How Can Risk Attitudes be Measured?
Different individuals can have different risk attitudes. Among individuals who are risk averse, some may be more risk averse than others. Similarly, among individuals who are risk preferring, some may be more risk preferring than others. Furthermore, an individual’s risk attitudes may vary depending on factors like the type of risk (e.g., the risk to health, wealth, or crop yields). Therefore, a variety of strategies have been used to characterize the intensity of an individual’s risk attitudes.
Arguably, the most natural way to characterize the intensity of risk attitudes is the risk premium. Intuitively, the risk premium measures how much an individual is willing to give up to avoid risk. Technically, it is the expected outcome of the risk minus the certainty equivalent of the risk where the certainty equivalent of the risk is defined as the least certain outcome an individual would accept to give up risk. To make this definition tangible, suppose an individual has the risky opportunity of an equal chance at $100 and nothing. Furthermore, suppose that the least the individual is willing to take to give up this risky opportunity is $30. Since individuals with this risky opportunity can expect to earn $50 on average, the individual’s risk premium is $20 = $50 - $30.
© Rainer Hillebrand
The risk premium provides one way to measure the intensity of an individual’s risk attitudes and determine if the individual is risk averse, risk neutral, or risk preferring. Individuals with a positive risk premium are risk averse because they are willing to accept less on average to give up the risky opportunity. Individuals with a negative risk premium are risk preferring because they require more on average to give up the risky opportunity. Individuals with no risk premium are risk neutral because what they are willing to accept to give up the risky opportunity is exactly what they can expect to get on average.
While the risk premium is a natural way to characterize the intensity of risk attitudes, it is not the only or most common way used by economic researchers. Instead, most use the Arrow-Pratt Coefficient of Absolute Risk Aversion (CARA), Arrow-Pratt Coefficient of Relative Risk Aversion (CRRA), or the coefficient of Partial Relative Risk Aversion (PRRA). These measures of risk aversion were developed in the context of the Expected Utility Hypothesis, which is the most common paradigm used by economists to explain how individuals make risky choices. For risk averse individuals, CARA, CRRA, and PRRA are positive, with larger values indicating a greater degree of risk aversion. For risk preferring individuals, CARA, CRRA, and PRRA are negative, with smaller or more negative values indicating a stronger preference for risk. For risk neutral individuals, CARA, CRRA, and PRRA are zero.