Risk is the potential of gaining or losing something of value. Values (such as physical health, social status, emotional well-being or financial wealth) can be gained or lost when taking risk resulting from a given action or inaction, foreseen or unforeseen. Risk can additionally be defined as the intentional interaction with uncertainty. Uncertainty is a potential, unpredictable, and uncontrollable outcome; risk is a consequence of action taken in spite of uncertainty.

Risk perception is the subjective judgement people make about the severity and probability of a risk, and might vary person to person. Any human endeavour carries a few risk, but a few are much riskier than others.

## Definitions

The Oxford English Dictionary cites the earliest use of the word in English (in the spelling of risque from its from French original, 'risque' ) as of 1621, and the spelling as risk from 1655. It defines risk as:

(Exposure to) the possibility of loss, injury, or additional adverse or unwelcome circumstance; a chance or situation involving such a possibility.

1. Risk is an uncertain event or condition that, if it occurs, has an effect on at least one [project] objective. (This definition, using project terminology, is easily made universal by removing references to projects).
2. The probability of something happening multiplied by the resulting cost or benefit if it does. (This concept is more properly known as the 'Expectation Value' or 'Risk Factor' and is used to compare levels of risk)
3. The probability or threat of quantifiable damage, injury, liability, loss, or any additional negative occurrence that's caused by external or internal vulnerabilities, and that might be avoided through preemptive action.
4. Finance: The possibility that an actual return on an investment will be lower than the expected return.
5. Insurance: A situation where the probability of a variable (such as burning down of a building) is known but when a mode of occurrence or the actual value of the occurrence (whether the fire will occur at a particular property) is not.(Reference needed) A risk isn't an uncertainty (where neither the probability nor the mode of occurrence is known), a peril (cause of loss), or a hazard (something that makes the occurrence of a peril more likely or more severe).
6. Securities trading: The probability of a loss or drop in value. Trading risk is divided into two general categories: (1) Systematic risk affects all securities in the same class and is linked to the overall capital-market system and therefore can't be eliminated by diversification. Also called market risk. (2) Non-systematic risk is any risk that isn't market-related. Also called non-market risk, extra-market risk or diversifiable risk.
7. Workplace: Product of the consequence and probability of a hazardous event or phenomenon. For example, the risk of developing cancer is estimated as the incremental probability of developing cancer over a lifetime as a result of exposure to potential carcinogens (cancer-causing substances).

### International Organization for Standardization

The ISO 31000 (2009) / ISO Guide 73:2002 definition of risk is the 'effect of uncertainty on objectives'. In this definition, uncertainties include events (which might or might not happen) and uncertainties caused by ambiguity or a lack of information. It additionally includes both negative and positive impacts on objectives. Many definitions of risk exist in common usage, however this definition was developed by an international committee representing over 30 countries and is based on the input of several thousand subject matter experts.

### Other

Very different approaches to risk management are taken in different fields, e.g. "Risk is the unwanted subset of a set of uncertain outcomes" (Cornelius Keating).

Risk can be seen as relating to the probability of uncertain future events. For example, according to factor analysis of information risk, risk is: the probable frequency and probable magnitude of future loss. In computer science this definition is used by The Open Group.
OHSAS (Occupational Health & Safety Advisory Services) defines risk as the combination of the probability of a hazard resulting in an adverse event, and the severity of the event.
In information security risk is defined as "the potential that a given threat will exploit vulnerabilities of an asset or group of assets and thereby cause harm to the organization".
Financial risk is often defined as the unpredictable variability or volatility of returns, and this would include both potential better-than-expected and worse-than-expected returns. References to negative risk below should be read as additionally applying to positive impacts or opportunity (e.g. for "loss" read "loss or gain") unless the context precludes this interpretation.
The related terms "threat" and "hazard" are often used to mean something that could cause harm.

## Practice areas

Risk is ubiquitous in all areas of life and risk management is something that we all must do, whether we're managing a major organisation or simply crossing the road. When describing risk however, it is convenient to consider that risk practitioners operate in a few specific practise areas.

### Economic risk

Economic risks can be manifested in lower incomes or higher expenditures than expected. The causes can be many, for instance, the hike in the price for raw materials, the lapsing of deadlines for construction of a new operating facility, disruptions in a production process, emergence of a serious competitor on the market, the loss of key personnel, the change of a political regime, or natural disasters.

### Health

Risks in personal health might be reduced by primary prevention actions that decrease early causes of illness or by secondary prevention actions after a person has clearly measured clinical signs or symptoms recognised as risk factors. Tertiary prevention reduces the negative impact of an already established disease by restoring function and reducing disease-related complications. Ethical medical practise requires careful discussion of risk factors with individual patients to obtain informed consent for secondary and tertiary prevention efforts, whereas public health efforts in primary prevention require education of the entire population at risk. In each case, careful communication about risk factors, likely outcomes and certainty must distinguish between causal events that must be decreased and associated events that might be merely consequences rather than causes.

In epidemiology, the lifetime risk of an effect is the cumulative incidence, additionally called incidence proportion over an entire lifetime.

### Health, safety, and environment

Health, safety, and environment (HSE) are separate practise areas; however, they're often linked. The reason for this is typically to do with organisational management structures; however, there are strong links among these disciplines. One of the strongest links between these is that a single risk event might have impacts in all three areas, albeit over differing timescales. For example, the uncontrolled release of radiation or a toxic chemical might have immediate short-term safety consequences, more protracted health impacts, and much longer-term environmental impacts. Events such as Chernobyl, for example, caused immediate deaths, and in the longer term, deaths from cancers, and left a lasting environmental impact leading to birth defects, impacts on wildlife, etc.

Over time, a form of risk analysis called environmental risk analysis has developed. Environmental risk analysis is a field of study that attempts to understand events and activities that bring risk to human health or the environment.

Human health and environmental risk is the likelihood of an adverse outcome (See adverse outcome pathway). As such, risk is a function of hazard and exposure. Hazard is the intrinsic danger or harm that's posed, e.g. the toxicity of a chemical compound. Exposure is the likely contact with that hazard. Therefore, the risk of even a quite hazardous substance approaches zero as the exposure nears zero, given a person's (or additional organism's) biological makeup, activities and location (See exposome).

### Information technology and information security

Information technology risk, or IT risk, IT-related risk, is a risk related to information technology. This relatively new term was developed as a result of an increasing awareness that information security is simply one facet of a multitude of risks that are relevant to IT and the real world processes it supports.

The increasing dependencies of modern society on information and computers networks (both in private and public sectors, including military) has led to new terms like IT risk and Cyberwarfare.

Information security means protecting information and information systems from unauthorised access, use, disclosure, disruption, modification, perusal, inspection, recording or destruction. Information security grew out of practises and procedures of computer security.
Information security has grown to information assurance (IA) i.e. is the practise of managing risks related to the use, processing, storage, and transmission of information or data and the systems and processes used for those purposes.
While focused dominantly on information in digital form, the full range of IA encompasses not only digital but additionally analogue or physical form.
Information assurance is interdisciplinary and draws from multiple fields, including accounting, fraud examination, forensic science, management science, systems engineering, security engineering, and criminology, in addition to computer science.

So, is narrowly focused on computer security, while information security extends to risks related to additional forms of information (paper, microfilm). Information assurance risks include the ones related to the consistency of the business information stored in IT systems and the information stored by additional means and the relevant business consequences.

### Insurance

Insurance is a risk treatment option which involves risk sharing. It can be considered as a form of contingent capital and is akin to purchasing an option in which the buyer pays a small premium to be protected from a potential large loss.

Insurance risk is often taken by insurance companies, who then bear a pool of risks including market risk, credit risk, operational risk, interest rate risk, mortality risk, longevity risks, etc.

Means of assessing risk vary widely between professions. Indeed, they might define these professions; for example, a doctor manages medical risk, while a civil engineer manages risk of structural failure. A professional code of ethics is usually focused on risk assessment and mitigation (by the professional on behalf of client, public, society or life in general).

In the workplace, incidental and inherent risks exist. Incidental risks are those that occur naturally in the business but aren't part of the core of the business. Inherent risks have a negative effect on the operating profit of the business.

### In human services

The experience of a large number of people who rely on human services for support is that 'risk' is often used as a reason to prevent them from gaining further independence or fully accessing the community, and that these services are often unnecessarily risk averse. "People's autonomy used to be compromised by institution walls, now it's too often our risk management practices", according to John O'Brien. Michael Fischer and Ewan Ferlie (2013) find that contradictions between formal risk controls and the role of subjective factors in human services (such as the role of emotions and ideology) can undermine service values, so producing tensions and even intractable and 'heated' conflict.

### High reliability organisations (HROs)

A high reliability organization (HRO) is an organisation that has succeeded in avoiding catastrophes in an environment where normal accidents can be expected due to risk factors and complexity. Most studies of HROs involve areas such as nuclear aircraft carriers, air traffic control, aerospace and nuclear power stations. Organizations such as these share in common the ability to consistently operate safely in complex, interconnected environments where a single failure in one component could lead to catastrophe. Essentially, they're organisations which appear to operate 'in spite' of an enormous range of risks.

Some of these industries manage risk in a highly quantified and enumerated way. These include the nuclear power and aircraft industries, where the possible failure of a complex series of engineered systems could result in highly undesirable outcomes. The usual measure of risk for a class of events is then: R = probability of the event × the severity of the consequence.

The total risk is then the sum of the individual class-risks; see below.

In the nuclear industry, consequence is often measured in terms of off-site radiological release, and this is often banded into five or six decade-wide bands.

The risks are evaluated using fault tree/event tree techniques (see safety engineering). Where these risks are low, they're normally considered to be "broadly acceptable". A higher level of risk (typically up to 10 to 100 times what's considered broadly acceptable) has to be justified against the costs of reducing it further and the possible benefits that make it tolerable—these risks are described as "Tolerable if ALARP". Risks beyond this level are classified as "intolerable".

The level of risk deemed broadly acceptable has been considered by regulatory bodies in various countries—an early attempt by UK government regulator and academic F. R. Farmer used the example of hill-walking and similar activities, which have definable risks that people appear to find acceptable. This resulted in the so-called Farmer Curve of acceptable probability of an event versus its consequence.

The technique as a whole is usually referred to as probabilistic risk assessment (PRA) (or probabilistic safety assessment, PSA). See WASH-1400 for an example of this approach.

### Finance

In finance, risk is the chance that the return achieved on an investment will be different from that expected, and additionally takes into account the size of the difference. This includes the possibility of losing a few or all of the original investment. In a view advocated by Damodaran, risk includes not only "downside risk" but additionally "upside risk" (returns that exceed expectations). Some regard the standard deviation of the historical returns or average returns of a specific investment as providing a few historical measure of risk; see modern portfolio theory. Financial risk might be market-dependent, determined by numerous market factors, or operational, resulting from fraudulent behaviour (e.g. Bernard Madoff). Recent studies suggest that endocrine levels might play a role in risk-taking in financial decision-making.

A fundamental idea in finance is the relationship between risk and return (see modern portfolio theory). The greater the potential return one might seek, the greater the risk that one generally assumes. A free market reflects this principle in the pricing of an instrument: strong demand for a safer instrument drives its price higher (and its return correspondingly lower) while weak demand for a riskier instrument drives its price lower (and its potential return thereby higher). For example, a US Treasury bond is considered to be one of the safest investments. In comparison to an investment or speculative grade corporate bond, US Treasury notes and bonds yield lower rates of return. The reason for this is that a corporation is more likely to default on debt than the U.S. government. Because the risk of investing in a corporate bond is higher, investors are offered a correspondingly higher rate of return.

A popular risk measure is value-at-risk (VaR).

There are different types of VaR: long term VaR, marginal VaR, factor VaR and shock VaR. The latter is used in measuring risk throughout the extreme market stress conditions.

In finance, risk has no single definition.

Artzner et al. write "we call risk the investor's future net worth". In Novak "risk is a possibility of an undesirable event".

In financial markets, one might need to measure credit risk, information timing and source risk, probability model risk, and legal risk if there are regulatory or civil actions taken as a result of "investor's regret".

It isn't always obvious if financial instruments are "hedging" (purchasing/selling a financial instrument specifically to reduce or cancel out the risk in another investment) or "speculation" (increasing measurable risk and exposing the investor to catastrophic loss in pursuit of quite high windfalls that increase expected value).

Some people might be "risk seeking", i.e. their utility function's second derivative is positive. Such an individual willingly pays a premium to assume risk (e.g. buys a lottery ticket). Knowing one's risk appetite in conjunction with one's financial well-being are important.

### Security

Popular labeling

Security risk management involves protection of assets from harm caused by deliberate acts. A more detailed definition is: "A security risk is any event that could result in the compromise of organisational assets i.e. the unauthorised use, loss, damage, disclosure or modification of organisational assets for the profit, personal interest or political interests of individuals, groups or additional entities constitutes a compromise of the asset, and includes the risk of harm to people. Compromise of organisational assets might adversely affect the enterprise, its business units and their clients. As such, consideration of security risk is a vital component of risk management."

### Human factors

One of the growing areas of focus in risk management is the field of human factors where behavioural and organisational psychology underpin our understanding of risk based decision making. This field considers questions such as "how do we make risk based decisions?", "why are we irrationally more scared of sharks and terrorists than we're of motor vehicles and medications?"

In decision theory, regret (and anticipation of regret) can play a significant part in decision-making, distinct from risk aversion (preferring the status quo in case one becomes worse off).

Framing is a fundamental problem with all forms of risk assessment. In particular, because of bounded rationality (our brains get overloaded, so we take mental shortcuts), the risk of extreme events is discounted because the probability is too low to assess intuitively. As an example, one of the leading causes of death is road accidents caused by drunk driving – partly because any given driver frames the problem by largely or totally ignoring the risk of a serious or fatal accident.

For instance, an extremely disturbing event (an attack by hijacking, or moral hazards) might be ignored in analysis notwithstanding the fact it has occurred and has a nonzero probability. Or, an event that everyone agrees is inevitable might be ruled out of analysis due to greed or an unwillingness to admit that it is believed to be inevitable. These human tendencies for error and wishful thinking often affect even the most rigorous applications of the scientific method and are a major concern of the philosophy of science.

All decision-making under uncertainty must consider cognitive bias, cultural bias, and notational bias: No group of people assessing risk is immune to "groupthink": acceptance of obviously wrong answers simply because it is socially painful to disagree, where there are conflicts of interest.

Framing involves additional information that affects the outcome of a risky decision. The right prefrontal cortex has been shown to take a more global perspective while greater left prefrontal activity relates to local or focal processing.

From the Theory of Leaky Modules McElroy and Seta proposed that they could predictably alter the framing effect by the selective manipulation of regional prefrontal activity with finger tapping or monaural listening. The result was as expected. Rightward tapping or listening had the effect of narrowing attention such that the frame was ignored. This is a practical way of manipulating regional cortical activation to affect risky decisions, especially because directed tapping or listening is easily done.

### Psychology of risk taking

A growing area of research has been to examine various psychological aspects of risk taking. Researchers typically run randomised experiments with a treatment and control group to ascertain the effect of different psychological factors that might be associated with risk taking. Thus, positive and negative feedback about past risk taking can affect future risk taking. In an experiment, people who were led to believe they're quite competent at decision making saw more opportunities in a risky choice and took more risks, while those led to believe they weren't quite competent saw more threats and took fewer risks.

### Maintenance

The concept of risk-based maintenance is an advanced form of Reliability centred maintenance. In case of chemical industries, apart from probability of failure, consequences of failure is additionally quite important. Therefore, the selection of maintenance policies should be based on risk, instead of reliability. Risk-based maintenance methodology acts as a tool for maintenance planning and decision making to reduce the probability of failure and its consequences. In risk-based maintenance decision making, the maintenance resources can be utilised optimally based on the risk class (high, medium, or low) of equipment or machines, to achieve tolerable risk criteria.

## Risk assessment and analysis

Since risk assessment and management is essential in security management, both are tightly related. Security assessment methodologies like CRAMM contain risk assessment modules as an important part of the first steps of the methodology. On the additional hand, risk assessment methodologies like Mehari evolved to become security assessment methodologies. An ISO standard on risk management (Principles and guidelines on implementation) was published under code ISO 31000 on 13 November 2009.

### Quantitative analysis

There are a large number of formal methods used to "measure" risk.

Often the probability of a negative event is estimated by using the frequency of past similar events. Probabilities for rare failures might be difficult to estimate. This makes risk assessment difficult in hazardous industries, for example nuclear energy, where the frequency of failures is rare, while harmful consequences of failure are severe.

Statistical methods might additionally require the use of a cost function, which in turn might require the calculation of the cost of loss of a human life. This is a difficult problem. One approach is to ask what people are willing to pay to insure against death or radiological release (e.g. GBq of radio-iodine), but as the answers depend quite strongly on the circumstances it isn't clear that this approach is effective.

Risk is often measured as the expected value of an undesirable outcome. This combines the probabilities of various possible events and a few assessment of the corresponding harm into a single value. See additionally Expected utility. The simplest case is a binary possibility of Accident or No accident. The associated formula for calculating risk is then:

${displaystyle {text{R}}=({text{probability of the accident occurring}})times ({text{expected loss in case of the accident}})}$

For example, if performing activity X has a probability of 0.01 of suffering an accident of A, with a loss of 1000, then total risk is a loss of 10, the product of 0.01 and 1000.

Situations are at times more complex than the simple binary possibility case. In a situation with several possible accidents, total risk is the sum of the risks for each different accident, provided that the outcomes are comparable:

${displaystyle {text{R}}=sum _{text{For all accidents}}({text{probability of the accident occurring}})times ({text{expected loss in case of the accident}})}$

For example, if performing activity X has a probability of 0.01 of suffering an accident of A, with a loss of 1000, and a probability of 0.000001 of suffering an accident of type B, with a loss of 2,000,000, then total loss expectancy is 12, which is equal to a loss of 10 from an accident of type A and 2 from an accident of type B.

One of the first major uses of this concept was for the planning of the Delta Works in 1953, a flood protection programme in the Netherlands, with the aid of the mathematician David van Dantzig. The kind of risk analysis pioneered there has become common today in fields like nuclear power, aerospace and the chemical industry.

In statistical decision theory, the risk function is defined as the expected value of a given loss function as a function of the decision rule used to make decisions in the face of uncertainty.

### Fear as intuitive risk assessment

People might rely on their fear and hesitation to keep them out of the most profoundly unknown circumstances. Fear is a response to perceived danger. Risk can be said to be the way we collectively measure and share this "true fear"—a fusion of rational doubt, irrational fear, and a set of unquantified biases from our own experience.

The field of behavioral finance focuses on human risk-aversion, asymmetric regret, and additional ways that human financial behaviour varies from what analysts call "rational". Risk in that case is the degree of uncertainty associated with a return on an asset. Recognizing and respecting the irrational influences on human decision making might do much to reduce disasters caused by naive risk assessments that presume rationality but in fact merely fuse a large number of shared biases.

## Anxiety, risk and decision making

### Fear, anxiety and risk

According to one set of definitions, fear is a fleeting emotion ascribed to a particular object, while anxiety is a trait of fear (this is referring to "trait anxiety", as distinct from how the term "anxiety" is generally used) that lasts longer and isn't attributed to a specific stimulus (these particular definitions aren't used by all authors cited on this page). Some studies show a link between anxious behaviour and risk (the chance that an outcome will have an unfavourable result). Joseph Forgas introduced valence based research where emotions are grouped as either positive or negative (Lerner and Keltner, 2000). Positive emotions, such as happiness, are believed to have more optimistic risk assessments and negative emotions, such as anger, have pessimistic risk assessments. As an emotion with a negative valence, fear, and therefore anxiety, has long been associated with negative risk perceptions. Under the more recent appraisal tendency framework of Jennifer Lerner et al., which refutes Forgas’ notion of valence and promotes the idea that specific emotions have distinctive influences on judgments, fear is still related to pessimistic expectations.

Psychologists have demonstrated that increases in anxiety and increases in risk perception are related and people who're habituated to anxiety experience this awareness of risk more intensely than normal individuals. In decision-making, anxiety promotes the use of biases and quick thinking to assess risk. This is referred to as affect-as-information according to Clore, 1983. Notwithstanding the accuracy of these risk perceptions when making choices isn't known.

### Consequences of anxiety

Experimental studies show that brief surges in anxiety are correlated with surges in general risk perception. Anxiety exists when the presence of threat is perceived (Maner and Schmidt, 2006). As risk perception increases, it stays related to the particular source impacting the mood change as opposed to spreading to unrelated risk factors. This increased awareness of a threat is significantly more emphasised in people who're conditioned to anxiety. For example, anxious individuals who're predisposed to generating reasons for negative results tend to exhibit pessimism. Also, findings suggest that the perception of a lack of control and a lower inclination to participate in risky decision-making (across various behavioural circumstances) is associated with individuals experiencing relatively high levels of trait anxiety. In the previous instance, there's supporting clinical research that links emotional evaluation (of control), the anxiety that's felt and the option of risk avoidance.

There are various views presented that anxious/fearful emotions cause people to access involuntary responses and judgments when making decisions that involve risk. Joshua A. Hemmerich et al. probes deeper into anxiety and its impact on choices by exploring "risk-as-feelings" which are quick, automatic, and natural reactions to danger that are based on emotions. This notion is supported by an experiment that engages physicians in a simulated perilous surgical procedure. It was demonstrated that a measurable amount of the participants' anxiety about patient outcomes was related to previous (experimentally created) regret and worry and ultimately caused the physicians to be led by their feelings over any information or guidelines provided throughout the mock surgery. Additionally, their emotional levels, adjusted along with the simulated patient status, suggest that anxiety level and the respective decision made are correlated with the type of bad outcome that was experienced in the earlier part of the experiment. Similarly, another view of anxiety and decision-making is dispositional anxiety where emotional states, or moods, are cognitive and provide information about future pitfalls and rewards (Maner and Schmidt, 2006). When experiencing anxiety, individuals draw from personal judgments referred to as pessimistic outcome appraisals. These emotions promote biases for risk avoidance and promote risk tolerance in decision-making.

It is common for people to dread a few risks but not others: They tend to be quite afraid of epidemic diseases, nuclear power plant failures, and plane accidents but are relatively unconcerned about a few highly frequent and deadly events, such as traffic crashes, household accidents, and medical errors. One key distinction of dreadful risks seems to be their potential for catastrophic consequences, threatening to kill a large number of people within a short period of time. For example, immediately after the September 11 attacks, a large number of Americans were afraid to fly and took their car instead, a decision that led to a significant increase in the number of fatal crashes in the time period following the 9/11 event compared with the same time period before the attacks.

Different hypotheses have been proposed to explain why people fear dread risks. First, the psychometric paradigm suggests that high lack of control, high catastrophic potential, and severe consequences account for the increased risk perception and anxiety associated with dread risks. Second, because people estimate the frequency of a risk by recalling instances of its occurrence from their social circle or the media, they might overvalue relatively rare but dramatic risks because of their overpresence and undervalue frequent, less dramatic risks. Third, according to the preparedness hypothesis, people are prone to fear events that have been particularly threatening to survival in human evolutionary history. Given that in most of human evolutionary history people lived in relatively small groups, rarely exceeding 100 people, a dread risk, which kills a large number of people at once, could potentially wipe out one’s whole group. Indeed, research found that people’s fear peaks for risks killing around 100 people but doesn't increase if larger groups are killed. Fourth, fearing dread risks can be an ecologically rational strategy. Besides killing a large number of people at a single point in time, dread risks reduce the number of children and young adults who would have potentially produced offspring. Accordingly, people are more concerned about risks killing younger, and hence more fertile, groups.

### Anxiety and judgmental accuracy

The relationship between higher levels of risk perception and "judgmental accuracy" in anxious individuals remains unclear (Joseph I. Constans, 2001). There is a chance that "judgmental accuracy" is correlated with heightened anxiety. Constans conducted a study to examine how worry propensity (and current mood and trait anxiety) might influence college student’s estimation of their performance on an upcoming exam, and the study found that worry propensity predicted subjective risk bias (errors in their risk assessments), even after variance attributable to current mood and trait anxiety had been removed. An Additional experiment suggests that trait anxiety is associated with pessimistic risk appraisals (heightened perceptions of the probability and degree of suffering associated with a negative experience), while controlling for depression.

## Risk in auditing

The audit risk model expresses the risk of an auditor providing an inappropriate opinion of a commercial entity's financial statements. It can be analytically expressed as:

AR = IR x CR x DR

Where AR is audit risk, IR is inherent risk, CR is control risk and DR is detection risk.

### Risk and uncertainty

In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) 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 a few cases a quantity susceptible of measurement, while at additional 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 isn't 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 by Douglas Hubbard:

Uncertainty: The lack of complete certainty, that is, the existence of more than one possibility. The "true" outcome/state/result/value isn't known.
Measurement of uncertainty: A set of probabilities assigned to a set of possibilities. Example: "There is a sixty percent chance this market will double in five years"
Risk: A state of uncertainty where a few of the possibilities involve a loss, catastrophe, or additional undesirable outcome.
Measurement of risk: A set of possibilities each with quantified probabilities and quantified losses. Example: "There is a forty percent chance the proposed oil well will be dry with a loss of \$12 million in exploratory drilling costs".

In this sense, one might have uncertainty without risk but not risk without uncertainty. We can be uncertain about the winner of a contest, but unless we have a few 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 might be used to describe a risk attitude. Risk tolerance looks at acceptable/unacceptable deviations from what's expected. Risk appetite looks at how much risk one is willing to accept. There can still be deviations that are within a risk appetite. For example, recent research finds that insured individuals are significantly likely to divest from risky asset holdings in response to a decline in health, controlling for variables such as income, age, and out-of-pocket medical expenses.

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 quite risky investment with a high chance of no return and a small chance of a quite 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 additional investments with possibly higher gain. The possibility of getting no return on an investment is additionally known as the rate of ruin.

### Risk as a vector quantity

Hubbard additionally argues that defining risk as the product of impact and probability presumes (probably incorrectly) that the decision makers are risk neutral. Only for a risk neutral person is the "certain monetary equivalent" exactly equal to the probability of the loss times the amount of the loss. For example, a risk neutral person would consider twenty percent chance of winning \$1 million exactly equal to \$200,000 (or a twenty percent chance of losing \$1 million to be exactly equal to losing \$200,000). Notwithstanding most decision makers aren't actually risk neutral and wouldn't consider these equivalent choices. This gave rise to Prospect theory and Cumulative prospect theory. Hubbard proposes instead that risk is a kind of "vector quantity" that doesn't collapse the probability and magnitude of a risk by presuming anything about the risk tolerance of the decision maker. Risks are simply described as a set or function of possible loss amounts each associated with specific probabilities. How this array is collapsed into a single value can't be done until the risk tolerance of the decision maker is quantified.

Risk can be both negative and positive, but it tends to be the negative side that people focus on. This is because a few things can be dangerous, such as putting their own or someone else’s life at risk. Risks concern people as they think that they'll have a negative effect on their future.

## List of related books

This is a list of books about risk issues.

TitleAuthor(s)Year
Acceptable RiskBaruch Fischhoff, Sarah Lichtenstein, Paul Slovic, Steven L. Derby, and Ralph Keeney1984
Against the Gods: The Remarkable Story of RiskPeter L. Bernstein1996
At risk: Natural hazards, people's vulnerability and disastersPiers Blaikie, Terry Cannon, Ian Davis, and Ben Wisner1994
Building Safer Communities. Risk Governance, Spatial Planning and Responses to Natural HazardsUrbano Fra Paleo2009
Dangerous Earth: An introduction to geologic hazardsBarbara W. Murck, Brian J. Skinner, Stephen C. Porter1998
Disasters and DemocracyRutherford H. Platt1999
Earth Shock: Hurricanes, volcanoes, earthquakes, tornadoes and additional forces of natureW. Andrew Robinson1993
Human System Response to Disaster: An Inventory of Sociological FindingsThomas E. Drabek1986
Judgment Under Uncertainty: heuristics and biasesDaniel Kahneman, Paul Slovic, and Amos Tversky1982
Mapping Vulnerability: disasters, development, and peopleGreg Bankoff, Georg Frerks, and Dorothea Hilhorst2004
Man and Society in Calamity: The Effects of War, Revolution, Famine, Pestilence upon Human Mind, Behavior, Social Organization and Cultural LifePitirim Sorokin1942
Mitigation of Hazardous Comets and AsteroidsMichael J.S. Belton, Thomas H. Morgan, Nalin H. Samarasinha, Donald K. Yeomans2005
Natural Disaster Hotspots: a global risk analysisMaxx Dilley2005
Natural Hazard Mitigation: Recasting disaster policy and planningDavid Godschalk, Timothy Beatley, Philip Berke, David Brower, and Edward J. Kaiser1999
Natural Hazards: Earth’s processes as hazards, disasters, and catastrophesEdward A. Keller, and Robert H. Blodgett2006
Normal Accidents. Living with high-risk technologiesCharles Perrow1984
Paying the Price: The status and role of insurance against natural disasters in the United StatesHoward Kunreuther, and Richard J. Roth1998
Planning for Earthquakes: Risks, politics, and policyPhilip R. Berke, and Timothy Beatley1992
Practical Project Risk Management: The ATOM MethodologyDavid Hillson and Peter Simon2012
Reduction and Predictability of Natural DisastersJohn B. Rundle, William Klein, Don L. Turcotte1996
Regions of Risk: A geographical introduction to disastersKenneth Hewitt1997
Risk Analysis: a quantitative guideDavid Vose2008
Risk: An introduction (ISBN 978-0-415-49089-4)Bernardus Ale2009
Risk and Culture: An essay on the selection of technical and environmental dangersMary Douglas, and Aaron Wildavsky1982
Socially Responsible Engineering: Justice in Risk Management (ISBN 978-0-471-78707-5)Daniel A. Vallero, and P. Aarne Vesilind2006
Swimming with Crocodiles: The Culture of Extreme DrinkingMarjana Martinic and Fiona Measham (eds.)2008
The Challenger Launch Decision: Risky Technology, Culture and Deviance at NASADiane Vaughan1997
The Environment as HazardIan Burton, Robert Kates, and Gilbert F. White1978
The Social Amplification of RiskNick Pidgeon, Roger E. Kasperson, and Paul Slovic2003
What is a Disaster? New answers to old questionsRonald W. Perry, and Enrico Quarantelli2005
Floods: From Risk to Opportunity (IAHS Red Book Series)Ali Chavoshian, and Kuniyoshi Takeuchi2013
The Risk Factor: Why Every Organization Needs Big Bets, Bold Characters, and the Occasional Spectacular FailureDeborah Perry Piscione2014