Risk

The Oxford English Dictionary (OED) cites the earliest use of the word in English (in the spelling of risque from its French original, 'risque') as of 1621, and the spelling as risk from 1655. While including several other definitions, the OED 3rd edition defines risk as:

(Exposure to) the possibility of loss, injury, or other adverse or unwelcome circumstance; a chance or situation involving such a possibility.[3]

The International Organization for Standardization (ISO) Guide 73 provides basic vocabulary to develop common understanding on risk management concepts and terms across different applications. ISO Guide 73:2009 defines risk as:

effect of uncertainty on objectives

Note 1: An effect is a deviation from the expected – positive or negative.

Note 2: Objectives can have different aspects (such as financial, health and safety, and environmental goals) and can apply at different levels (such as strategic, organization-wide, project, product and process).

Note 3: Risk is often characterized by reference to potential events and consequences or a combination of these.

Note 4: Risk is often expressed in terms of a combination of the consequences of an event (including changes in circumstances) and the associated likelihood of occurrence.

Note 5: Uncertainty is the state, even partial, of deficiency of information related to, understanding or knowledge of, an event, its consequence, or likelihood.[4]

This definition was developed by an international committee representing over 30 countries and is based on the input of several thousand subject matter experts. It was first adopted in 2002. Its complexity reflects the difficulty of satisfying fields that use the term risk in different ways. Some restrict the term to negative impacts (“downside risks”), while others include positive impacts (“upside risks”).

ISO 31000:2018 “Risk management — Principles” uses the same definition with a simpler set of notes.[5]

Many other definitions of risk have been influential:

“Source of harm”. The earliest use of the word “risk” was as a synonym for the much older word “hazard”, meaning a potential source of harm. This definition comes from Blount’s “Glossographia” (1661)[6] and was the main definition in the OED 1st (1914) and 2nd (1989) editions. Modern equivalents refer to “unwanted events” [7] or “something bad that might happen”.[1]

“Chance of harm”. This definition comes from Johnson’s “Dictionary of the English Language” (1755), and has been widely paraphrased, including “possibility of loss” [8] or “probability of unwanted events”.[7]

“Uncertainty about loss”. This definition comes from Willett’s “Economic Theory of Risk and Insurance” (1901).[9] This links “risk” to “uncertainty”, which is a broader term than chance or probability.

“Measurable uncertainty”. This definition comes from Knight’s “Risk, Uncertainty and Profit” (1921).[10] It allows “risk” to be used equally for positive and negative outcomes. In insurance, risk involves situations with unknown outcomes but known probability distributions.[11]

“Variance of return”. This definition comes from Markovitz’s “Portfolio Selection” (1952).[12] In practice, risk was measured using the standard deviation of returns.[7]

“Statistically expected loss”. The probability of an event multiplied by its magnitude was proposed as a definition of risk by the US Nuclear Regulatory Commission (1975),[13] and remains widely used.[7] It is properly known as the ‘expectation value’.

“Likelihood and severity of events”. The “triplet” definition of risk as “scenarios, probabilities and consequences” was proposed by Kaplan & Garrick (1981).[14] Many definitions refer to the likelihood/probability of events/effects/losses of different severity/consequence, e.g. ISO Guide 73 Note 4.[4]

“Consequences and associated uncertainty”. This was proposed by Kaplan & Garrick (1981).[14] This definition is preferred in Bayesian analysis, which sees risk as the combination of events and uncertainties about them.[15]

“Uncertain events affecting objectives”. This definition was adopted by the Association for Project Management (1997).[16][17] With slight rewording it became the definition in ISO Guide 73.[4]

“Uncertainty of outcome”. This definition was adopted by the UK Cabinet Office (2002)[18] to encourage innovation to improve public services. It allowed “risk” to describe either “positive opportunity or negative threat of actions and events”.

“Human interaction with uncertainty”. This definition comes from Cline (2015)[19] in the context of adventure education.

Some resolve these differences by arguing that the definition of risk is subjective. For example:

No definition is advanced as the correct one, because there is no one definition that is suitable for all problems. Rather, the choice of definition is a political one, expressing someone’s views regarding the importance of different adverse effects in a particular situation.[20]

The Society for Risk Analysis concludes that “experience has shown that to agree on one unified set of definitions is not realistic”. The solution is “to allow for different perspectives on fundamental concepts and make a distinction between overall qualitative definitions and their associated measurements.”[2]

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.

Risks in personal health may 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 practice 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 may be merely consequences rather than causes.

In epidemiology, the lifetime risk of an effect is the cumulative incidence, also called incidence proportion over an entire lifetime.[21]

In terms of occupational health & safety management, the term 'risk' may be defined as the most likely consequence of a hazard, combined with the likelihood or probability of it occurring.

Health, safety, and environment (HSE) are separate practice areas; however, they are often linked. The reason for this is typically to do with organizational management structures; however, there are strong links among these disciplines. One of the strongest links between these is that a single risk event may have impacts in all three areas, albeit over differing timescales. For example, the uncontrolled release of radiation or a toxic chemical may 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.[22]

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 is posed, e.g. the toxicity of a chemical compound. Exposure is the likely contact with that hazard. Therefore, the risk of even a very hazardous substance approaches zero as the exposure nears zero, given a person's (or other organism's) biological makeup, activities and location (See exposome).[23] Another example of health risks are when certain behaviours, such as risky sexual behaviours, increase the likelihood of contracting HIV.[24]

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)[25][26][27] 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.[28] Information security grew out of practices and procedures of computer security.
Information security has grown to information assurance (IA) i.e. is the practice 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 also 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, IT risk is narrowly focused on computer security, while information security extends to risks related to other 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 other means and the relevant business consequences.

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.[29]

Means of assessing risk vary widely between professions. Indeed, they may 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 are not part of the core of the business. Inherent risks have a negative effect on the operating profit of the business.

The experience of many 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.[30] "People's autonomy used to be compromised by institution walls, now it's too often our risk management practices", according to John O'Brien.[31] 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.[32]

A high reliability organisation (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 are 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.[33]

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 are normally considered to be "broadly acceptable". A higher level of risk (typically up to 10 to 100 times what is 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", where ALARP stands for "as low as reasonably practicable". 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.

In finance, risk is the chance that the return achieved on an investment will be different from that expected, and also takes into account the size of the difference. This includes the possibility of losing some or all of the original investment. In a view advocated by Damodaran, risk includes not only "downside risk" but also "upside risk" (returns that exceed expectations).[34] Some regard the standard deviation of the historical returns or average returns of a specific investment as providing some historical measure of risk; see modern portfolio theory. Financial risk may be market-dependent, determined by numerous market factors, or operational, resulting from fraudulent behaviour (e.g. Bernard Madoff).

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 US 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 during the extreme market stress conditions.

In finance, risk has no single definition.

Artzner et al.[35] write "we call risk the investor's future net worth". In Novak[36] "risk is a possibility of an undesirable event".

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

With the advent of automation in financial markets, the concept of "real-time risk" has gained a lot of attention. Aldridge and Krawciw[37] define real-time risk as the probability of instantaneous or near-instantaneous loss, and can be due to flash crashes, other market crises, malicious activity by selected market participants and other events. A well-cited example[38] of real-time risk was a US$440 million loss incurred within 30 minutes by Knight Capital Group (KCG) on 1 August 2012; the culprit was a poorly-tested runaway algorithm deployed by the firm. Regulators have taken notice of real-time risk as well. Basel III[39] requires real-time risk management framework for bank stability.

It is not 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 very high windfalls that increase expected value).

Some people may 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).

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

${\displaystyle {\text{AR}}={\text{IR}}\times {\text{CR}}\times {\text{DR}}}$

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

Note: As defined, audit risk does not consider the impact of an auditor misstatement and so is stated as a simple probability. The impact of misstatement must be considered when determining an acceptable audit risk.[40]

AT YOUR OWN RISK
Popular labelling

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 organizational assets i.e. the unauthorized use, loss, damage, disclosure or modification of organizational assets for the profit, personal interest or political interests of individuals, groups or other entities constitutes a compromise of the asset, and includes the risk of harm to people. Compromise of organizational assets may adversely affect the enterprise, its business units and their clients. As such, consideration of security risk is a vital component of risk management."[41]

One of the growing areas of focus in risk management is the field of human factors where behavioural and organizational 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 are 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[42][43](preferring the status quo in case one becomes worse off).

Framing[44] 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 evaluate 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) may be ignored in analysis despite the fact it has occurred and has a nonzero probability. Or, an event that everyone agrees is inevitable may 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 other information that affects the outcome of a risky decision. The right prefrontal cortex has been shown to take a more global perspective[45] while greater left prefrontal activity relates to local or focal processing.[46]

From the Theory of Leaky Modules[47] 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.[48] 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.

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 may 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 are very competent at decision making saw more opportunities in a risky choice and took more risks, while those led to believe they were not very competent saw more threats and took fewer risks.[49]

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 also very 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 used optimally based on the risk class (high, medium, or low) of equipment or machines, to achieve tolerable risk criteria.[50]

Closely related to information assurance and security risk, cybersecurity is the application of system security engineering[52] in order to address the compromise of company cyber-assets required for business or mission purposes. In order to address cyber-risk, cybersecurity applies security to the supply chain, the design and production environment for a product or service, and the product itself in order to provide efficient and appropriate security commensurate with the value of the asset to the mission or business process.

There are many 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 may 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 may also require the use of a cost function, which in turn may 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[53] or radiological release (e.g. GBq of radio-iodine), but as the answers depend very strongly on the circumstances it is not 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 some assessment of the corresponding harm into a single value. See also 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 sometimes 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 program in the Netherlands, with the aid of the mathematician David van Dantzig.[54] 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.

People may rely on their fear and hesitation to keep them out of the most profoundly unknown circumstances. Fear is a response to perceived danger. Risk could 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 behavioural finance focuses on human risk-aversion, asymmetric regret, and other 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 may do much to reduce disasters caused by naive risk assessments that presume rationality but in fact merely fuse many shared biases.

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 is not attributed to a specific stimulus (these particular definitions are not used by all authors cited on this page).[55] Some studies show a link between anxious behaviour and risk (the chance that an outcome will have an unfavorable result).[56] 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.[57]

Psychologists have demonstrated that increases in anxiety and increases in risk perception are related and people who are habituated to anxiety experience this awareness of risk more intensely than normal individuals.[58] In decision-making, anxiety promotes the use of biases and quick thinking to evaluate risk. This is referred to as affect-as-information according to Clore, 1983. However, the accuracy of these risk perceptions when making choices is not known.[59]

Experimental studies show that brief surges in anxiety are correlated with surges in general risk perception.[59] Anxiety exists when the presence of threat is perceived (Maner and Schmidt, 2006).[58] As risk perception increases, it stays related to the particular source impacting the mood change as opposed to spreading to unrelated risk factors.[59] This increased awareness of a threat is significantly more emphasised in people who are conditioned to anxiety.[60] For example, anxious individuals who are predisposed to generating reasons for negative results tend to exhibit pessimism.[60] 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.[58] In the previous instance, there is supporting clinical research that links emotional evaluation (of control), the anxiety that is felt and the option of risk avoidance.[58]

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 during 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.[61] 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.[60]

It is common for people to dread some risks but not others: They tend to be very afraid of epidemic diseases, nuclear power plant failures, and plane accidents but are relatively unconcerned about some 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,[62] threatening to kill a large number of people within a short period of time.[63] For example, immediately after the 11 September attacks, many 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.[64][65]

Different hypotheses have been proposed to explain why people fear dread risks. First, the psychometric paradigm[62] 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 may overvalue relatively rare but dramatic risks because of their overpresence and undervalue frequent, less dramatic risks.[65] Third, according to the preparedness hypothesis, people are prone to fear events that have been particularly threatening to survival in human evolutionary history.[66] Given that in most of human evolutionary history people lived in relatively small groups, rarely exceeding 100 people,[67] a dread risk, which kills many people at once, could potentially wipe out one's whole group. Indeed, research found[68] that people's fear peaks for risks killing around 100 people but does not increase if larger groups are killed. Fourth, fearing dread risks can be an ecologically rational strategy.[69] 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.[70]

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.[59] Another 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.[58]

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 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.:[71]

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:[72][73]

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, 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.

The terms risk attitude, appetite, and tolerance are often used similarly to describe an organisation's or individual's attitude towards risk-taking. One's attitude may be described as risk-averse, risk-neutral, or risk-seeking. 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. 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.[74]

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.

Hubbard also argues that defining risk as the product of impact and probability presumes, unrealistically, that decision-makers are risk-neutral.[73] A risk-neutral person's utility is proportional to the expected value of the payoff. For example, a risk-neutral person would consider 20% chance of winning $1 million exactly as desirable as getting a certain $200,000. However, most decision-makers are not actually risk-neutral and would not consider these equivalent choices. This gave rise to prospect theory and cumulative prospect theory. Hubbard proposes to instead describe risk as a vector quantity that distinguishes the probability and magnitude of a risk. Risks are simply described as a set or function of possible payoffs (gains or losses) with their associated probabilities. This array is collapsed into a scalar value according to a decision-maker's risk tolerance.

• James Franklin, 2001: The Science of Conjecture: Evidence and Probability Before Pascal, Baltimore: Johns Hopkins University Press.
• John Handmer and Paul James (2005). "Trust Us and Be Scared: The Changing Nature of Risk". Global Society. 21 (1): 119–30.CS1 maint: uses authors parameter (link)
• Niklas Luhmann, 1996: Modern Society Shocked by its Risks (= University of Hong Kong, Department of Sociology Occasional Papers 17), Hong Kong, available via HKU Scholars HUB

• Historian David A. Moss' book When All Else Fails explains the US government's historical role as risk manager of last resort.
• Bernstein P. L. Against the Gods ISBN 0-471-29563-9. Risk explained and its appreciation by man traced from earliest times through all the major figures of their ages in mathematical circles.
• Rescher, Nicholas (1983). A Philosophical Introduction to the Theory of Risk Evaluation and Measurement. University Press of America.
• Porteous, Bruce T.; Pradip Tapadar (December 2005). Economic Capital and Financial Risk Management for Financial Services Firms and Conglomerates. Palgrave Macmillan. ISBN 978-1-4039-3608-0.
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