Risk aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome.[1]
For the related psychological concept, see Risk aversion (psychology).Risk aversion explains the inclination to agree to a situation with a more predictable, but possibly lower payoff, rather than another situation with a highly unpredictable, but possibly higher payoff. For example, a risk-averse investor might choose to put their money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value.
A person is given the choice between two scenarios: one with a guaranteed payoff, and one with a risky payoff with same average value. In the former scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. The expected payoff for both scenarios is $50, meaning that an individual who was insensitive to risk would not care whether they took the guaranteed payment or the gamble. However, individuals may have different risk attitudes.[2][3][4]
A person is said to be:
The average payoff of the gamble, known as its expected value, is $50. The smallest guaranteed dollar amount that an individual would be indifferent to compared to an uncertain gain of a specific average predicted value is called the certainty equivalent, which is also used as a measure of risk aversion. An individual that is risk averse has a certainty equivalent that is smaller than the prediction of uncertain gains. The risk premium is the difference between the expected value and the certainty equivalent. For risk-averse individuals, risk premium is positive, for risk-neutral persons it is zero, and for risk-loving individuals their risk premium is negative.
of the form is unique in exhibiting constant absolute risk aversion (CARA): is constant with respect to c.
Exponential utility
Limitations of expected utility treatment of risk aversion[edit]
Using expected utility theory's approach to risk aversion to analyze small stakes decisions has come under criticism. Matthew Rabin has showed that a risk-averse, expected-utility-maximizing individual who,
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.[17]
Rabin criticizes this implication of expected utility theory on grounds of implausibility—individuals who are risk averse for small gambles due to diminishing marginal utility would exhibit extreme forms of risk aversion in risky decisions under larger stakes. 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 considering only the final wealth.
Another limitation is the reflection effect, which demonstrates the reversing of risk aversion. This effect was first presented by Kahneman and Tversky as a part of the prospect theory, in the behavioral economics domain.
The reflection effect is an identified pattern of opposite preferences between negative as opposed to positive prospects: people tend to avoid risk when the gamble is between gains, and to seek risks when the gamble is between losses.[18] For example, most people prefer a certain gain of 3,000 to an 80% chance of a gain of 4,000. When posed the same problem, but for losses, most people prefer an 80% chance of a loss of 4,000 to a certain loss of 3,000.
The reflection effect (as well as the certainty effect) is inconsistent with the expected utility hypothesis. It is assumed that the psychological principle which stands behind this kind of behavior is the overweighting of certainty. Options which are perceived as certain are over-weighted relative to uncertain options. This pattern is an indication of risk-seeking behavior in negative prospects and eliminates other explanations for the certainty effect such as aversion for uncertainty or variability.[18]
The initial findings regarding the reflection effect faced criticism regarding its validity, as it was claimed that there are insufficient evidence to support the effect on the individual level. Subsequently, an extensive investigation revealed its possible limitations, suggesting that the effect is most prevalent when either small or large amounts and extreme probabilities are involved.[19][20]
Bargaining and risk aversion[edit]
Numerous studies have shown that in riskless bargaining scenarios, being risk-averse is disadvantageous. Moreover, opponents will always prefer to play against the most risk-averse person.[21] Based on both the von Neumann-Morgenstern and Nash Game Theory model, a risk-averse person will happily receive a smaller commodity share of the bargain.[22] This is because their utility function concaves hence their utility increases at a decreasing rate while their non-risk averse opponents may increase at a constant or increasing rate.[23] Intuitively, a risk-averse person will hence settle for a smaller share of the bargain as opposed to a risk-neutral or risk-seeking individual.
The behavioural approach to employment status[edit]
The basis of the theory, on the connection between employment status and risk aversion, is the varying income level of individuals. On average higher income earners are less risk averse than lower income earners. In terms of employment the greater the wealth of an individual the less risk averse they can afford to be, and they are more inclined to make the move from a secure job to an entrepreneurial venture. The literature assumes a small increase in income or wealth initiates the transition from employment to entrepreneurship-based decreasing absolute risk aversion (DARA), constant absolute risk aversion (CARA), and increasing absolute risk aversion (IARA) preferences as properties in their utility function.[33] The apportioning risk perspective can also be used to as a factor in the transition of employment status, only if the strength of downside risk aversion exceeds the strength of risk aversion.[33] If using the behavioural approach to model an individual’s decision on their employment status there must be more variables than risk aversion and any absolute risk aversion preferences.
Incentive effects are a factor in the behavioural approach an individual takes in deciding to move from a secure job to entrepreneurship. Non-financial incentives provided by an employer can change the decision to transition into entrepreneurship as the intangible benefits helps to strengthen how risk averse an individual is relative to the strength of downside risk aversion. Utility functions do not equate for such effects and can often screw the estimated behavioural path that an individual takes towards their employment status.[34]
The design of experiments, to determine at what increase of wealth or income would an individual change their employment status from a position of security to more risky ventures, must include flexible utility specifications with salient incentives integrated with risk preferences.[34] The application of relevant experiments can avoid the generalisation of varying individual preferences through the use of this model and its specified utility functions.