I have recently been interested in statistics / misinformation /wrong interpretation of statistics / probabilities etc, and a dear friend knowing about this interest has sent me this amazing story, obviously an extract from some article or book that I am unable to locate to give credit to.
It gives me great pleasure to share it with my readers.
Jeanne was in her late 80s. Her husband had already passed away twenty years back. Her only daughter, Yvonne, had died much earlier at a relatively young age. Yvonne’s son, Frédéric, was raised by Jeanne herself. Unfortunately, like his mother, Frédéric too had a premature demise when he was killed in an automobile accident at a young age of 36.
All her life Jeanne had lived in Arles, France and had no wish to leave the place in her final years. However, living alone with no source of income, it was hard to support herself.
That’s when a forty-seven-year-old lawyer named André-François Raffray offered a deal to the old lady.
At age ninety and with no heirs, Jeanne agreed to sell her apartment to Raffray for the price of a low monthly subsistence payment of 2,500 francs. The contract said that the payments would stop upon her death, at which point she would be carried out and Raffray could move in.
Jeanne would thus have an ongoing source of cash to live on in her last years, and the lawyer would get an apartment cheaply, with no money down, in return for accepting the uncertainty as to when he would take possession.
If you were at Jeanne’s place, would you do that deal? I guess most people would be satisfied with the terms of such contract.
Would you do the deal if you were Raffray? Well, Raffray wasn’t rich. His offer to Jeanne wasn’t motivated by only charity in mind. Raffray figured that it was a reasonable bet.
The ninety-year-old French woman had already exceeded the French life expectancy by more than ten years. She could die any day. He was probably making arrangements for his own retirement.
The deal seemed mutually advantageous.
In 1975, ten years after the deal, Jeanne Calment celebrated her 100th birthday in good health. While the astonished attorney kept wondering where did he go wrong in his calculations, Ms. Calment continued her life comfortably. As another decade went by, Raffray turned sixty-seven and Jeanne qualified as supercentenarian (a term for those who go past the age of 110).
It took another decade for the attorney’s long wait came to an end. Unfortunately, it wasn’t the end he expected. In 1995, after making payments for more than 30 years, André-François Raffray died of cancer while Jeanne Calment lived on. At age 114 she even appeared briefly in the 1990 film Vincent and Me as herself, becoming the oldest actress ever to appear in a motion picture.
Raffary’s family inherited the agreement, i.e., they would be in line to get the apartment, but in order to do so they would have to assume the original deal, continuing the monthly payments until she died.
Jeanne Louise Calment turned out to be the biggest outlier in human history. She holds the record for the longest confirmed human lifespan. In 1995, a documentary film entitled Beyond 120 Years with Jeanne Calment, was made about her life.
Jeanne’s day of reckoning finally came on August 4, 1997, at the age of 122. Her age at death exceeded the lawyer’s age at this death by forty-five years!
Jeanne Louise Calment
I found this story in Bart Holland’s brilliant book What Are the Chances? Holland writes –
Obviously it turned out that this was not a good way for the lawyer to obtain an apartment “on the cheap”; in fact, he never occupied it. However, his expectation that it was a good deal was a reasonable one, based as it was on typical human life spans. He had no way of knowing that the woman with whom he has struck the deal would have such an exceptionally long life—indeed, the longest well-documented lifespan on record at that time. Nor did she have any way of anticipating her own longevity, although she did feel that the abundance of olive oil in her diet—and her moderate drinking of port—could have salutary effects (an opinion that most epidemiologists would agree with today).
In 1789, in his letter to Jean-Baptiste Leroy, Benjamin Franklin said, “In this world, nothing can be said to be certain, except death and taxes.”
Raffery bet on supposedly the certain thing, i.e., death of an extremely old woman. So where did the smart lawyer go wrong in his bet?
When he struck the deal, he observed that Jeanne had already lived ten years more than what French life expectancy tables predicted. But he didn’t know that the relevant issue was not whether she should be expected to die in minus ten years but that her life expectancy, given that she had already made it to ninety, was about six more years. Even when Ms. Calment reached 100, her life expectancy was still two more years. He probably had never heard of Bayes’s theory. But that was only a small part of his miscalculation.
Individual lifespans are unpredictable, but when data are collected from groups and analyzed en masse, regular patterns emerge.
His blunder was in taking the statistics and applying it to a sample size of one. He tried to play a game similar to life insurance business. But unlike the unlucky lawyer, the insurance company does not bet on one life but on millions.
The second mistake was that he agreed to a deal where the worst case could (and it did) cost him a significant portion of his net worth. He ended up paying Calment the equivalent of €140,000. That was more than double the apartment’s value.
Statistically, the deal was a very attractive bet for Raffary. However, statistics by definition apply to a group. Bigger the sample size, higher is the statistical significance of the pattern observed.
Ideally, he should have done few more such deals with a couple of more 90-year olds. But by putting all his money on an almost-sure-shot bet, he made the biggest financial mistake of his life.
Legendary investor, Howard Marks relates a funny story his father told him about a gambler who bet everything on a race with only one horse in it. How could he lose? “Halfway around the track, the horse jumped over the fence and ran away. Invariably things can get worse than people expect.”
Jeanne and Raffray’s story has a valuable lesson for investors.
Never bet the farm on a single stock no matter how certain you are about the outcome. You never know when the luck hands you the equivalent of a crazy horse or a supercentenarian.