Ted
O’Donoghue and Jason Somerville, “Modeling Risk Aversion in Economics.”
Journal of Economic Perspectives
32(2): 91-114, Spring, 2018.
• As Rabin and Thaler (2001) indicate, expected utility (EU) maximization seems incapable of explaining people’s risk preferences – even though it does suggest some nice measures of the degree of risk aversion.
• Other models of risk aversion, however, might prove more empirically sound, while maintaining tractability. That is, we might not need expected utility to analyze problems involving risk aversion, as alternative models could replicate current standard, EU-based results, while offering still more or avoiding the shortcomings associated with the assumption of EU maximization.
• Consider standard findings associated with insurance: (1) A more risk averse person is willing to pay more for insurance (than is a less risk averse person); and (2) at a fixed price per dollar of insurance (fixed in excess of the actuarially fair price), a more risk averse person will purchase more insurance (than will a less risk averse person).
• Consider standard findings associated with financial investments: (1) In a world with one safe (riskless) and one risky asset, more risk averse people invest less in the risky asset; and (2) if the population as a whole becomes more risk averse, the price of the risky asset must fall (equivalently, the expected return from holding the risky asset must rise).
• Consider standard findings of principal/agent analysis, say, when a risk neutral principal hires a risk averse agent: (1) if the agent’s effort is not observable, then to encourage effort, the agent will have to bear some risk (so that lower output leads to less pay); and (2) the unobservability of effort is costly to the principal, who would prefer to contract on effort directly.
• The various claims made concerning risk aversion in the three previous bullet points do require risk aversion – but they do not require expected utility maximization. That is, many of the ideas that have been developed around the concept of risk aversion – developed in the context of expected utility maximization – remain valid even when expected utility maximization is not descriptively accurate.
• Consider loss aversion as an alternative approach, one where outcomes are judged against a reference point and “losses loom larger than gains.” For prospects with some loss and some gain outcomes, loss aversion can generate risk averse behavior. (This style of loss aversion does not require "diminished sensitivity," the feature of prospect theory that leads to risk averse behavior in the gains domain and risk seeking behavior in the losses domain.)
• A second alternative, also featured in prospect theory, is probability weighting. The general notion is that, in practice, decision weights might not equal objective probabilities. Specifically, probability weighting typically involves the overweighting of low probability events and the underweighting of high probability events. This type of probability weighting can generate, depending on the options, either risk seeking or risk averse behavior. Lotteries, for instance, might be attractive (induce risk seeking behavior) due to the overweighting of the low-probability outcome of a large win.
• Finally, consider contextual features and salience. Extreme or vivid outcomes (like deaths in terrorist attacks) might garner intense attention, leading to higher decision weights on those outcomes. The contextual feature of the available (although unchosen) options can exert influence by shifting the salience of other outcomes. Again, choices displaying risk aversion can arise from these factors. Expected utility maximization is neither necessary nor sufficient for explaining risk-averse behavior.
• As Rabin and Thaler (2001) indicate, expected utility (EU) maximization seems incapable of explaining people’s risk preferences – even though it does suggest some nice measures of the degree of risk aversion.
• Other models of risk aversion, however, might prove more empirically sound, while maintaining tractability. That is, we might not need expected utility to analyze problems involving risk aversion, as alternative models could replicate current standard, EU-based results, while offering still more or avoiding the shortcomings associated with the assumption of EU maximization.
• Consider standard findings associated with insurance: (1) A more risk averse person is willing to pay more for insurance (than is a less risk averse person); and (2) at a fixed price per dollar of insurance (fixed in excess of the actuarially fair price), a more risk averse person will purchase more insurance (than will a less risk averse person).
• Consider standard findings associated with financial investments: (1) In a world with one safe (riskless) and one risky asset, more risk averse people invest less in the risky asset; and (2) if the population as a whole becomes more risk averse, the price of the risky asset must fall (equivalently, the expected return from holding the risky asset must rise).
• Consider standard findings of principal/agent analysis, say, when a risk neutral principal hires a risk averse agent: (1) if the agent’s effort is not observable, then to encourage effort, the agent will have to bear some risk (so that lower output leads to less pay); and (2) the unobservability of effort is costly to the principal, who would prefer to contract on effort directly.
• The various claims made concerning risk aversion in the three previous bullet points do require risk aversion – but they do not require expected utility maximization. That is, many of the ideas that have been developed around the concept of risk aversion – developed in the context of expected utility maximization – remain valid even when expected utility maximization is not descriptively accurate.
• Consider loss aversion as an alternative approach, one where outcomes are judged against a reference point and “losses loom larger than gains.” For prospects with some loss and some gain outcomes, loss aversion can generate risk averse behavior. (This style of loss aversion does not require "diminished sensitivity," the feature of prospect theory that leads to risk averse behavior in the gains domain and risk seeking behavior in the losses domain.)
• A second alternative, also featured in prospect theory, is probability weighting. The general notion is that, in practice, decision weights might not equal objective probabilities. Specifically, probability weighting typically involves the overweighting of low probability events and the underweighting of high probability events. This type of probability weighting can generate, depending on the options, either risk seeking or risk averse behavior. Lotteries, for instance, might be attractive (induce risk seeking behavior) due to the overweighting of the low-probability outcome of a large win.
• Finally, consider contextual features and salience. Extreme or vivid outcomes (like deaths in terrorist attacks) might garner intense attention, leading to higher decision weights on those outcomes. The contextual feature of the available (although unchosen) options can exert influence by shifting the salience of other outcomes. Again, choices displaying risk aversion can arise from these factors. Expected utility maximization is neither necessary nor sufficient for explaining risk-averse behavior.
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