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Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. Risk aversion occurs when a person is willing to accept a lower expected payoff if it means they can have a more predictable outcome. For a more general discussion see the main article risk. Economics (from the Greek οίκος [oikos], house, and νÎμω [nemo], rules, hence household management) is the social science that studies the production, distribution, trade and consumption of goods and services in the context of the competing alternative allocations of goods and courses of action. ...
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. ...
In probability theory (and especially gambling), 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 to win per bet if bets with identical...
Risk is the potential harm that may arise from some present process or from some future event. ...
Example A person is given the choice between a bet of either receiving $100 or nothing, both with a probability of 50%. Now she is risk averse if she would accept a payoff of $40 with probability 100%, risk neutral if she would accept no less than $50 or risk-loving (risk-proclive) for a payoff of $60.
(The average payoff of the bet, the expected value would be $50. The amount accepted is called the certainty equivalent, the difference between it and expected value the risk premium). In probability theory (and especially gambling), 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 to win per bet if bets with identical...
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 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. New File links The following pages link to this file: Risk aversion ...
New File links The following pages link to this file: Risk aversion ...
This article is about utility in economics and in game theory. ...
Money is any marketable good or token used by a society as a store of value, a medium of exchange, or a unit of account. ...
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 ($50 − $40) / $40 or 25%.
Measures of 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 linear 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 In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it preserves linear combinations. Definition and first consequences Formally, if V and W are...
Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ...
ru(c) = − u''(c) / u'(c).
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.
Also used is the Arrow-Pratt measure of relative risk-aversion (RRA) or coefficient of relative risk aversion, which is defined as Ru(c) = x * ru(c) = − xu''(c) / u'(c). As above, 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.
Limitations The notion of (constant) risk aversion has come under criticism from behavioral economics. According to Matthew Rabin of 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. ...
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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.
Rabin claims that this effect brings doubt upon the applicability of utility theory. However, it should be noted that examples such as this one hinge on the assumption that the consumer turns down the low-stakes gamble no matter what their initial wealth. The usual criticism of this assumption is that the existence of such a consumer is highly dubious. See [1] for more on this.
A perhaps more believable criticism of utility theory is the difficulty by laypersons of estimating very small probabilities and the preference of gains versus losses (loss aversion). In prospect theory, loss aversion refers to the tendency for people to strongly prefer avoiding losses than acquiring gains. ...
Experiments with primates suggest risk aversion is a hard-wired biological behaviour[2].
See also Risk is the potential harm that may arise from some present process or from some future event. ...
This article is about utility in economics and in game theory. ...
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. ...
THE BUSINESS TIMES Trader of our time Retail investor’s head-on competition with fund managers no longer fun By Scooby [Singapore] Big and Budgeted fund operators are busy crafting a niche in the heartland of retail investment. ...
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