Risk and uncertainty
What is the difference between outcomes with known odds and outcomes whose odds we simply do not know?
In plain words
Risk describes outcomes whose odds can be estimated from history or data, like a known probability distribution of returns. Uncertainty describes outcomes for which no reliable odds exist, because the situation is new or the drivers are unmeasurable. Many markets carry both at once.
Why it matters
Sizing and hedging usually rely on estimated odds, so uncertainty is the harder problem to plan for. A position sized from a measured volatility can still be caught by a week whose range and direction were not represented in the sample used to set that volatility.
In a real week: ETH, week of 13 April 2020
For the week starting 13 April 2020, ETH rose 13.54%, with a range of 27.78% and annualised realised volatility of 87.2%. Its return ranked at the 88.0 percentile against 113 weeks of history, while the price sat 49.69% below its 52-week high. The return sat at the 88.0 percentile of that history, so a move of this size had precedent; the measured odds describe how large swings can be, not which way the week would go.
A common mistake
Treating measured volatility as if it covered all future outcomes. It describes past swings; it cannot price events that have no precedent in the data window.