Within the space of four days last week, two of the most original, independent and influential thinkers in the fields of mathematics and economics passed away. The first was Maurice Allais, aged 99 in Paris, and the other Benoît Mandelbrot, aged 85 in his adopted United States (he too coincidentally was originally a Frenchman).
 Allais will be remembered for the “Allais Paradox”, an economic experiment in 1953 which debunked the popularly held view that humans always act to maximise their expected utility (or gains). He proved that under empirical experimental conditions, the theory of maximising expected utility did not apply in realistic decisions under risk and uncertainty. This has been proved since in multiple real world experiments. The most famous of which was conducted by Daniel Kahneman and Amos Tversky, culminating in “Prospect Theory”, which went on to prove that humans value losses approximately twice as much as gains.
Allais won the Nobel Price for Economics in 1988, for his work on efficient utilization of resources and markets. However, the most important observation about the life of Allais was that most of his writing was limited to French journals, thus denying at least a decade of English-speaking economists from studying an alternate theory. Many of Allais work was independently rediscovered in the English speaking world, most notably by Paul Samuelson and Edmund Phelps.
Allais’ proof that people care more about losing money than making money has now entered the realm of Neuroscience with interdisciplinary research efforts being directed to understand the true meaning of investment risk. Recently, this effort has been expanded to include the role of genetics in decision-making under uncertainty.
Allais’ other great contribution was his own wide interests in a range of subjects. While his economic models made him famous, his interest physics caused controversy when he questioned and suggested weaknesses in Einstein’s Theory of Relativity (which came to be dubbed the Allais effect). The wider interest made him a true interdisciplinary student, as opposed to the siloed world of research and thinking that currently takes place in both business and academia.
Mandelbrot was the father of fractal geometry – finding underlying patterns in roughness and irregularity – and was a key figure in the broader field of chaos theory. Mandelbrot had enormously wide interests. For over 60 years he applied his findings to physics, biology and economics, publishing devastating critiques of modern mathematical finance.
A fractal is essentially a fragmented shape whose structure remains the same however much it is blown up or scaled down. Fractal analysis has become a powerful tool to measure and model apparently chaotic shapes and patterns. His most famous creation is the “Mandelbrot set”, a mathematical creation of infinite complexity.
But it was his work in mathematical finance that should deserve special attention by any serious student of investment markets and finance. In 2004 he published “The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward” – a devastating attack on the failure of mainstream economists and mathematicians to understand the likelihood of wild swings in prices and the risk of financial disaster.
Mandelbrot it is reported, felt vindicated by subsequent events, such as the near collapse of the global financial system in 2008. Mandelbrot disproved two caveats on which most concepts on modern investment analysis and portfolio construction are based. First to go was the belief that outcomes in investment markets take on a bell-curve distribution (meaning that observations tend to be cluttered around the average). The second to be decimated was that market prices are independent of each other (thus what happened yesterday in the stock market has no bearing on performance today).
In the process, Mandelbrot shot down the pillars of modern finance, starting from the Efficient Market Hypothesis (EMH), Black-Scholes Option Pricing theory and the Capital Asset Pricing Model (CAPM).
The works of both these men will rightfully live well beyond their lifetime. What they articulated over their long careers have yet to become mainstream, because it is emotionally taxing for people to overcome decades of belief. After all it took more than 200 years for Europeans to admit that the earth revolved around the sun, and not the other way around. The ivory towers, diploma mills and professional bodies will hang on to preaching the defunct mathematics of the EMH/CAPM variety. Both these men were outsiders in the world of finance, and were often not welcome due to their disestablishmentarian views. For that alone, the investment world will miss them dearly.
(Kajanga is an Investment Specialist based in Sydney, Australia. You can write to him at kajangak@gmail.com). |
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