Risk aversion is a concept in economics, finance, and psychology related to the behaviour of consumers and investors under uncertainty. Economics is the social science that studies the production distribution, and consumption of goods and services. The field of finance refers to the concepts of Time, Money and Risk and how they are interrelated Psychology (from Greek grc ψῡχή psȳkhē, "breath life soul" and grc -λογία -logia) is an Academic and Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.
The inverse of a person's risk aversion is sometimes called their risk tolerance (for a more general discussion of the concept, see risk). Risk is a Concept that denotes the precise probability of specific eventualities
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Example
A person is given the choice between two scenarios, one certain and one not. In the uncertain scenario, the person is to make a gamble with an equal probability between receiving $100 or nothing. The alternative scenario is to receive a specific dollar amount with certainty (probability of 1).
Investors have different risk attitudes. See Investor AB for the Swedish investment company An investor is any party that makes an Investment. A person is
- risk-averse if he or she would accept a certain payoff of less than $50 (for example, $40) rather than the gamble.
- risk neutral if he or she is indifferent between the bet and a certain $50 payment. In Economics, risk neutral behavior is in between Risk aversion and Risk seeking.
- risk-seeking (or risk-loving) if the certain payment must be more than $50 (for example, $60) to induce him or her to take the certain option over the gamble.
The average payoff of the gamble, known as its expected value, is $50. The dollar amount accepted instead of the bet is called the certainty equivalent, and the difference between it and the expected value is called the risk premium. In Economics, Game theory, and Decision theory the expected utility theorem or expected utility hypothesis predicts that the "betting preferences" A risk premium (plural risk premia) is the minimum difference a person requires to be willing to take an uncertain Bet, between the expected value of the bet and the
Utility of money
In utility theory, a consumer has a utility function U(xi) where xi are amounts of goods with index i. In Economics, utility is a measure of the relative satisfaction from or desirability of Consumption of various Goods and services. From this, it is possible to derive a function u(c), of utility of consumption c as a whole. Here, consumption c is equivalent to money in real terms, i. Money is anything that is generally accepted as Payment for Goods and services and repayment of Debts. e. without inflation. In economics inflation or price inflation is a rise in the general level of prices of goods and services over a period of time The utility function u(c) is defined only modulo linear transformation. The word modulo (Latin with respect to a modulus of ___ is the Latin Ablative of Modulus which itself means "a small measure In Mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two Vector spaces that
The graph shows this situation for the risk-averse player: The utility of the bet,
- E(u) = (u(0) + u(100)) / 2
is as big as that of the certainty equivalence, CE. The risk premium is
or 25%.
Measures of risk aversion
Absolute risk aversion
The higher the curvature of u(c), the higher the risk aversion. However, since expected utility functions are not uniquely defined (only up to affine transformations), a measure that stays constant is needed. In Geometry, an affine transformation or affine map or an affinity (from the Latin affinis, "connected with" between two Vector This measure is the Arrow-Pratt measure of absolute risk-aversion (ARA), after the economists Kenneth Arrow and John W. Kenneth Joseph Arrow (born August 23, 1921) is an American Economist and joint winner of the Nobel Memorial Prize in Economics Pratt or coefficient of absolute risk aversion, defined as
.
The following expressions relate to this term:
- Exponential utility of the form u(c) = − e − αc is unique in exhibiting constant absolute risk aversion (CARA): ru(c) = α is constant with respect to c. In Economics exponential utility refers to a specific form of the Utility function, used in many contexts because of its convenience when Uncertainty is
- Decreasing/increasing absolute risk aversion (DARA/IARA) if ru(c) is decreasing/increasing. An example for a DARA utility function is u(c) = ln(c),ru(c) = 1 / c, while u(c) = c − αc2,α > 0,ru(c) = 2α / (1 − 2αc) would represent a utility function exhibiting IARA.
- Experimental and empirical evidence is mostly consistent with decreasing absolute risk aversion.
Relative risk aversion
The Arrow-Pratt measure of relative risk-aversion (RRA) or coefficient of relative risk aversion is defined as
.
Like for absolute risk aversion, the corresponding terms constant relative risk aversion (CRRA) and decreasing/increasing relative risk aversion (DRRA/IRRA) are used. This measure has the advantage that it is still a valid measure of risk aversion, even if it changes from risk-averse to risk-loving, i. e. is not strictly convex/concave over all c.
In intertemporal choice problems, the elasticity of intertemporal substitution is often unable to be disentangled from the coefficient of relative risk aversion. Intertemporal choice is the study of the relative value people assign to two or more payoffs at different points in time The "isoelastic" utility function
exhibits constant relative risk aversion with Ru(c) = ρ and the elasticity of intertemporal substitution 
. When ρ = 1 this simplifies to the case of log utility, and the income effect and substitution effect on saving exactly offset. Consumer theory is a theory of Microeconomics that relates Preferences to consumer demand curves. Consumer theory is a theory of Microeconomics that relates Preferences to consumer demand curves.
Portfolio theory
In modern portfolio theory, risk aversion is measured as the additional marginal reward an investor requires to accept additional risk. Modern portfolio theory ( MPT) proposes how rational investors will use diversification to optimize their portfolios and how a risky asset should In modern portfolio theory, risk is being measured as standard deviation of the return on investment, i. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values e. the square root of its variance. In Mathematics, a square root of a number x is a number r such that r 2 = x, or in words a number r whose In Probability theory and Statistics, the variance of a Random variable, Probability distribution, or sample is one measure of In advanced portfolio theory, different kinds of risk are taken into consideration. They are being measured as the n-th radical of the n-th central moment. In Mathematics, an n th root of a Number a is a number b such that bn = a. In Probability theory and Statistics, the k th moment about the Mean (or k th central moment The symbol used for risk aversion is A or An.
![A_n = \frac{dE(r)}{d\sqrt[n]{\mu_n}} = \frac{1}{n} \frac{dE(r)}{d\mu_n}](../../../../math/b/c/4/bc4a948e9a3bb8e0ed8e54797f559679.png)
Limitations
The notion of (constant) risk aversion has come under criticism from behavioral economics. Behavioral economics and behavioral finance are closely related fields which apply scientific research on human and social cognitive and emotional factors to better According to Matthew Rabin of UC Berkeley, a consumer who,
from any initial wealth level [. Matthew Joel Rabin (born December 27, 1963) is the Edward G and Nancy S The University of California Berkeley (also referred to as Cal, Berkeley and UC Berkeley) is a major research university located in Berkeley . . ] turns down gambles where she loses $100 or gains $110, each with 50% probability [. . . ] will turn down 50-50 bets of losing $1,000 or gaining any sum of money.
The point is that if we calculate the constant relative risk aversion (CRRA) from the first small-stakes gamble it will be so great that the same CRRA, applied to gambles with larger stakes, will lead to absurd predictions. The bottom line is that we cannot infer a CRRA from one gamble and expect it to scale up to larger gambles.
It is noteworthy that Rabin's article has often been wrongly quoted as a justification for assuming risk neutral behavior of people in small stake gambles.
One solution to the problem observed by Rabin is that proposed by prospect theory and cumulative prospect theory, where outcomes are considered relative to a reference point (usually the status quo), rather than to consider only the final wealth. Prospect theory is a theory that describes decisions between alternatives that involve Risk, i Cumulative Prospect Theory is a model for descriptive decisions under risk which has been introduced by Amos Tversky and Daniel Kahneman in 1992 (Tversky
Other categories
See "Harm Reduction". Harm reduction is a Philosophy of Public health, intended to be a progressive alternative to the prohibition of certain potentially dangerous
Risk aversion theory can be applied to many aspects of life and its challenges, for example:
- Bribery and corruption - whether the risk of being implicated or caught outweighs the potential personal or professional rewards
- Drugs - whether the risk of having a bad trip outweighs the benefits of possible transformative one; whether the risk of defying social bans is worth the experience of alteration. Bribery, a form of pecuniary corruption is an act usually implying money or gift given that alters the behaviour of the recipient in ways not consistent with the duties of that person Political corruption is the use of governmental powers by government officials for illegitimate private gain A drug, broadly speaking is any chemical substance that when absorbed into the body Bad trip is a slang term for a psychedelic crisis, a disturbing experience sometimes associated with use of a psychedelic drug such as LSD, salvinorin Spiritual transformation is the act of Transforming the Deepest Aspects of the Human Spirit via a Self-induced or Divine
- Sex - judgement whether an experience that goes against social convention, ethical mores or common health prescriptions is worth the risk. An organism's sex is defined by the gametes it produces males produce male gametes (spermatozoa or Sperm) while females produce female gametes (ova or Egg cells; individual A convention is a set of agreed, stipulated or generally accepted Standards norms social norms or criteria, often taking the form of Ethics is a major branch of Philosophy, encompassing right conduct and good life
- Extreme sports - having the ability to go against biological predepositions like the fear of height. Extreme sport (also called action sport and adventure sport) is a media term for certain activities perceived as having a high level of inherent Instinct is the inherent disposition of a living Organism toward a particular Behavior. Acrophobia (from Greek, meaning "summit" is an extreme or irrational Fear of Heights It belongs to a category of Specific
See also
- Optimism bias
- Utility
- Risk premium
- Equity premium puzzle
- Investor profile
- St. Petersburg paradox
- Compulsive gambling, a contrary behavior
External links
- More thorough introduction
- Prof. Rabin's homepage
- A response (2001) by Ariel Rubinstein
- Paper about problems with risk aversion
- Economist article on monkey experiments showing behaviours resembling risk aversion
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