Higher-order risk preferences in social settings

We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual’s decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.     

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

Risk aversion and prudence in the large

The familiar measures of absolute and relative risk aversion constructed by Pratt and Arrow, along with the measures of absolute and relative prudence inspired by Leland and later developed by Kimball, are local instruments based on the first and second derivatives of utility at a specific level of wealth. As such, they are applicable only to infinitesimal risks—those for which differential calculus is a suitable analytical tool. Consequently, they may not accurately gauge preferences regarding the larger risks typically encountered in practice. To address this problem, the present paper develops more general, closed-form index measures of risk aversion and prudence that are applicable to either large or small risks. The new measures are exact in that they do not rely on approximations, they can be implemented empirically without knowledge of the functional form of utility, and they do not require information regarding pre-existing wealth.     

Survey measures of risk aversion and prudence

This paper utilizes a thought experiment conducted by the Bank of Italy to estimate absolute and relative risk aversion along with absolute and relative prudence for a broad cross-section of Italian households. Upper and lower bounds are calculated for each parameter, and comparisons are made across socio-demographic groups. Evidence is found of decreasing absolute risk aversion, decreasing absolute prudence, increasing relative risk aversion, and increasing relative prudence.     

Comparative risk aversion: A formal approach with applications to saving behavior

We consider a formal approach to comparative risk aversion and apply it to intertemporal choice models. This allows us to ask whether standard classes of utility functions, such as those inspired by Kihlstrom and Mirman (1974) [16], Selden (1978) [27], Epstein and Zin (1989) [10] and Quiggin (1982) [25] are well ordered in terms of risk aversion. Moreover, opting for this model-free approach allows us to establish new general results on the impact of risk aversion on savings behaviors. In particular, we show that risk aversion enhances precautionary savings, clarifying the link that exists between the notions of prudence and risk aversion.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

ON NON‐MONETARY MEASURES IN THE FACE OF RISKS AND THE SIGNS OF THE DERIVATIVES

Vulnerability of both prudence and temperance towards a sure loss and towards a zero‐mean background risk seems to be a very realistic assumption on individual preference. This paper shows that when the concepts of prudence and temperance are defined in non‐monetary terms, the above assumption is equivalent to the usual signs of the successive derivatives of the utility function.     

ON THE CONCAVITY AND QUASICONCAVITY PROPERTIES OF UTILITY FUNCTIONS

Concavity and quasiconcavity have always been important properties in financial economics particularly in decision problems when an objective function has to be maximized over a convex set. Both properties have mainly been used as purely technical assumptions. In this paper, we link concavity and quasiconcavity of a utility function to the basic concepts of risk aversion, prudence, risk vulnerability and temperance. We show that concavity means the agent is more risk vulnerable than prudent. In particular, we can see when a function is both concave and quasiconcave and when it is only quasiconcave.     

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.     

Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

Real estate and relative risk aversion with generalized recursive preferences

This paper investigates how real estate wealth affects the household’s attitude toward risk, and derives the closed-form expressions for risk aversion with generalized recursive preferences. We find three channels through which real estate wealth affects risk aversion, and these channels are absent in the traditional measure of relative risk aversion as in Arrow (1965) and Pratt (1964). First, illiquidity and fluctuations in real estate value increase consumption risk, thereby increasing risk aversion. Second, real estate as an asset provides a cushion for absorbing negative shocks to households, reducing risk aversion. Third, an increase in real estate prices lowers the profit of the firm that uses real estate as a factor of production, induces a decline in the real wage, and causes a rise in consumption risk. This channel increases risk aversion. We study how these channels as a whole determine relative risk aversion using a basic real business cycle model with generalized recursive preferences and compare the results with the case of expected utility preferences. Finally, we explore the implications of the firm’s and the household’s real estate holdings and illiquidity of real estate on the risk premiums for equity and real estate.     

Background risk and the demand for state-contingent claims

Summary. We consider the demand for state-contingent claims, in the presence of an independent zero-mean, non-hedgeable background risk. An agent is defined to be generalized risk averse if he/she chooses a demand function for contingent claims with a smaller slope everywhere, given a simple increase in background risk. We show that the conditions for standard risk aversion, that is positive, declining absolute risk aversion and prudence, are necessary and sufficient for generalized risk aversion.Received: 13 February 2002, Revised: 10 February 2003, JEL Classification Numbers: D52, D81, G11. Correspondence to: Guenter FrankeWe are grateful to Louis Eeckhoudt, Christian Gollier, Harris Schlesinger and an unknown referee for valuable comments.     

Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences

From the expected‐utility approach, relative risk aversion being smaller than one and relative prudence being smaller than two emerge as preference restrictions that fully determine the optimal responses of decisions under uncertainty to certain shifts in probability distributions. We characterize the magnitudes of relative risk aversion and relative prudence in terms of the two‐parameter, mean‐standard deviation approach. We demonstrate that this characterization is instrumental in obtaining comparative static results in the two‐parameter setting. We further relate our findings to the results in the expected‐utility framework.     

State-dependent preferences can explain the equity premium puzzle

We introduce state-dependent recursive preferences into the Mehra–Prescott economy. We show that such preferences can match the historical first two moments of the returns on equity and the risk-free rate. Other authors have reported similar results using state-dependent expected utility preferences. These authors have tended to emphasize the importance of countercyclical risk aversion in explaining the equity premium puzzle. We find that countercyclical risk aversion plays an important role but only when combined with modest cyclical variation in intertemporal substitution.     

Made for the job or by the job? A lab-in-the-field experiment with firefighters

A large body of evidence supports a negative association between risk aversion of workers and the level of risk they face in their occupations. This relationship could be explained by the self-selection of workers into jobs according to their risk preferences or by the effect on risk attitudes of occupations in which people face or witness dangerous situations. We use incentivized experiments to measure risk preferences among three different groups: experienced firefighters, novice firefighters, and students. We find that experienced firefighters are less risk-averse than novice firefighters, and these in turn are less risk-averse than students. The effects remain significant even after controlling for other relevant differences between these groups. Our findings suggest that the observed relationship between risk aversion and high-risk occupations is not only a result of self-selection but also of people’s preferences being shaped by their work lives.     

Skewed background risks and higher-order risk preferences: prudent versus temperate behavior

In recent economic experiments, lotteries with left-skewed background risks elicit more prudent choices than lotteries with right-skewed background risks. In this letter, we use an expected utility framework to show that a skewed zero-mean background risk may induce not only prudent but also temperate behaviour. We suggest that the experimental findings could also be due to temperance, rather than merely to prudence.     

Risk sensitivity in bargaining with more than two participants

In two-person bargaining over riskless outcomes where the outcome is chosen according to the Nash solution or the Kalai-Smorodinsky solution, an increase in a player's risk aversion is to the advantage of the opponent. It is shown in this note that for the n-person Nash solution, an increase in risk aversion is to the player's own disadvantage but needs not be advantageous to all the opponents. For the n-person Kalai-Smorodinsky solution, the increase is to the player's own disadvantage and to the advantage of all the opponents.     

Time Horizon and the Discount Rate

We consider an economy à la Lucas (1978, Econometrica46 , 1429-1446) with a risk-averse representative agent. The exogenous growth rate of the economy follows a random walk. We characterize the set of utility functions for which it is efficient to discount more distant cash flows at a lower rate. The benchmark result is that, when the growth rate is almost surely nonnegative, the yield curve is decreasing if and only if relative risk aversion is decreasing with wealth. Relaxing the assumption on the absence of recession requires more restrictions on preferences, such as increasing relative prudence. Journal of Economic Literature Classification Numbers: D81, D91, Q25, Q28.     

Risk and regret aversions on optimal bank interest margin under capital regulation

This paper examines the bank's optimal loan rate (and thus the bank's interest margin) under more stringent capital regulation when the bank is not only risk-averse but also regret-averse. Risk-averse preferences are characterized by an option-based utility function that includes disutility from the dislike of bank equity risk. Regret-averse preferences feature an option-based utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that an increase in bank capital requirement results in an increased margin under risk aversion dominating regret aversion, whereas it results in a reduced margin under regret aversion dominating risk aversion. The former holds when risk aversion domination stems from increasing risk-averse preference, but not from decreasing regret-averse preference, while the latter holds when regret aversion domination results from either decreasing risk-averse or increasing regret-averse preference. Risk aversion, as such, makes the bank more prudent and less prone to risk-taking, while regret aversion, as such, makes the bank less prudent and more prone to risk-taking.     

Economic efficiency adjusted for risk preferences

This study investigates the impact of risk preferences on cost and revenue efficiency for a sample of farms. Risk preference scores were used to measure risk aversion. Cost and revenue efficiency were estimated using traditional input and output measures, and then re-estimated including each farm’s risk preference score. Comparisons were made between farms with and without a change in efficiency when each farm’s risk preference was included in the analysis. As expected, risk preference plays an important role in explaining farm inefficiency. Failure to account for risk preferences overstates inefficiency, particularly for slightly risk averse and risk neutral farms.