Engines of Our Ingenuity

No. 2603
CORRELATION

by Andrew Boyd

Today, eggs and baskets. The University of Houstonís College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

"Donít put all your eggs in one basket." Itís great advice, especially when it comes to money. But thereís a catch — a catch surfaced by Nobel laureate Harry Markowitz. And it can lead to big trouble.

image of a women holding eggs in a basket

To understand the catch, letís play a game. Weíll flip a coin. If it comes up heads, I pay you two million dollars. Not bad. But if it comes up tails, you pay me one million dollars. Itís still a great deal for you — my two million against your one million — but it carries a lot of risk. If you lose, youíll have a huge debt to pay. The risk is so high many of us wouldnít want to play, and shouldnít.

image of both sides of a quarter

But the risk can be reduced with one small trick. Donít flip the coin once with a one-million-or-two-million outcome. Instead, convince me to flip the coin a million times with a one-dollar-or-two-dollar outcome. Now youíre not putting all your eggs in one basket. And with a little mathematics, we can make some very strong predictions.

With this new game, itís more likely to snow in Houston for the entire month of August than for you to lose any money. And with a 99.99999 percent chance, youíll win half a million dollars, give or take a couple of thousand. The chance of a two million dollar jackpot has evaporated. But youíve assured yourself of a smaller win while reducing your risk of loss to effectively nothing.

The catch that makes the game work is that the coin flips arenít correlated. When I flip a coin once, it has no effect on the outcome of the next flip, and thatís very important. Suppose instead we play with a two-headed or two-tailed coin but donít know which at the start. Then once we see the first flip, weíll know itís either all heads or all tails from there on out. The flips are now perfectly correlated, and youíre back to winning two million or losing one million, with nothing in between. You havenít reduced your risk at all.

image of a two headed coin

Thanks in part to the work of Harry Markowitz, good financial analysts worry incessantly about the correlation of their coin flips — what amounts to the assets they buy. They donít want to buy a single asset; they want to buy a portfolio of assets such that when one fails, it doesnít portend failure in the others. If analysts arenít careful about the price correlation of their assets, they arenít reducing their risk — or at least not by as much as they think. So how do financial analysts determine the price correlation of two assets? Itís not nearly as easy as looking at the two sides of a coin. Analysts have a wealth of data and powerful statistical tools, but ultimately humans must interpret the results. And as we know, human judgment isnít always perfect.

Iím Andy Boyd at the University of Houston, where weíre interested in the way inventive minds work.

(Theme music)


Notes and references:

One of the factors that contributed to the 2008 financial disaster was a failure to appreciate the correlation between defaults on individual home mortgages. If defaults were truly uncorrelated, then individually risky mortgages could, in fact, be relatively safe when bundled together — just like the flipping of a coin with heads on one side and tails on the other. But the failures proved to be highly correlated, and quantitative analysts as a group failed to understand how correlated they were.

The picture of the eggs is from Wikimedia Commons. The pictures of the quarters are by E. A. Boyd.


The Engines of Our Ingenuity is Copyright © 1988-2010 by John H. Lienhard.