Risk

TheInfoList

In simple terms, risk is the possibility of something bad happening. Risk involves
uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially o ...

about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is “effect of uncertainty on objectives”. The understanding of risk, the methods of assessment and management, the descriptions of risk and even the definitions of risk differ in different practice areas (
business Business is the activity of making one's living or making money by producing or buying and selling products (such as goods and services). Simply put, it is "any activity or enterprise entered into for profit." Having a business name A trad ...

,
economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. The term was fo ...

,
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
,
finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money available which could ...

, information technology,
health Health, according to the , is "a state of complete physical, and social and not merely the absence of and ".. (2006)''Constitution of the World Health Organization''– ''Basic Documents'', Forty-fifth edition, Supplement, October 2006. A var ...

,
insurance Insurance is a means of protection from financial loss. It is a form of risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. R ...

,
safety Safety is the state of being "safe", the condition of being protected from harm Harm is a moral A moral (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages ...

,
security Security is freedom from, or resilience against, potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics Physics (from grc, φυσική (ἐπιστήμη), phys ...

etc). This article provides links to more detailed articles on these areas. The international standard for risk management,
ISO 31000 ISO 31000 is a family of standards relating to risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about th ...
, provides principles and generic guidelines on managing risks faced by organizations.

# Definitions of risk

## Oxford English Dictionary

The
Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the principal of the , published by (OUP). It traces the historical development of the English language, providing a comprehensive resource to scholars and academic researchers, as well as desc ...
(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.
The Cambridge Advanced Learner’s Dictionary gives a simple summary, defining risk as “the possibility of something bad happening”.

## International Organization for Standardization

The
International Organization for Standardization The International Organization for Standardization (ISO ) is an international standard An international standard is a technical standard A technical standard is an established norm (social), norm or requirement for a repeatable technical task ...
(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.
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 ISO 31000 is a family of standards relating to risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about th ...
:2018 “Risk management — Guidelines” uses the same definition with a simpler set of notes.

## Other

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 A hazard is a potential source of harm. Substances, events, or circumstances can constitute hazards when their nature would allow them, even just theoretically, to cause damage to health, life, property, or any other interest of value. The probabil ...

”, meaning a potential source of harm. This definition comes from Blount’s “Glossographia” (1661) and was the main definition in the OED 1st (1914) and 2nd (1989) editions. Modern equivalents refer to “unwanted events” Hansson, Sven Ove
"Risk"
''The Stanford Encyclopedia of Philosophy (Fall 2018 Edition)'', Edward N. Zalta (ed.)
or “something bad that might happen”. :“Chance of harm”. This definition comes from Johnson’s “Dictionary of the English Language” (1755), and has been widely paraphrased, including “possibility of loss” or “probability of unwanted events”. :“Uncertainty about loss”. This definition comes from Willett’s “Economic Theory of Risk and Insurance” (1901). This links “risk” to “
uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially o ...

”, which is a broader term than chance or probability. :“Measurable uncertainty”. This definition comes from Knight’s “Risk, Uncertainty and Profit” (1921). It allows “risk” to be used equally for positive and negative outcomes. In insurance, risk involves situations with unknown outcomes but known probability distributions. :“Volatility of return”. Equivalence between risk and variance of return was first identified in Markovitz’s “Portfolio Selection” (1952). In finance, volatility of return is often equated to risk. :“Statistically expected loss”. The
expected value In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by exp ...
of loss was used to define risk by Wald (1939) in what is now known as
decision theory Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent's choices. Decision theory can be broken into two branches: normative Normative generally means relating to an evaluative standard. Normativi ...
. The probability of an event multiplied by its magnitude was proposed as a definition of risk for the planning of the
Delta Works The Delta Works ( nl, Deltawerken) is a series of construction projects in the southwest of the Netherlands to protect a large area of land around the Rhine–Meuse–Scheldt delta from the sea. Constructed between 1954 and 1997, the works cons ...
in 1953, a flood protection program in the
Netherlands ) , national_anthem = ( en, "William of Nassau") , image_map = EU-Netherlands.svg , map_caption = , image_map2 = BES islands location map.svg , map_caption2 = , image_map3 ...

. It was adopted by the US Nuclear Regulatory Commission (1975), and remains widely used. :“Likelihood and severity of events”. The “triplet” definition of risk as “scenarios, probabilities and consequences” was proposed by Kaplan & Garrick (1981). Many definitions refer to the likelihood/probability of events/effects/losses of different severity/consequence, e.g. ISO Guide 73 Note 4. :“Consequences and associated uncertainty”. This was proposed by Kaplan & Garrick (1981). This definition is preferred in
Bayesian analysis Bayesian inference is a method of statistical inference in which Bayes' theorem In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule; recently Bayes–Price theorem), named after the Reverend Thomas Bay ...
, which sees risk as the combination of events and uncertainties about them. :“Uncertain events affecting objectives”. This definition was adopted by the Association for Project Management (1997). With slight rewording it became the definition in ISO Guide 73. :“Uncertainty of outcome”. This definition was adopted by the UK Cabinet Office (2002) to encourage innovation to improve public services. It allowed “risk” to describe either “positive opportunity or negative threat of actions and events”. :“Asset, threat and vulnerability”. This definition comes from the Threat Analysis Group (2010) in the context of computer security. :“Human interaction with uncertainty”. This definition comes from Cline (2015) 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.
The
Society for Risk Analysis The Society for Risk Analysis (SRA) is a learned society A learned society (; also known as a learned academy, scholarly society, or academic association) is an organization that exists to promote an discipline (academia), academic discipline, p ...
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.”

# Practice areas

The understanding of risk, the common methods of management, the measurements of risk and even the definition of risk differ in different practice areas. This section provides links to more detailed articles on these areas.

## Business risk

Business risks arise from uncertainty about the profit of a commercial business due to unwanted events such as changes in tastes, changing preferences of consumers, strikes, increased competition, changes in government policy, obsolescence etc. Business risks are controlled using techniques of
risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something ...

. In many cases they may be managed by intuitive steps to prevent or mitigate risks, by following regulations or standards of good practice, or by
insurance Insurance is a means of protection from financial loss. It is a form of risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. R ...

.
Enterprise risk managementEnterprise risk management (ERM) in business includes the methods and processes used by organizations to manage risks and seize opportunities related to the achievement of their objectives. ERM provides a framework for risk management, which typical ...
includes the methods and processes used by organizations to manage risks and seize opportunities related to the achievement of their objectives.

## Economic risk

Economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. The term was fo ...

is concerned with the production, distribution and consumption of goods and services. Economic risk arises from uncertainty about economic outcomes. For example, economic risk may be the chance that macroeconomic conditions like exchange rates, government regulation, or political stability will affect an investment or a company’s prospects. In economics, as in finance, risk is often defined as quantifiable uncertainty about gains and losses.

## Environmental risk

Environmental risk arises from
environmental hazards A biophysical environment is a biotic Biotics describe living or once living components of a community; for example organisms, such as animals and plants. Biotic may refer to: *Life, the condition of living organisms *Biology, the study of life ...
or
environmental issues Environmental issues are harmful effects of human activity on the biophysical environment. Environmental protection is a practice of protecting the natural environment The natural environment or natural world encompasses all life, living an ...
. In the environmental context, risk is defined as “The chance of harmful effects to human health or to ecological systems”. Environmental risk assessment aims to assess the effects of stressors, often chemicals, on the local environment.

## Financial risk

Finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money available which could ...

is concerned with money management and acquiring funds.
Financial risk Financial risk is any of various types of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information ...
arises from uncertainty about financial returns. It includes
market risk Market risk is the risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predic ...
,
credit risk A credit risk is risk of default Default may refer to: Law * Default (law), the failure to do something required by law ** Default (finance) In finance Finance is the study of financial institutions, financial markets and how they oper ...
, liquidity risk and
operational risk Operational risk is "the risk of a change in value caused by the fact that actual losses, incurred for inadequate or failed internal processes, people and systems, or from external events (including legal risk), differ from the expected losses". ...
. In finance, risk is the possibility that the actual return on an investment will be different from its expected return. This includes not only "
downside riskDownside risk is the financial risk Financial risk is any of various types of risk associated with financingFunding is the act of providing resources to finance a need, program, or project. While this is usually in the form of money, it can also ...
" (returns below expectations, including the possibility of losing some or all of the original investment) but also "upside risk" (returns that exceed expectations). In Knight’s definition, risk is often defined as quantifiable uncertainty about gains and losses. This contrasts with
Knightian uncertainty In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods a ...
, which cannot be quantified.
Financial risk modelingFinancial risk modeling is the use of formal econometric techniques to determine the aggregate financial risk, risk in a financial Portfolio (finance), portfolio. Risk modeling is one of many subtasks within the broader area of financial modeling. R ...
determines the aggregate risk in a financial portfolio.
Modern portfolio theory Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of Diversification ...
measures risk using the
variance In probability theory Probability theory is the branch of concerned with . Although there are several different , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of . Typically these ax ...

(or standard deviation) of asset prices. More recent risk measures include
value at risk Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by fi ...

. Because investors are generally risk averse, investments with greater inherent risk must promise higher expected returns. Financial risk management uses financial instruments to manage exposure to risk. It includes the use of a Hedge (finance), hedge to offset risks by adopting a position in an opposing market or investment. In financial audit, audit risk refers to the potential that an audit report may fail to detect material misstatement either due to error or fraud.

## Health risk

Health risks arise from disease and other biological hazards. Epidemiology is the study and analysis of the distribution, patterns and determinants of health and disease. It is a cornerstone of public health, and shapes policy decisions by identifying risk factors for disease and targets for preventive healthcare. In the context of public health, risk assessment is the process of characterizing the nature and likelihood of a harmful effect to individuals or populations from certain human activities. Health risk assessment can be mostly qualitative or can include statistical estimates of probabilities for specific populations. A health risk assessment (also referred to as a health risk appraisal and health & well-being assessment) is a questionnaire screening tool, used to provide individuals with an evaluation of their health risks and quality of life

## Health, safety, and environment risks

Health, safety, and environment (HSE) are separate practice areas; however, they are often linked. The reason is typically to do with organizational management structures; however, there are strong links among these disciplines. One of the strongest links 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.

## Information technology risk

Information technology (IT) is the use of computers to store, retrieve, transmit, and manipulate data. IT risk (or cyber risk) arises from the potential that a threat may exploit a vulnerability to breach security and cause harm. IT risk management applies risk management methods to IT to manage IT risks. Computer security is the protection of IT systems by managing IT risks. Information security is the practice of protecting information by mitigating information risks. While IT risk is narrowly focused on computer security, information risks extend to other forms of information (paper, microfilm).

## Insurance risk

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 (finance), 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. The term “risk” has a long history in insurance and has acquired several specialised definitions, including “the subject-matter of an insurance contract”, “an insured peril” as well as the more common “possibility of an event occurring which causes injury or loss”.

## Occupational risk

Occupational health and safety is concerned with occupational hazards experienced in the workplace. The Occupational Health and Safety Assessment Series (OHSAS) standard OHSAS 18001 in 1999 defined risk as the “combination of the likelihood and consequence(s) of a specified hazardous event occurring”. In 2018 this was replaced by ISO 45001 “Occupational health and safety management systems”, which use the ISO Guide 73 definition.

## Project risk

A project is an individual or collaborative undertaking planned to achieve a specific aim. Project risk is defined as, "an uncertain event or condition that, if it occurs, has a positive or negative effect on a project’s objectives”. Project risk management aims to increase the likelihood and impact of positive events and decrease the likelihood and impact of negative events in the project.

## Safety risk

Safety is concerned with a variety of hazards that may result in accidents causing harm to people, property and the environment. In the safety field, risk is typically defined as the “likelihood and severity of hazardous events”. Safety risks are controlled using techniques of
risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something ...

. A high reliability organisation (HRO) involves complex operations in environments where catastrophic accidents could occur. Examples include aircraft carriers, air traffic control, aerospace and nuclear power stations. Some HROs manage risk in a highly quantified way. The technique is usually referred to as probabilistic risk assessment (PRA). See WASH-1400 for an example of this approach. The incidence rate can also be reduced due to the provision of better occupational health and safety programmes

## Security risk

Security is freedom from, or resilience against, potential harm caused by others. 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." Security risk management involves protection of assets from harm caused by deliberate acts.

# Assessment and management of risk

## Risk management

Risk is ubiquitous in all areas of life and we all manage these risks, consciously or intuitively, whether we are managing a large organization or simply crossing the road. Intuitive risk management is addressed under the Risk#Psychology of risk, psychology of risk below. Risk management refers to a systematic approach to managing risks, and sometimes to the profession that does this. A general definition is that risk management consists of “coordinated activities to direct and control an organization with regard to risk".
ISO 31000 ISO 31000 is a family of standards relating to risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about th ...
, the international standard for risk management, describes a risk management process that consists of the following elements: :Communicating and consulting :Establishing the scope, context and criteria :Risk#Risk assessment, Risk assessment - recognising and characterising risks, and evaluating their significance to support decision-making. This includes Risk#Risk identification, risk identification, Risk#Risk analysis, risk analysis and Risk#Risk evaluation and risk criteria, risk evaluation. :Risk treatment - selecting and implementing options for addressing risk. :Monitoring and reviewing :Recording and reporting In general, the aim of risk management is to assist organizations in “setting strategy, achieving objectives and making informed decisions”. The outcomes should be “scientifically sound, cost-effective, integrated actions that [treat] risks while taking into account social, cultural, ethical, political, and legal considerations”. In contexts where risks are always harmful, risk management aims to “reduce or prevent risks”. In the safety field it aims “to protect employees, the general public, the environment, and company assets, while avoiding business interruptions”. For organizations whose definition of risk includes “upside” as well as “downside” risks, risk management is “as much about identifying opportunities as avoiding or mitigating losses”. It then involves “getting the right balance between innovation and change on the one hand, and avoidance of shocks and crises on the other”.

## Risk assessment

Risk assessment is a systematic approach to recognising and characterising risks, and evaluating their significance, in order to support decisions about how to manage them.
ISO 31000 ISO 31000 is a family of standards relating to risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about th ...
defines it in terms of its components as “the overall process of risk identification, risk analysis and risk evaluation”. Risk assessment can be qualitative, semi-quantitative or quantitative: :Qualitative approaches are based on qualitative descriptions of risks and rely on judgement to evaluate their significance. :Semi-quantitative approaches use numerical rating scales to group the consequences and probabilities of events into bands such as “high”, “medium” and “low”. They may use a risk matrix to evaluate the significance of particular combinations of probability and consequence. :Quantitative approaches, including Quantitative risk assessment (QRA) and probabilistic risk assessment (PRA), estimate probabilities and consequences in appropriate units, combine them into risk metrics, and evaluate them using numerical risk criteria. The specific steps vary widely in different Risk#Practice areas, practice areas.

## Risk identification

Risk identification is “the process of finding, recognizing and recording risks”. It “involves the identification of risk sources, events, their causes and their potential consequences.”
ISO 31000 ISO 31000 is a family of standards relating to risk management Risk management is the identification, evaluation, and prioritization of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about th ...
describes it as the first step in a risk assessment process, preceding risk analysis and risk evaluation. In safety contexts, where risk sources are known as hazards, this step is known as “hazard identification”. There are many different methods for identifying risks, including: :Checklists or taxonomies based on past data or theoretical models. :Evidence-based methods, such as literature reviews and analysis of historical data. :Team-based methods that systematically consider possible deviations from normal operations, e.g. hazard and operability study, HAZOP, failure mode and effects analysis, FMEA and Structured What If Technique, SWIFT. :Empirical methods, such as testing and modelling to identify what might happen under particular circumstances. :Techniques encouraging imaginative thinking about possibilities of the future, such as scenario analysis. :Expert-elicitation methods such as brainstorming, interviews and audits. Sometimes, risk identification methods are limited to finding and documenting risks that are to be analysed and evaluated elsewhere. However, many risk identification methods also consider whether control measures are sufficient and recommend improvements. Hence they function as stand-alone qualitative risk assessment techniques.

## Risk analysis

Risk analysis is about developing an understanding of the risk. ISO defines it as “the process to comprehend the nature of risk and to determine the level of risk”. In the ISO 31000 risk assessment process, risk analysis follows risk identification and precedes risk evaluation. However, these distinctions are not always followed. Risk analysis may include: :Determining the sources, causes and drivers of risk :Investigating the effectiveness of existing controls :Analysing possible consequences and their likelihood :Understanding interactions and dependencies between risks :Determining measures of risk :Verifying and validating results :Uncertainty and sensitivity analysis Risk analysis often uses data on the probabilities and consequences of previous events. Where there have been few such events, or in the context of systems that are not yet operational and therefore have no previous experience, various analytical methods may be used to estimate the probabilities and consequences: :Proxy or analogue data from other contexts, presumed to be similar in some aspects of risk. :Theoretical models, such as Monte Carlo method, Monte Carlo simulation and Quantitative risk assessment software. :Logical models, such as Bayesian networks, fault tree analysis and event tree analysis :Expert judgement, such as absolute probability judgement or the Delphi method.

## Risk evaluation and risk criteria

Risk evaluation involves comparing estimated levels of risk against risk criteria to determine the significance of the risk and make decisions about risk treatment actions. In most activities, risks can be reduced by adding further controls or other treatment options, but typically this increases cost or inconvenience. It is rarely possible to eliminate risks altogether without discontinuing the activity. Sometimes it is desirable to increase risks to secure valued benefits. Risk criteria are intended to guide decisions on these issues. Types of criteria include: :Criteria that define the level of risk that can be accepted in pursuit of objectives, sometimes known as risk appetite, and evaluated by risk/reward analysis. :Criteria that determine whether further controls are needed, such as benefit-cost ratio. :Criteria that decide between different risk management options, such as multiple-criteria decision analysis. The simplest framework for risk criteria is a single level which divides acceptable risks from those that need treatment. This gives attractively simple results but does not reflect the uncertainties involved both in estimating risks and in defining the criteria. The tolerability of risk framework, developed by the UK Health and Safety Executive, divides risks into three bands: :Unacceptable risks – only permitted in exceptional circumstances. :Tolerable risks – to be kept as low as reasonably practicable (ALARP), taking into account the costs and benefits of further risk reduction. :Broadly acceptable risks – not normally requiring further reduction.

# Descriptions of risk

There are many different risk metrics that can be used to describe or “measure” risk.

## Triplets

Risk is often considered to be a set of triplets (also described as a vector): :$\text = <\text_\text _\text _\text >$ for i = 1,2,....,N where: :$\text_\text$ is a scenario describing a possible event :$\text_\text$ is the probability of the scenario :$\text_\text$ is the consequence of the scenario :$\text$ is the number of scenarios chosen to describe the risk These are the answers to the three fundamental questions asked by a risk analysis: :What can happen? :How likely is it to happen? :If it does happen, what would the consequences be? Risks expressed in this way can be shown in a table or risk register. They may be quantitative or qualitative, and can include positive as well as negative consequences. The scenarios can be plotted in a consequence/likelihood matrix (or risk matrix). These typically divide consequences and likelihoods into 3 to 5 bands. Different scales can be used for different types of consequences (e.g. finance, safety, environment etc.), and can include positive as well as negative consequences. An updated version recommends the following general description of risk: :$\text = \left(\text \right)$ where: :$\text$ is an event that might occur :$\text$ is the consequences of the event :$\text$ is an assessment of uncertainties :$\text$ is a knowledge-based probability of the event :$\text$ is the background knowledge that U and P are based on

## Probability distributions

If all the consequences are expressed in the same units (or can be converted into a consistent loss function), the risk can be expressed as a probability density function describing the “uncertainty about outcome”: :$\text = \text$ This can also be expressed as a cumulative distribution function (CDF) (or S curve). One way of highlighting the tail of this distribution is by showing the probability of exceeding given losses, known as a cumulative distribution function#Derived functions, complementary cumulative distribution function, plotted on logarithmic scales. Examples include frequency-number (FN) diagrams, showing the annual frequency of exceeding given numbers of fatalities. A simple way of summarising the size of the distribution’s tail is the loss with a certain probability of exceedance, such as the Value at Risk.

## Expected values

Risk is often measured as the
expected value In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by exp ...

## Mild Versus Wild Risk

Benoit Mandelbrot distinguished between "mild" and "wild" risk and argued that risk assessment and analysis must be fundamentally different for the two types of risk. Mild risk follows Normal distribution, normal or near-normal probability distributions, is subject to Regression toward the mean, regression to the mean and the law of large numbers, and is therefore relatively predictable. Wild risk follows fat-tailed distributions, e.g., Pareto distribution, Pareto or power-law distributions, is subject to regression to the tail (infinite mean or variance, rendering the law of large numbers invalid or ineffective), and is therefore difficult or impossible to predict. A common error in risk assessment and analysis is to underestimate the wildness of risk, assuming risk to be mild when in fact it is wild, which must be avoided if risk assessment and analysis are to be valid and reliable, according to Mandelbrot.

## Risk attitude, appetite and tolerance

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. 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. Risk compensation is a theory which suggests that people typically adjust their behavior in response to the perceived level of risk, becoming more careful where they sense greater risk and less careful if they feel more protected. By way of example, it has been observed that motorists drove faster when wearing seatbelts and closer to the vehicle in front when the vehicles were fitted with Anti-lock braking system, anti-lock brakes.

## Risk and autonomy

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. "People's autonomy used to be compromised by institution walls, now it's too often our risk management practices", according to John O'Brien (human services thinker), 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.

# List of related books

This is a list of books about risk issues.

# See also

* Ambiguity aversion * Audit risk * Benefit shortfall * Civil defence * Countermeasure * Early case assessment * External risk * Enterprise risk * Event chain methodology *
Financial risk Financial risk is any of various types of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information ...
* Fuel price risk management * Global catastrophic risk * Hazard (risk) * Identity resolution * Information assurance * Inherent risk * Inherent risk (accounting) * International Risk Governance Council * ISO/PAS 28000 * IT risk * Legal risk * Life-critical system * Liquidity risk * Loss aversion * Moral hazard * Operational risk * Preventive maintenance * Probabilistic risk assessment * Process risk * Reputational risk * Reliability engineering * Risk analysis (business), Risk analysis * Risk assessment * Risk compensation ** Peltzman effect * Risk management * Risk-neutral measure * Risk perception * Risk register * Sampling risk * Systemic risk * Systematic risk * Uncertainty * Vulnerability

# Bibliography

## Referred literature

* James Franklin (philosopher), James Franklin, 2001: ''The Science of Conjecture: Evidence and Probability Before Pascal'', Baltimore: Johns Hopkins University Press. * * Niklas Luhmann, 1996: ''Modern Society Shocked by its Risks'' (= University of Hong Kong, Department of Sociology Occasional Papers 17), Hong Kong, available vi
HKU Scholars HUB

## Books

* 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'' . Risk explained and its appreciation by man traced from earliest times through all the major figures of their ages in mathematical circles. * * * * * * * Gardner D. ''Risk: The Science and Politics of Fear'', Random House Inc. (2008) . * Novak S.Y. Extreme value methods with applications to finance. London: CRC. (2011) . * Hopkin P. Fundamentals of Risk Management. 2nd Edition. Kogan-Page (2012)

## Articles and papers

* * * * * * * Hansson, Sven Ove. (2007). "Risk", ''The Stanford Encyclopedia of Philosophy'' (Summer 2007 Edition), Edward N. Zalta (ed.), forthcomin

* Holton, Glyn A. (2004). "Defining Risk", ''Financial Analysts Journal'', 60 (6), 19–25. A paper exploring the foundations of risk. (PDF file). * Knight, F. H. (1921) ''Risk, Uncertainty and Profit'', Chicago: Houghton Mifflin Company. (Cited at

§ I.I.26.). * Kruger, Daniel J., Wang, X.T., & Wilke, Andreas (2007) "Towards the development of an evolutionarily valid domain-specific risk-taking scale" ''Evolutionary Psychology'' (PDF file). * * * * Neill, M. Allen, J. Woodhead, N. Reid, S. Irwin, L. Sanderson, H. 2008 "A Positive Approach to Risk Requires Person Centred Thinking" London, CSIP Personalisation Network, Department of Health. Available from: https://web.archive.org/web/20090218231745/http://networks.csip.org.uk/Personalisation/Topics/Browse/Risk/ [Accessed 21 July 2008]. *

# External links

Risk
– The entry of the Stanford Encyclopedia of Philosophy {{DEFAULTSORT:Risk Risk, Actuarial science Environmental social science concepts