The Illusion of Probability

Did you spot the fallacy in yesterday’s post?

Here it is: It is misleading of me—and frankly of the whole financial profession—to assign probabilities to levels of confidence. How do you know that it’s 50% probable that you’ll be able to spend this amount or that? Nobody knows the future. And nobody even knows how to assign probabilities to the future. Nonetheless, I will continue to do so, because it serves a useful purpose.

I think I better explain myself.

When you flip a coin, you don’t know what the outcome will be—heads or tails. But at least you know that it’s 50% likely to be heads. You have some certainty about your uncertainty. But with financial matters, we don’t even have that. We can pretend to assign probabilities to various outcomes, e.g., “the stock market is 50% likely to return 9% or more over the long-term.” We might glean these false probabilities from the market’s historical performance. Or we might glean them from sophisticated modeling employing Monte Carlo simulations (which are, at bottom, based on historical performance). But the fact is that the financial markets simply don’t follow the same neat laws of probability as coin flips do.

In his eye-opening book, The (Mis)behavior of Markets, the eminent mathematician (and some-time economist) Benoit Mandelbrot totally debunks the illusion that market prices bear any resemblance to coin flips. Rather than following the same neat laws of probability, markets follow their own logic. Millions of people buying and selling, each motivated by their own needs, opinions, and prejudices, create a turbulence that can’t be explained by the same rules that govern coins and dice. See 2008 for an example.

(By the way, Mandelbrot has earned his credibility. He is one of the founders of chaos theory, and the discoverer of the “Mandelbrot set.” Should you happen to get a case of the visual munchies, gaze at a picture of the Mandelbrot set for a while. You can see an animation of it in Wikipedia here. Scroll down to the heading labeled "Zoom Animation.")

So if we can’t legitimately assign probabilities to financial outcomes, why did I do that in yesterday’s post? And in January 14’s post? What kind of double-talk is this? I think assigning fake probabilities serves a useful purpose. It provides a basis for comparison. We can all agree that “50% confident” is better than “25% confident.” But just don’t fall for the illusion of precision. I can’t legitimately say that “50% confident” is twice as confident as “25% confident.” The numbers are just not that meaningful.