Learn English – the difference between “risk” and “uncertainty”

Risk and Uncertainty have a specialized meaning in the financial world.

The Wikipedia article on Risk has an extended quote from Risk, Uncertainty, and Profit by Frank Knight (1921). He implies that risk is sometimes mathematically quantifiable, but uncertainty is never quantifiable.

By Knight's reasoning, you would use risk when examining a stock's previous return to predict its future return. If a stock were volatile in the past, one might expect that it would be more volatile in the future and thus have a higher risk. If the price changes of a stock were small and predictable, then one might expect that the price changes would continue to be less volatile in the future and thus have a lower risk.

There is a mathematical concept called expected value that can be used to quantify the risk. It may be based on a probability (such as a coin turning up heads 50% of the time). It may instead be based on statistics (using a concept of variance, which is related to standard deviation). Financial risk is based on expected value, and is quantifiable.

In contrast, by Knight's reasoning, uncertainty would not be quantifiable. The returns of both the volatile and the steady stock in the future are neither knowable nor quantifiable, so the returns are uncertain.

The face that turns up on a die before it is cast is unknowable and therefore uncertain. The probability that it will turn up a 1, 2, or 3 is quantifiable (it will happen in half the cases). So there is a known risk in casting the die and winning $10 if it turns up 1, 2, or 3 while losing $10 if it turns up 4, 5, or 6.