Risk aversion is the preference for a guaranteed outcome over a gamble with higher or equal expected value. Conversely, rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior. The psychophysics of chance induce overweighting of sure things and of improbable events, relative to events of moderate probability. Underweighting of moderate and high probabilities relative to sure things contributes to risk aversion in the realm of gains by reducing the attractiveness of positive gambles. The same effect also contributes to risk seeking in losses by attenuating the aversiveness of negative gambles. Low probabilities, however, are overweighted, which reverses the pattern described above: low probabilities enhance the value of long-shots and amplify aversion to a small chance of a severe loss. Consequently, people are often risk seeking in dealing with improbable gains and risk averse in dealing with unlikely losses.
Related theories Most theoretical analyses of risky choices depict each option as a gamble that can yield various outcomes with different probabilities. Widely accepted risk-aversion theories, including Expected Utility Theory (EUT) and Prospect Theory (PT), arrive at risk aversion only indirectly, as a side effect of how outcomes are valued or how probabilities are judged. In these analyses, a value function indexes the attractiveness of varying outcomes, a weighting function quantifies the impact of probabilities, and value and weight are combined to establish a utility for each course of action. This last step, combining the weight and value in a meaningful way to make a decision, remains sub-optimal in EUT and PT, as people's psychological assessments of risk do not match objective assessments.
Expected utility theory Expected Utility Theory (EUT) poses a utility calculation linearly combining weights and values of the probabilities associated with various outcomes. By presuming that decision-makers themselves incorporate an accurate weighting of probabilities into calculating expected values for their decision-making, EUT assumes that people's subjective probability-weighting matches objective probability differences, when they are, in reality, exceedingly disparate. Consider the choice between a prospect that offers an 85% chance to win $1000 (with a 15% chance to win nothing) and the alternative of receiving $800 for sure. A large majority of people prefer the sure thing over the gamble, although the gamble has higher (mathematical) expected value (also known as expectation). The expected value of a monetary gamble is a weighted average, in which each possible outcome is weighted by its probability of occurrence. The expected value of the gamble in this example is .85 X $1000 + .15 X $0 = $850, which exceeds the expected value of $800 associated with the sure thing. Research suggests that people do not evaluate prospects by the expected value of their monetary outcomes, but rather by the expected value of the subjective value of these outcomes (see also Expected utility). In most real-life situations, the probabilities associated with each outcome are not specified by the situation, but have to be subjectively estimated by the decision-maker. The subjective value of a gamble is again a weighted average, but now it is the subjective value of each outcome that is weighted by its probability. To explain risk aversion within this framework, Bernoulli proposed that subjective value, or utility, is a concave function of money. In such a function, the difference between the utilities of $200 and $100, for example, is greater than the utility difference between $1,200 and $1,100. It follows from concavity that the subjective value attached to a gain of $800 is more than 80% of the value of a gain of $1,000. Consequently, the concavity of the utility function entails a risk averse preference for a sure gain of $800 over an 80% chance to win $1,000, although the two prospects have the same monetary expected value. While EUT has dominated the analysis of decision-making under risk and has generally been accepted as a normative model of rational choice (telling us how we should make decisions), descriptive models of how people actually behave deviate significantly from this normative model.
Modern Portfolio Theory Modern Portfolio Theory (MPT) was created by economist Harry Markowitz in 1952 to mathematically measure an individual's risk tolerance and reward expectations. The theory was that constant variance allowed for a maximized expected return and to gain a constant expected return variance should be minimized. An asset must be considered in regard to how they will move within the market and by taking these movements into account an investment portfolio can be constructed that decreased risk and had a constant expected return. The levels of additional expected returns are calculated as the standard deviation of the return on investment (square root of the variance). Standard deviation illustrates the fluctuation of an asset's returns over the period of time creating an accepted trading range to estimate possible returns on the asset. This tool enables individuals to determine their level of risk aversion to create a diversified portfolio. MPT has been critiqued for using standard deviation as a form of measurement. Standard deviation is a relative form of measurement and investors using this index for their risk assessment must analyse an appropriate context in which the market sits to ensure a quantified understanding of what the standard deviation means. MPT automatically assumes that investors have an aversion towards risk however can be used by all types of investors to suit their needs individually. Furthermore, under MPT, two portfolios could be represented by the same level of variance hence would be considered equally desirable. The first portfolio may experience small losses frequently, and the second may experience a singular decline. This contrast between portfolios needs to be examined by investors prior to their purchasing of assets. By eliminating downside risk instead of volatility, Post-modern portfolio theory aims to build on MPT.
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