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Risk aversion is a concept in economics, finance, and psychology explaining the behaviour of consumers and investors under uncertainty. 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 see the main article risk. Face-to-face trading interactions among on the New York Stock Exchange trading floor Economics or oeconomics is the study of human choice behaviour. ...
Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ...
Psychology is an academic and applied field involving the scientific study of mental processes and behavior. ...
In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are...
Risk is a concept that denotes a potential negative impact to an asset or some characteristic of value that may arise from some present process or future event. ...
Example
A person is given the choice between a bet of either receiving $100 or nothing, both with a probability of 50%, or instead, receiving some amount with certainty. Now he is risk-averse if he would rather accept a payoff of less than $50 (for example, $40) with probability 100% than the bet, risk neutral if he was indifferent between the bet and a certain $50 payment, risk-loving if it's required that the payment be more than $50 (for example, $60) to induce him to take the certain option over the bet. In Economics, the term risk neutral is used to describe an individual who cares only about the expected outcome of an investment, and not the risk (variance of outcomes or the potential gains or losses). ...
The average payoff of the bet, the expected value would be $50. The certain amount accepted instead of the bet is called the certainty equivalent, the difference between it and the expected value is called the risk premium. In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are...
The expected utility hypothesis is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. ...
A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ...
Utility of money Image:Risk aversion.jpg Risk aversion example In utility theory, a consumer has a utility function U(xi) where xi are amounts of goods with index i. 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.e. without inflation. The utility function u(c) is defined only modulo linear transformation. In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained by consuming different bundles of goods and services. ...
An example of Money. ...
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 utility functions are not uniquely defined (only up to monotonic transformations), a measure that stays constant is needed. This measure is the Arrow-Pratt measure of absolute risk-aversion (ARA, after the economists Kenneth Arrow and John W. Pratt) or coefficient of absolute risk aversion, defined as Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ...
 . The following expressions relate to this term: - Constant absolute risk aversion (CARA) if ru(c) is constant with respect to c
- Decreasing/increasing absolute risk aversion (DARA/IARA) if ru(c) is decreasing/increasing.
Relative risk aversion The Arrow-Pratt measure of relative risk-aversion (RRA) or coefficient of relative risk aversion is defined as  . As 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.
Portfolio theory In modern portfolio theory, risk aversion is measured as the marginal reward an investor wants to receive if he takes for a new amount of risk. In Modern Portfolio Theory, risk is being measured as standard deviation of the return on investment, i.e. the square root of its variance. In advanced portfolio theory, different kinds of risk are taken in consideration. They are being measured as the n-th radical of the n-th central moment. The symbol used for risk aversion is A or An. Capital Market Line Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how an asset should be priced given its risk relative to the market as a whole. ...
In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is defined as the square root of the variance. ...
In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x. ...
In probability theory and statistics, the variance of a random variable (or equivalently, of a probability distribution) is a measure of its statistical dispersion, indicating how its possible values are spread around the expected value. ...
In mathematics, an nth root of a number a is a number b, such that bn=a. ...
The kth moment about the mean (or kth central moment) of a real-valued random variable X is the quantity E[(X − E[X])k], where E is the expectation operator. ...
 ![A_n = frac{dE(r)}{dsqrt[n]{mu_n}} = frac{1}{n} frac{dE(r)}{dmu_n}](http://upload.wikimedia.org/math/b/c/4/bc4a948e9a3bb8e0ed8e54797f559679.png)
Limitations The notion of (constant) risk aversion has come under criticism from behavioral economics. According to Matthew Rabin of UC Berkeley, a consumer who, Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ...
Matthew Rabin (born December 27, 1963) is Edward G. and Nancy S. Jordan Professor of Economics in the Department of Economics at the University of California -- Berkeley. ...
The University of California, Berkeley (also known as Cal, UC Berkeley, UCB, or simply Berkeley) is a prestigious, public, coeducational university situated in the foothills of Berkeley, California to the east of San Francisco Bay, overlooking the Golden Gate and its bridge. ...
from any initial wealth level [...] 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.
The major solution to the problem observed by Rabin is the one 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 was developed by Daniel Kahneman and Amos Tversky in 1979 as a psychologically realistic alternative to expected utility theory. ...
Cumulative Prospect Theory is a model for descriptive decisions under risk which has been introduced by Amos Tversky and Daniel Kahneman in 1992 (Tversky, Kahneman, 1992). ...
Other Categories See "Harm Reduction". Harm reduction is a philosophy of public health, intended to be a progressive alternative to the prohibition of certain lifestyle choices. ...
Risk aversion theory can be applied to many aspects of life and it's challenges, for example:
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See also Risk is a concept that denotes a potential negative impact to an asset or some characteristic of value that may arise from some present process or future event. ...
In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained by consuming different bundles of goods and services. ...
A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ...
An investor profile or style defines an investors preferences in money decisions, for example: Short term trading or Long term holding (buy and hold Risk averse or risk tolerant / seeker All classes of assets or just one (stocks for example) Value or growth stocks, big cap or small cap...
In probability theory and decision theory the St. ...
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