Where does risk collide?

The variance of a portfolio's return, and nothing else: Markowitz's 1952 investor chooses among portfolios by expected return and variance alone, and diversification works because covariances can cancel. Sharpe's capital asset pricing model split that variance into a part the market prices, beta, and a part it does not. Upside deviation counts as risk exactly as much as downside. This is the meaning in which a stock that only ever goes up by unpredictable amounts is risky.[1][2]

Unit

An asset or portfolio, over a return distribution

Recovery means

Not applicable, drawdown recovery is a separate, non-variance measure

Measured by

Standard deviation of returns; beta; value at risk as a later, loss-oriented alternative

Knight in 1921 reserved risk for situations whose outcome probabilities are known or estimable and uncertainty for those where they are not, arguing that only the second yields profit. Kahneman and Tversky kept the known-probability setting and replaced the utility function with a value function that is concave for gains, convex for losses, and steeper for losses, so a gamble's riskiness depends on where the reference point sits. Risk is a property of the choice situation; risk attitude is a property of the curve.[3][4]

Unit

A choice among prospects with known probabilities

Recovery means

Not applicable, loss aversion is about the reference point, not returning to it

Measured by

Certainty equivalents; lottery choices; estimated loss-aversion coefficient

Kaplan and Garrick's 1981 answer to the question of what risk is: the complete set of triplets (what can go wrong, how likely it is, and what the consequences are) with a probability curve over each. Risk is not a number but a curve, and collapsing it to expected loss throws away the shape that matters for rare, severe events. ISO 31000 later generalized the definition to the effect of uncertainty on objectives, which admits positive effects and does not require a hazard at all; the two definitions are cited together and do not agree.[5][6]

Unit

A system or activity, over its failure scenarios

Recovery means

Return to a safe state after an initiating event; resilience as a design property

Measured by

Probabilistic risk assessment; fault and event trees; risk matrices; F–N curves

The expected loss of a function over the true data distribution. Since the distribution is unknown, Vapnik's empirical risk minimization chooses the function that minimizes the average loss on the training sample, and statistical learning theory asks when the empirical risk converges to the true risk uniformly over a function class. The word carries no connotation of danger: a classifier's risk is its error rate under the loss you chose, and minimizing it is the whole learning problem. This is closest to the finance meaning in being a functional of a distribution and furthest from it in being an expectation, not a variance.[7]

Unit

A predictor, under a loss, over a distribution

Recovery means

Not applicable, generalization gap, not recovery

Measured by

Empirical risk on training data; held-out estimate of true risk; VC-dimension bounds

What laypeople mean when they call something risky, which Slovic showed is organized along two factors (dread (catastrophic, uncontrollable, involuntary) and unknown (unobservable, delayed, new to science)) and correlates weakly with expert estimates of annual fatalities. Weber, Blais, and Betz then showed that risk-taking is not a single trait: a person's willingness to take financial risks says little about their willingness to take health, social, or recreational ones, and the differences trace to perceived risk and benefit in each domain. Risk here is a judgment, and the judgment is domain-specific.[8][9]

Unit

A person, about a hazard or an activity in a domain

Recovery means

Not applicable, perceived risk shifts with events and framing, not with repair

Measured by

Psychometric paradigm ratings of hazards; DOSPERT likelihood, perceived-risk, and expected-benefit subscales

Three lines of work share the field. Risk propensity is a disposition to take or avoid risks, and Stewart and Roth's meta-analysis found entrepreneurs modestly higher on it than managers, with the gap larger for growth-oriented founders. At the firm level, risk taking is one of the behaviours Miller in 1983 used to define the entrepreneurial firm, and one of the five dimensions of entrepreneurial orientation that Lumpkin and Dess clarified in 1996: a firm's willingness to commit resources to projects whose outcomes are uncertain, rated as a strategic posture rather than a personal trait. Sarasvathy's effectuation turned the question around: expert entrepreneurs do not estimate expected return and accept the variance, they fix what they can afford to lose and act within it. One treats risk as an individual trait to be scored, one as a firm's strategic posture, and one as a quantity to be chosen. All three differ from the finance meaning in caring about loss, not dispersion.[10][12][13][11]

Unit

A founder, as a person or as a decision maker

Recovery means

Return after venture failure, the serial-entrepreneur literature

Measured by

Risk-propensity self-report scales; firm-level entrepreneurial-orientation risk-taking ratings; choice dilemmas; affordable loss inferred from decision protocols