Risk vs. Uncertainty

Risk
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Risk is the potential that a chosen action or activity (including the choice of inaction) will lead to a loss (an undesirable outcome). The notion implies that a choice having an influence on the outcome exists (or existed). Potential losses themselves may also be called "risks". Almost any human endeavor carries some risk, but some are much more risky than others.

Risk versus uncertainty:

In his seminal work Risk, Uncertainty, and Profit, Frank Knight established the distinction between risk and uncertainty.

“Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. The term "risk," as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, in their causal relations to the phenomena of economic organization, are categorically different. The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We accordingly restrict the term "uncertainty" to cases of the non-quantitive type.”


Thus, Knightian uncertainty is immeasurable, not possible to calculate, while in the Knightian sense risk is measurable.

Another distinction between risk and uncertainty is proposed in How to Measure Anything: Finding the Value of Intangibles in Business and The Failure of Risk Management: Why It's Broken and How to Fix It by Doug Hubbard:

Uncertainty: The lack of complete certainty, that is, the existence of more than one possibility. The "true" outcome/state/result/value is not known.

Measurement of uncertainty: A set of probabilities assigned to a set of possibilities. Example: "There is a 60% chance this market will double in five years"

Risk: A state of uncertainty where some of the possibilities involve a loss, catastrophe, or other undesirable outcome.
Measurement of risk: A set of possibilities each with quantified probabilities and quantified losses.
Example: "There is a 40% chance the proposed oil well will be dry with a loss of $12 million in exploratory drilling costs".

In this sense, Hubbard uses the terms so that one may have uncertainty without risk but not risk without uncertainty. We can be uncertain about the winner of a contest, but unless we have some personal stake in it, we have no risk. If we bet money on the outcome of the contest, then we have a risk. In both cases there are more than one outcome. The measure of uncertainty refers only to the probabilities assigned to outcomes, while the measure of risk requires both probabilities for outcomes and losses quantified for outcomes.

Risk attitude, appetite and tolerance:

The terms attitude, appetite and tolerance are often used similarly to describe an organization's or individual's attitude towards risk taking. Risk averse, risk neutral and risk seeking are examples of the terms that may be used to describe a risk attitude. Risk tolerance looks at acceptable/unacceptable deviations from what is expected. Risk appetite looks at how much risk one is willing to accept. There can still be deviations that are within a risk appetite.

Gambling is a risk-increasing investment, wherein money on hand is risked for a possible large return, but with the possibility of losing it all. Purchasing a lottery ticket is a very risky investment with a high chance of no return and a small chance of a very high return. In contrast, putting money in a bank at a defined rate of interest is a risk-averse action that gives a guaranteed return of a small gain and precludes other investments with possibly higher gain. The possibility of getting no return on an investment is also known as the Rate of Ruin.