The Problem of the Upper Bound
Taleb argues that an unknown upper cutoff offers little practical protection when modeling a fractal variable. Choosing an arbitrary cap can hide the effects of extreme outcomes.
THE IDEA
The Problem of the Upper Bound
Some people have researched and accepted the fractal “up to a point.” They argue that wealth, book sales, and market returns all have a certain level when things stop being fractal. “Truncation” is what they propose. I agree that there is a level where fractality might stop, but where? Saying that there is an upper limit but I don’t know how high it is, and saying there is no limit carry the same consequences in practice. Proposing an upper limit is highly unsafe. You may say, Let us cap wealth at $150 billion in our analyses. Then someone else might say, Why not $151 billion? Or why not $152 billion? We might as well consider that the variable is unlimited.
When to use it
Risk management: evaluating tail risks in financial markets where losses can be unbounded.
Startup growth: Check whether a market-size cap in a growth model has a defensible basis.
Wealth inequality analysis: using arbitrary caps distorts understanding of extreme wealth.
Insurance: Assess aggregate exposure without assuming that the largest past claim is the largest possible claim.
FROM THEORY TO EVERYDAY LIFE
In practice
Wealth cap arbitrary
If you set a maximum wealth cap at $150 billion for analysis, but the true maximum might be $500 billion or more, your model will underestimate the impact of extreme wealth. The exact cap is arbitrary and changes with economic growth.
Market crash predictions
Assuming that a stock-market decline cannot exceed 20% excludes larger falls from the analysis. An arbitrary modeling cap does not establish a real bound on the quantity being modeled.
A MOMENT TO REFLECT
Put it to work.
In what situations might assuming an upper bound lead to catastrophic errors?
How can you identify when a variable might be effectively unbounded?
What are the practical consequences of assuming a limit on a fractal system?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)