Against the Gods: The Remarkable Story of Risk (18 page)

In 1690 a local scientist and clergyman named Caspar Naumann
went through the Breslaw records with a view to "disproving certain
current superstitions with regard to the effect of the phases of the moon
and the so-called `climacteric' years on health." Naumann sent the
results of his study to Leibniz, who in turn sent them on to the Royal
Society in London. 16

Naumann's data soon attracted the attention of Halley. Halley was
then only 35 years old but already one of England's most distinguished
astronomers. Indeed, he was responsible for persuading Isaac Newton in
1684 to publish his Principia, the work in which Newton first set forth
the laws of gravity. Halley paid all the costs of publication out of his own
modest resources, corrected the page proofs, and put his own work
aside until the job was done. The historian James Newman conjectures
that the Principia might never have appeared without Halley's efforts.

Widely recognized as a child genius in astronomy, Halley carried
his 24-inch telescope with him when he arrived as an undergraduate at
Queen's College, Oxford. He left Oxford without receiving a degree,
however, and set off to study the heavens in the southern hemisphere;
the results of that study established his reputation before he was even 20 years old. By the age of 22, he was already a member of the Royal
Society. Oxford turned him down for a professorship in 1691 because
he held "materialistic views" that did not match the religious orthodoxy of Oxford. But the dons relented in 1703 and gave him the job.
In 1721, he became Royal Astronomer at Greenwich. Meanwhile, he
had received his degree by the King's command.

Halley would live to the age of 86. He appears to have been a jolly
man, with an "uncommon degree of sprightliness and vivacity," and
had many warm friendships that included Peter the Great of Russia. In
1705, in his pathbreaking work on the orbits of comets, Halley identified a total of 24 comets that had appeared between the years 1337 and
1698. Three seemed to be so similar that he concluded that all three
were a single comet that had appeared in 1531, 1607, and 1682.
Observations of this comet had been reported as far back as 240 BC.
Halley's prediction that the comet would reappear in 1758 electrified
the world when the comet arrived right on schedule. Halley's name is
celebrated every 76 years as his comet sweeps across the skies.

The Breslaw records were not exactly in Halley's main line of work,
but he had promised the Royal Society a series of papers for its newly
established scholarly journal, Transactions, and he had been scouting
around for something unusual to write about. He was aware of certain
flaws in Graunt's work, flaws that Graunt himself had acknowledged,
and he decided to take the occasion to prepare a paper for Transactions
on the Breslaw data by trying his hand at the analysis of social rather than
heavenly statistics for a change.

Graunt, lacking any reliable figure for the total population of
London, had had to estimate it on the basis of fragmentary information.
He had numbers and causes of deaths but lacked complete records of
the ages at which people had died. Given the constant movement of
people into and out of London over the years, the reliability of Graunt's
estimate was now open to question.

The data delivered by Leibniz to the Royal Society contained
monthly data for Breslaw for the years 1687 through 1691, "seeming to
be done," according to Halley, "with all the Exactness and Sincerity
possible"; the data included age and sex for all deaths and the number
of births each year. Breslaw, he pointed out, was far from the sea, so
that the "Confluence of Strangers is but small." Births exceeded the
"Funerals" by only a small amount and the population was much more stable than London's. All that was lacking was a number for the total
population. Halley was convinced that the figures for mortality and
birth were sufficiently accurate for him to come up with a reliable estimate of the total.

He found an average of 1,238 births and 1,174 deaths a year over
the five-year period, for an annual excess of about 64, which number,
he surmised, "may perhaps be balanced by the Levies for the Emperor's
Service in his Wars." Directing his attention to the 1,238 annual births
and examining the age distribution of those who died, Halley calculated
that "but 692 of the Persons born do survive Six whole Years," a much
smaller proportion than Graunt's estimate that 64% of all births survived
beyond six years. About a dozen of the deaths in Breslaw, on the other
hand, occurred between the ages of 81 and 100. Combining a variety
of estimates of the percentage of each age group who die each year,
Halley worked back from the age distribution of the people dying
annually to a grand estimate of 34,000 for the town's total population.

The next step was to devise a table breaking down the population
into an age distribution, "from birth to extream Old Age." This table,
Halley asserts, offered manifold uses and gave "a more just Idea of the
State and condition of Mankind, than any thing yet extant that I know
of." For example, the table provided useful information on how many
men were of the right age for military service-9,000-and Halley
suggested that this estimate of 9/34ths of the population could "pass
for a Rule for other places."

Halley's entire analysis embodies the concept of probability and ultimately moves into risk management. Halley demonstrates that his table
"shews the odds" that a "Party" of any given age "does not die in a
Year." As an illustration, he offers the 25-year age group, which numbered 567, while the 26-year age group numbered 560. The difference
of only 7 between the two age groups meant that the probability that a
25-year-old would die in any one year was 7/567, or odds of 80-to-1 that
a 25-year-old would make it to 26. Using the same procedure of
subtraction between a later age and a given age, and taking the given age
as the base, the table could also show the odds that a man of 40 would
live to 47; the answer in this instance worked out to odds of 5 1/2-to-1.

Halley carried the analysis further: "[I]f it be enquired at what number Years, it is an even Lay that a Person of any Age shall die, this Table
readily performs it." For instance, there were 531 people aged 30, and half that number is 265. One could then look through the table for the
age group numbering 265, which appeared to be between 57 and 58.
Hence, it would be "an even Wager that ... a Man of 30 may reasonably expect to live between 27 and 28 years."

The next level of Halley's analysis was the most important of all.
The table could be used to reckon the price of insuring lives at different ages, "it being 100 to 1 that a man of 20 dies not in a year, and but
38 to 1 for a Man of 50 Years of Age." On the basis of the odds of
dying in each year, the table furnished the necessary information for
calculating the value of annuities. At this point Halley launches into a
detailed mathematical analysis of the valuation of annuities, including
annuities covering two and three lives as well as one. He offers at the
same time to provide a table of logarithms to reduce the "Vulgar
Arithmetick" imposed by the mass of necessary calculations.

This was a piece of work that was long overdue. The first record
we have of the concept of annuities dates back to 225 AD, when an
authoritative set of tables of life expectancies was developed by a leading Roman jurist named Ulpian. Ulpian's tables were the last word for
over 1400 years!

Halley's work subsequently inspired important efforts in calculating
life expectancies on the Continent, but his own government paid no
attention to his life tables at the time. Taking their cue from the Dutch
use of annuities as a financing device, the English government had
attempted to raise a million pounds by selling annuities that would pay
back the original purchase price to the buyer over a period of 14
years-but the contract was the same for everyone, regardless of their
age! The result was an extremely costly piece of finance for the government. Yet the policy of selling annuities at the same price to everyone continued in England until 1789. The assumption that the average
life expectancy at birth was about 14 years was at least an improvement
over earlier assumptions: in 1540, the English government had sold
annuities that repaid their purchase price in seven years without regard
to the age of the buyer.'7

After the publication of Halley's life tables in Transactions in 1693,
a century would pass before governments and insurance companies
would take probability-based life expectancies into account. Like
his comet, Halley's tables turned out to be more than a flash in the sky
that appears once in a lifetime: his manipulation of simple numbers formed the basis on which the life-insurance industry built up the data
base it uses today.

One afternoon in 1637, when Graunt was just seventeen years old
and Halley had not yet been born, a Cretan scholar named Canopius sat
down in his chambers at Balliol College, Oxford, and made himself a
cup of strong coffee. Canopius's brew is believed to mark the first time
coffee was drunk in England; it proved so popular when it was offered
to the public that hundreds of coffee houses were soon in operation all
over London.

What does Canopius's coffee have to do with Graunt or Halley or
with the concept of risk? Simply that a coffee house was the birthplace
of Lloyd's of London, which for more than two centuries was the most
famous of all insurance companies.18 Insurance is a business that is
totally dependent on the process of sampling, averages, independence
of observations, and the notion of normal that motivated Graunt's
research into London's population and Halley's into Breslaw's. The
rapid development of the insurance business at about the time Graunt
and Halley published their research is no coincidence. It was a sign of
the times, when innovations in business and finance were flourishing.

The English word for stockbroker-stock jobber-first appeared
around 1688, a hundred years before people started trading stocks
around the Buttonwood tree on Wall Street, New York. Corporations
of all kinds suddenly appeared on the scene, many with curious names
like the Lute-String Company, the Tapestry Company, and the Diving
Company. There was even a Royal Academies Company that promised
to hire the greatest scholars of the age to teach the 2,000 winners of a
huge lottery a subject of their own choosing.

The second half of the seventeenth century was also an era of burgeoning trade. The Dutch were the predominant commercial power of
the time, and England was their main rival. Ships arrived daily from
colonies and suppliers around the globe to unload a profusion of products that had once been scarce or unknown luxuries-sugar and spice,
coffee and tea, raw cotton and fine porcelain. Wealth was no longer
something that had to be inherited from preceding generations: now it could be earned, discovered, accumulated, invested-and protected
from loss.

Moreover, toward the end of the century the English had to
finance the sequence of costly wars with the French that had begun
with Louis XIV's abortive invasion of England in May 1692 and ended
with the English victory at Blenheim and the signing of the Treaty of
Utrecht in 1713. On December 15, 1693, the House of Commons
established the English national debt with the issue of the million
pounds of annuities mentioned above. In 1849, Thomas Babington
Macaulay, the great English historian, characterized that momentous
event with these resounding words: "Such was the origin of that debt
which has since become the greatest prodigy that ever perplexed the
sagacity and confounded the pride of statesmen and philosophers."19

This was a time for London to take stock of itself and its role in the
world. It was also a time to apply the techniques of financial sophistication demanded by war, a rapidly growing wealthy class, and rising overseas trade. Information from remote areas of the world was now of
crucial importance to the domestic economy. With the volume of
shipping constantly expanding, there was a lively demand for current
information with which to estimate sailing times between destinations, weather patterns, and the risks lurking in unfamiliar seas.

In the absence of mass media, the coffee houses emerged as the primary source of news and rumor. In 1675, Charles II, suspicious as
many rulers are of places where the public trades information, shut the
coffee houses down, but the uproar was so great that he had to reverse
himself sixteen days later. Samuel Pepys frequented a coffee house to
get news of the arrival of ships he was interested in; he deemed the
news he received there to be more reliable than what he learned at his
job at the Admiralty.

The coffee house that Edward Lloyd opened in 1687 near the
Thames on Tower Street was a favorite haunt of men from the ships
that moored at London's docks. The house was "spacious ... wellbuilt and inhabited by able tradesmen," according to a contemporary
publication. It grew so popular that in 1691 Lloyd moved it to much
larger and more luxurious quarters on Lombard Street. Nat Ward, a
publican whom Alexander Pope accused of trading vile rhymes for
tobacco, reported that the tables in the new house were "very Neat and shined with Rubbing." A staff of five served tea and sherbet as
well as coffee.