Risk

Risk is quantified uncertainty. When you can assign probabilities to outcomes, you’re dealing with risk. When you can’t (when you don’t even know the possible outcomes) you’re dealing with true uncertainty. The distinction, formalized by Frank Knight in 1921, matters because different situations demand different approaches.

A casino faces risk. The odds are known. The house edge is calculable. Over thousands of hands, variance smooths out and expected value dominates. An insurance company faces risk. Actuarial tables predict claim rates. Premiums can be set to guarantee profit at the portfolio level.

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True uncertainty operates differently. What’s the probability that a new technology disrupts your industry? What’s the distribution of possible pandemic severities? These questions don’t have answers in the same sense. No reference class exists for the 2008 financial crisis or the COVID-19 pandemic. Each is, in important ways, unprecedented.

Finance tried to reduce uncertainty to risk. Models assumed asset returns followed known distributions. Value-at-risk calculations promised precise loss estimates. But the models failed precisely when they mattered most — in tail events that the models said were virtually impossible. The 2008 crisis exposed the difference between modeled risk and actual uncertainty.

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Expected value is the standard framework for risk. Multiply each outcome by its probability, sum across possibilities. Rational choice means maximizing expected value. But expected value assumes you can survive to reach the long run.

A 51% chance of doubling your wealth and 49% chance of losing everything has positive expected value. But go bankrupt once and you can’t play again. The Kelly criterion, ergodicity economics, and ruin theory all address this: strategies optimal across an ensemble of players can be ruinous for any individual playing through time.

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Nassim Taleb’s distinction between “Mediocristan” and “Extremistan” captures another divide. In Mediocristan, extreme observations don’t change the picture much: no single person’s height significantly affects the average height of a thousand people. In Extremistan, extremes dominate: one person’s wealth can exceed the rest combined.

Most intuitions about risk come from Mediocristan. Central limit theorems, normal distributions, regression to the mean. But many important domains are Extremistan: markets, wars, pandemics, bestsellers, startup outcomes. Applying Mediocristan thinking to Extremistan problems produces systematic blindness to tail risk.

Related: [[ergodicity]], [[kelly-criterion]], [[fat-tails]], [[risk-vs-uncertainty]]