World Futures: Statistics (And Probability) – Part Six

Los Alamos World Futures Institute

In the previous column we identified several areas where statistics play a major role in the decision making and management of a field or industry. Moving to greater detail, a good place to start is insurance, something we all purchase based on fear or required by law.

In 1653, Lorenzo de Tonti “invented” an investment plan (scheme?) that bears his name, the tontine. It was a way for an organization (government) to raise money, linked to the lives of the investors. Each investor received an annual dividend until he or she died and then the dividend was reapportioned among the surviving investors.

Let us say the investment was $1,000 per investor and 100 investors invested. The last investor would receive dividends based on $100,000 until his or her death. At that time, the dividends ceased and the invested money disappeared. While every tontine had its own details and variations, in 1792, the Tontine Coffee House was built on Wall Street in New York City. It was the first home of the New York Stock.

The tontine deals with life and death of individuals and the creator of the imaginary tontine described above benefits from early death of the participants. In contrast, life insurance companies are betting you will live a long time and that they will receive fee income on a regular, continuing basis. Customers are charged based on actuarial statistics of expected lifetime. These companies are heavily dependent on actuarial science involving statistics, risk (probability), mathematics, finance, economics and computer science. The insurance companies receive money for a contractual obligation that has as associated price tag.

But what does the insurance company do with the money? Whatever it wants to do as long as it meets its obligations (this includes mutual companies albeit the stockholders are the insured).

The insurance company is betting on you living, which is controlled by probability. The probabilities are estimated based on statistical data of population size, deaths and age at death. If you are 45, the insurance company can estimate your projected lifetime and calculate a premium. But it does this under the assumption that large numbers of 45 year olds will also place bets. It is playing the odds. You, in contrast, are betting on a single outcome in the gambling hall of life.

There are many variations of life insurance policies such as term life based on your current age and for a given period of time. While the statistical calculations change, the company is still betting that you will live. But what if you pay for insurance up to a certain age after which you receive a “pension” based on your investment? When you pass away, the contract is terminated, perhaps with a lump sum settlement, based on the statistics of the numbers.
Life insurance companies offer a variety of products with a myriad of terms and conditions. For simplicity, let us assume a whole life policy for $10,000 payable on death to a specified beneficiary. You make monthly payments of a fixed amount until you reach the age of 65, after which you receive a small “dividend” monthly. Now look at the chart below reflecting data from the Social Security Administration.

For a cohort of 100,000 people born at time zero it shows deaths per year per age. There is a spike at year one because of infant deaths during the first year of life and a peak around 85.

Per the actual data, 19,723 members of the cohort will die by the end of year 65 or before their 65th birthdays. This statistic affects the odds of the gamble. The insurance company is counting on 80 percent of its customers living. But wait a minute. After the member’s 65th birthday, it has to pay a dividend. Now it is in the best interest of the insurance company for the member to die early. While I do not believe that insurance companies want early deaths (accurate statistics are on their side), it is part of the actuarial calculations that must be made.

The values used to create the chart are government data published online ( The values are also continuously changing. In social security, we must invest from the day we start working until we reach a certain age. Let us assume it’s 65. It is sort of like a tontine that takes 50 years to buy into.

Then we receive a monthly dividend based on our investment. Great if the statistics remain constant. But what if the curve shifts to the right two or three years? Do the numbers continue to add up? Simply put, NO. But what do you do, individually and collectively. Pension plans are similar in model to social security. Can pension plans go broke? Yes. The pain and burden, however, remain with the worker. Can social security go broke? We hear about that possibility today. The pain and burden will again reside with the worker – us.

Yet we are the government. And as the government, we are making collective decisions based on statistics. Are we and our elected officials qualified? Do we even know the difference between the mean, mode and median?

Death Chart. Courtesy image

Till next time….

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