not a bet on God’s will but a simple, prudent provision against misfortune—like paying a fee to keep your money in the goldsmith’s strongbox. And, as the Digest recognized that risk could be different in different circumstances, it could be priced to suit the occasion—an important dist
inction in a world that insisted all bakers, for example, should charge the same for a loaf.

  The Aristotelian fiction of risk as a commodity moved insurance from the fringes of usury into the warp and weft of trade. It is a mark of the importance of this shift in perception that, once it had occurred, ship insurance hardly needed to change again. One of the first mentions of insurance in its modern sense is in Lombardy in 1182. In 1255, the state of Venice was pooling contributions—premiums—from merchants to indemnify loss from piracy, spoilage, or pillage. The first known true insurance contract is a Genoese document of 1343; contracts in England—written in Italian—date from the beginning of the sixteenth century. The first contract in English (on the Santa Crux, from 1555) states: “We will that this assurans shall be so strong and good as the most ample writinge of assurans, which is used to be maid in the strete of London, or in the burse of Andwerp, or in any other forme that shulde have more force.” This assumes that merchants were not only comparing contracts between countries, but were anxious to avoid any discrepancies in coverage. The two essential aspects of Marine insurance—its universality and its uniformity—were clearly already in place.

  The “strete of London” mentioned in 1555 was, appropriately enough, Lombard Street, originally a foreign outpost of those Italian adepts in financial alchemy. Today is a gray, chilly day on Lombard Street; burly marine underwriter Giles Wigram emerges from the Underground at Bank station and bustles past the headquarters of the great insurance companies on his way to the improbable tower that houses Lloyd’s of London.

  “It’s not rocket science or I wouldn’t be doing it,” he explains. “Of course, it can be complicated: we’re dealing with hulls, cargoes, offshore installations, pollution liability. Put a helicopter on a ship and it’s a Marine risk, take it off and it becomes Aviation. Tow a lightship from place to place, it’s Marine; once you stop, it isn’t. We’ve got to cover perils of the sea, like sinking or stranding; perils on the sea, like fire, jettison, barratry— that’s when a mutinous crew takes over hull or cargo; we cover war, strikes, and extraneous risks like pilferage, rust, ship’s-sweat damage. But boil it down to its essentials, I’m doing nothing different from what the chaps at Edward Lloyd’s coffeehouse were doing two-hundred-odd years ago: talking to other chaps, asking awkward questions, getting a feel for the risk.”

  Giles represents a syndicate of “Names”; until recently, these were individuals who agreed to take on risk with unlimited personal liability—in the Lloyd’s phrase “down to their last pair of cufflinks.” On their behalf, he negotiates with brokers representing particular risks: cargoes of running shoes from Taiwan, offshore platforms in the stormy North Sea, bulk carriers threading the pirate-infested Malacca Straits. If a deal is struck, he commits part of the capital at his disposal to cover part of the risk, literally underwriting—by adding his signature, percentage cover, and syndicate stamp—the insurance contract. “It’s basic diversification,” he says, “and it works both ways: If, God forbid, a supertanker caught fire in rough seas, I sure as hell wouldn’t want to own all of it. Similarly, if all my Names hit their last cufflinks at the same time and the syndicate went belly-up, Mr. Simonides or whoever it is wouldn’t be too chuffed at having all his risk with us. It’s a hazardous world, but we’re here to spread the hazard nice and thin.”

  The hazard is spread at a series of face-to-face meetings. The Lloyd’s tower looks, on the inside, like a pinball machine set on end. The brokers, each clutching a satchel full of risk, bounce around its many levels by escalator, stopping off at desks where the underwriters await them. They sit down, take a contract from the bag, introduce its essential elements, receive either a signature or a refusal, then move on. So far, no electronic system has been found to be more efficient at distributing risk—but that may be because Marine risk, although tradable, could never be a bulk commodity.

  “The thing is,” explains Giles, “that the information about the particular risk is more important than the statistics. I may know the overall chances of a ship being sunk this year—I should even have figures for, say, Liberian-registered crude carriers in the South China Sea in October—but that still doesn’t tell me enough about the proposal on the table. There are some dodgy characters in this business: the hazard can be predictable from all other standpoints, but if the beneficial owners include so-and-so, or the stated cargo doesn’t look right for the intended itinerary, the game’s a bogey—I don’t want any part of it. So it’s not what this particular risk is like—it’s how it’s different; that’s what I need to know.”

  This particularity is the reason Marine insurance has changed so little since it was a private matter between merchants. It is why the Lloyd’s basic contract lasted in its original form for more than 200 years, being dropped only in 1982. It is also the reason for an oddity governing the negotiations between Giles and the hundred-odd brokers who pass his desk every day: uberrimae fides—“utmost good faith.” Unusually—for what is otherwise a market transaction, with its concomitant haggling and bluster—the parties are expected, indeed required, to make known all material facts. Hull construction, flag of registry, ownership, cargo, packing method, season, itinerary, local conditions: all must be revealed to the best of the broker’s knowledge and belief—because all are pertinent in a system of probability with high fluctuation and low correlation between events. Five thousand years of experience have produced few valid generalities in Marine insurance; it seems the Law of Large Numbers breaks down on contact with seawater.

  I . . . walked through the City, the streets full of nothing but people and horses and carts loaden with goods, ready to run over one another, and removing goods from one burned house to another—they now removing out of Canning-street (which received goods in the morning) into Lumbard-street and further. . . . All over the Thames, with one’s face in the wind you were almost burned with a shower of Firedrops. . . . We saw the fire as only one entire arch of fire from this to the other side of the bridge and in a bow up the hill for an arch of above a mile long. It made me weep to see it.

  The Great Fire of September 1666 burns again in the clear, sympathetic prose of Samuel Pepys. This four days’ disaster, the worst destruction London suffered between Boadicea and the Blitz, razed nearly 436 acres, devouring 13,200 houses, 87 churches (including Saint Paul’s Cathedral), 44 livery-company halls, the Custom House, the Royal Exchange, and dozens of other public buildings. Only nine people died in the fire itself, but hundreds succumbed to shock and exposure.

  Catastrophic urban fires were nothing new in a world lit by tapers and fed from open hearths. The refugees set up their rag tents and scrap-wood cabins in the fields beyond the walls. The King, as good kings should, promised cheap bread. A Frenchman conveniently confessed to starting the blaze and was expeditiously hanged. In all qualities save size, the Great Fire was just another disaster of the medieval or ancient world. What set it apart as an intrinsically modern event, however, is that Pepys’ contemporaries could determine exactly what the damage was. Not “untold thousands of habitations” but 13,200; not “a dreadful holocaust of temples” but 87. This was not horror beyond the mind of man: it was a quantifiable event. A property-conscious, commercial, and thoroughly taxed city, London recorded itself to the last window and fireplace—and therefore knew exactly what was lost.

  Indeed, it was this prickly Protestant self-awareness that prevented its being reborn as Europe’s greatest Baroque city. John Evelyn, Christopher Wren’s colleague on the redevelopment committee, had visions of an Italianate capital of piazzas, boulevards, and an esplanade along the river—but to create this would be to ignore the rights of individual property holders, before which a British government (then, at least) was powerless. John Ogilby was commissioned to make a map, 52 inches to the mile, of the devastated area: ironically, the very first accurate plan of any city in the world was a record of what was not. Armed with it, the authorities painstakingly reconstituted the street-plan, even the huddled ho
use-plots, of the haphazard Roman-Medieval metropolis.

  Building went ahead at enormous speed. Most houses were up within four or five years. Churches took a little longer: one can barely imagine the stamina of Christopher Wren, negotiating steeple-shapes with 87 Boards of Overseers simultaneously. A decade of uniform building and careful regulation in a populous city gradually brought London’s fire risk under the dominion of the Law of Large Numbers. New outbreaks were no longer assumed to be the work of knavish Frenchmen or an angry God. They were scientific facts: exceptions that proved—that is, tested—a rule.

  In 1638, just before the Civil War, London had petitioned Charles I for the right to offer fire insurance, but the idea had been forgotten in the greater tumults of the realm. Now, however, everyone saw the need—so, in 1680, a private joint-stock company opened its office “at the back side of the Royal Exchange,” offering to insure London houses against fire for a premium of 2½ percent of yearly rent for brick houses and 5 percent for frame; rent was assumed to be 10 percent of the house’s value. The prime animator of this scheme was Nicholas Barbon, whose enterprise has left us the figures by which he estimated the risk his office could take on: in the fourteen years since the Great Fire, 750 houses had burned, with an average loss of £200. Seven hundred fifty houses, fourteen years—the average annual loss for all of London, insured or not, came to a little over £10,714 5s 8d hapenny. Let’s assume, roundly, that Barbon’s company insured half the City: 10,000 houses. Its likely annual payout would therefore be a little over £5,000, roughly 8 percent of the company’s subscribed capital—a sum that could almost be met out of contemporary bank interest alone. Yet each insured house was paying Barbon a yearly premium (assuming £200 represented the average insured loss) of 10s for brick, £1 for frame. Even if every house were brick, £5,000 a year would come in to the office—which would also be sufficient to pay almost all claims. Potential loss was doubly covered: the scheme represented total security with the chance of exceedingly gross profit.