The Million Act
The Million Act of 1692 was a flawed life annuity scheme where pricing ignored age; Edmond Halley used birth and death statistics to compute expected values, establishing fair prices based on life expectancy.
THE IDEA
THE MILLION ACT
The notion of expected value started to come into mathematical focus in the mid-1600s, and by the end of that century, the idea was understood well enough to be used by practical scientists like Edmond Halley, the Astronomer Royal of England.* Yep, the comet guy! But he was also one of the first scientists to study the correct pricing of insurance, which in the reign of William III was a matter of critical military importance. England had thrown itself enthusiastically into war on the continent, and war required capital. Parliament proposed to raise the necessary funds via the “Million Act” of 1692, which aimed to raise a million pounds by selling life annuities to the population. Signing up for an annuity meant paying the Crown a lump sum in exchange for a guaranteed lifetime annual payout. This is a kind of life insurance in reverse; purchasers of such an annuity are essentially betting that they won’t die anytime soon. As a measure of the rudimentary state of the actuarial science of the time, the cost of the annuity was set without reference to the annuitant’s age\* — Figure unavailable in the source files. A lifetime annuity for a grandfather, likely to require funding for at most a decade, cost as much as one for a child.
Halley was scientist enough to understand the absurdity of the age-independent pricing scheme. He determined to work out a more rational accounting of the value of a lifetime annuity. The difficulty is that people don’t arrive and depart on a rigid schedule, as comets do. But by using birth and death statistics, Halley was able to estimate the probability of various life spans for each annuitant, and thereby to compute the expected value of the annuity: “It is plain that the purchaser ought to pay for only such a part of the value of the annuity, as he has chances that he is living; and this ought to be computed yearly, and the sum of all those yearly values being added together, will amount to the value of the annuity for the life of the person proposed.”
In other words: Grandpa, with his shorter expected life span, pays less for an annuity than Junior.
When to use it
Pricing life insurance premiums based on age and risk factors.
Evaluating the expected return of different investment portfolios.
Deciding whether to purchase an extended warranty based on failure probabilities and costs.
Calculating the fair price for a lottery ticket or gamble.
FROM THEORY TO EVERYDAY LIFE
In practice
Million Act Annuity Pricing
In 1692, the English government sold life annuities without considering age, so a grandfather and a child paid the same price. Halley used expected value to compute fair prices based on life expectancy.
Halley's Actuarial Method
Edmond Halley used birth and death statistics to estimate the probability of survival each year, then summed the discounted values to determine the correct annuity price.
A MOMENT TO REFLECT
Put it to work.
How does the concept of expected value apply to insurance purchasing decisions?
Can you think of a situation where ignoring expected value led to a poor decision?
How might you use expected value to evaluate a career choice or business investment?
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)