Understanding Fat Tail Returns

Much statistical analysis in finance depends on the assumption that variables have normal distributions. This assumption is far from correct. As a result, as Nassim Nicholas Taleb has rightly pointed out, most statistical results in finance are wrong. Now, a disciple of Taleb has tried to extend Taleb’s research by relating it to an obscure mathematical concept. He is successful in one area: the study of unequal distributions of wealth. In others, such as portfolio optimization and explaining insurance, less so.

I was recently sent two messages about a researcher at the London Mathematical Laboratory named Ole Peters whom I had interviewed in 2016. One was a link to a December 11 Bloomberg article titled, “Everything We’ve Learned About Modern Economic Theory Is Wrong,” and the other to the 2019 Nature Physics paper on which the article was based.i The Bloomberg article said that Peters had, “won over two noted thinkers in the world of finance – Nassim Nicholas Taleb and Michael Mauboussin.” I have enormous respect for Professor Taleb, and a friend of mine knows Mauboussin well and has enormous respect for him.

I looked forward to reading Peters’ paper.

But when I read it, my first impression was that it was typical of many finance journal articles that I have encountered over the years: a presentation of mathematics, followed by overblown conclusions that are not well-grounded in the math – what Nobel Prize winning economist Paul Romer has called “mathiness.” I also made an initial error in thinking that some of the math was wrong.

However, Taleb’s backing made me think twice – and three times, then more times, about my first impression. It led me to read all of Peters’ papers that were referenced in his 2019 paper, as well as his other papers that those papers themselves referenced.

My overall impression was that there were some interesting things, but what Peters brands as “ergodicity economics” is overhyped, especially the idea that it tells us that “everything we’ve learned about modern economic theory is wrong.” And the implication in the Nature Physics article that it has huge practical implications is not borne out in Peters’ other articles that attempt to apply it.