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Wednesday, 29 September 2010

Dying to Invest

Pain and Gain

Death, they say, is a great leveller and historically it’s the case that this has been true. Back in the early part of the twentieth century the richest man in the world, Nathan de Rothschild, couldn’t stop tuberculosis taking his life. Today, of course, fifty cents could have saved him. On the other hand Steve Job’s vast wealth has helped him survive pancreatic cancer via the best medical treatment on the planet. Maybe, in economic terms, death isn’t what it was.

No matter, the Grim Reaper will eventually take Apple's saviour from us as he will us all. Sex is designed to mix genes to help humanity in its never-ending fight against microbes seeking to destroy us: infinite longevity would come at the price of eventual human annihilation, always assuming we didn't do the job ourselves first. In economics as in science, however, we advance one death at a time and death has been one of the most important subjects for economics: no pain, no gain.

Teeth, Suddenly

Way back in the seventeenth century the draper John Graunt alighted on the idea that he could analyse the death records – the bills of mortality – of London parishes to figure out the life expectancy of the English. Just like today there’s some evidence that the raw data wasn’t exactly reliable: so, for instance, in Westminster one person died of “piles”, two more simply stopped bothering and died of “lethargy” and a further eleven were overcome with “grief”. Most remarkably no less than 62 people simply died “suddenly” while 470 dropped dead from “teeth”.

What Graunt started and Edmund Halley – he of the comet, Newton’s Principia and other assorted ideas of genius – and Abraham de Moivre followed up on, was the fact that human life expectancy is generally predictable using age related statistics. This is the classical scientific method in action: get some data and analyse it, figure out how the data is distributed and then use this distribution to make a prediction – in this case, average life expectancy. As you’d expect people overwhelmingly die when they’re very young or very old – although our definition of “very old” is changing through time, as pension actuaries are scrambling to catch up and pension fund liabilities soar.

Reflexive Life Assurance

The idea that you can find some distribution that fits the data and then use this distribution to model the future is absolutely fundamental to science, economics and psychology. In general this works well in physics where the subject of study doesn’t think for itself but is less successful in economics and psychology where the tendency of people to change their behaviour in response to events makes it more difficult. As James Poterba points out in Annuities in Early Modern Europe this has always been true in life assurance:
“The English annuity sold in 1746 offers one of the first examples of an organized speculation designed to take advantage of flat-rate pricing … 35.6 percent of the 1746 nominees were Dutch. England’s chief government actuary … argued that the 1746 data suggested that Dutch syndicates had purchased a substantial share of the 1746 issue and that they had enrolled young Dutch girls as the nominees… The Dutch apparently appreciated what the English did not – that annuities based on younger lives were more valuable, and that women lived longer than men”.
Despite these and other adverse selection problems, the ongoing principles of life assurance remain more or less the same – people may change their behaviour in the short-term due to surprises but tend to revert to their normal behaviour over longer periods. It’s for this reason we struggle to make short-term predictions like where the market or a given stock will go tomorrow, but can be more confident over a period of years or decades.

Investing in an Outlier

At the same time we need to take into account major changes in the environment. So just as makers of buggy whips proved not to have great long-term investment potential in the late 1800’s, so life insurers who failed to update their data in the wake of the invention of antibiotics found themselves struggling. Even without such long-term structural changes there will still be individual outliers as the unfortunate Frenchman Andre-Francoise Raffray discovered, to his cost. He signed an agreement with a ninety year old woman, Jean Calment, to buy her house cheaply in return for a monthly life annuity.

Cunningly he'd used actuarial tables to ensure he was getting a good deal. Like so many investors, however, he assumed that because of a generally predictable truth – very old people die soon, stock markets always go up – he could rely on an individual example. Sadly for Raffray individual transactions always raise the possibility of an outlier and he was unlucky enough to find the ultimate one.

Calment lived to become the planet's oldest woman. She only gave up smoking at 119 when she couldn’t see well enough to light her smokes, and was still spritely almost up to her death at 122 when she was filling in her spare time recording popular CD's. Raffray died before her, and his family ended up paying Calment three times the value of her house in annuities. The lesson, of course, is that relying on individual investments, no matter how fundamentally sound, is dangerous. The other lesson is that old people tend to be cussedly unwilling to shuffle off their mortal coils when they know someone’s waiting for them to die.

Cholera No More

It’s not only individuals who can suddenly and unreasonably develop a nasty tendency to stay alive; sometimes whole groups of people may suddenly stop dying. Back in 1854’the Soho area of London was facing a cholera outbreak that eventually killed over 600 people. The lack of any real understanding of the causes of disease – an area which only really advanced in the twentieth century – should have meant that it was pretty much impossible to stop this.

However, John Snow, who should be popularly remembered as one of the heroes of the nineteenth century, figured out that the cholera distribution was clearly centred on one specific location, Broad Street in the Soho area. The London of the time relied on standpipes in the street to provide water for households; Snow’s data showed that the deaths were circling a single standpipe, on Broad Street and his follow-up research discovered that even deaths remote from the standpipe were actually caused by it.

In one fell swoop he was able to identify the specific cause of the outbreak – the standpipe – and home in on the transmission mechanism for the disease – drinking water. Of course, no one did anything very useful about it – the germ theory of disease took a long time to gain acceptance. Yet the simple act of having people wash their hands has contributed overwhelmingly to a reduction in deaths due to infectious diseases from about 30% of the total at the end of the nineteenth century to under 0.1% in the Western world today. Antibiotics have helped a bit too, of course.

Lessons from Death and Economics

Of course, this kind of change has modified the way actuaries determine life expectancy and these revisions are still going on, causing convulsions in the world of pensions. However, there’s hope for the pension funds yet: if the current epidemic of obesity continues the current cohort of middle aged people may end up outliving the next generation.

Yet the lessons of death and economics are more or less the same as those of investing. If we don’t learn the lessons of the past we run the risk of being gamed by clever Dutchmen armed with twelve year old girls, but if we do then there’s the ever-present possibility of some smart statistician figuring out how to change the odds against us in future. Worse still, sticking all your money in a concentrated set of investments opens you up to the possibility of a nasty outlier. It probably won’t happen but, if it does, it can ruin your life.

According to the ever fascinating CIA World Factbook people who live in Monaco live longest. Monaco has no income tax and no unemployment so, unsurprisingly, perhaps the way to live longest is to get rich first and retire to a tax haven. Still, perhaps even Andre-Francoise Raffray might have spotted the flaw in that argument ...

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