Risk aversion and self-insurance

This paper considers the effects of an increase in risk aversion on self-insurance. More risk-averse individuals invest more in self-insurance in the case of two states of the world. However, with more than two states, this standard conclusion does not hold. The reason is that self-insurance does not necessarily reduce larger losses more effectively than smaller losses. Self-insurance thus may not serve as insurance, and more risk-averse individuals may invest more or less in self-insurance. The paper provides a condition for more risk-averse individuals to invest more in self-insurance, and a condition for them to invest less.     

Risk breeds risk aversion

We examine whether exposure to a more or less risky environment affects people’s subsequent risk-taking behavior. In a laboratory setting, all subjects went through twelve rounds of multiple-price-list decisions between a risky alternative and a safe alternative. In the first six rounds, subjects were randomly assigned to a high-, moderate-, or low-risk environment, which differed in the variances of the lotteries they were exposed to. In the last six rounds, subjects in all treatments made decisions on an identical set of lotteries. We found that subjects who had experienced a riskier environment exhibited a higher degree of risk aversion. Our experimental design allows us to conclude that this effect is driven by the risk environment per se, rather than the realized outcomes of the risk. This finding has important theoretical and policy implications.     

Risk aversion in the Talmud

Summary. Evidence is adduced that the sages of the ancient Babylonian Talmud, as well as some of the medieval commentators thereon, were well aware of sophisticated concepts of modern theories of risk-bearing. Received: April 10, 2002; revised version: May 7, 2002 RID="*" ID="*"Presented at the Institute for Mathematical Studies in the Social Sciences-Economics, Stanford University, August 4, 1981. Subsequent to that presentation, the author's attention was drawn to an article by Zvi Ilani, “Models in the Economics of Uncertainty: The Cost of Concluding a Conditional Contract, according to the Talmud and the Halachic Literature,” Iyunim Bekalkala (Investigations in Economics), The Israel Association for Economics, Jerusalem, Nissan 5740 (April 1980), 246–261 (in Hebrew). Inter alia, Ilani treats the Talmudic passage that forms the subject of this paper, and provides a fairly comprehensive review of the medieval commentaries thereon; undoubtedly, he was the first to recognize in print the relevance of this passage to modern economic theories of uncertainty. It is not clear, though, whether or not his understanding of the passage agrees with ours. The current paper appeared in January 2002 in the Research Bulletin Series of the Research Center on Jewish Law and Economics, Department of Economics, Bar Ilan University.     

Risk aversion in the Eurozone

We propose a New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model where a risk aversion shock enters a separable utility function. We analyze five periods from 1971 through 2011, each lasting for 20 years, to follow over time the dynamics of several parameters such as the risk aversion parameter; the Taylor rule coefficients; and the role of the risk aversion shock in output, inflation, interest rate, and real money balances in the Eurozone. Our analysis suggests that risk aversion was a more important component of output and real money balance dynamics between 2006 and 2011 than it was between 1971 and 2006, at least in the short run.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

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.     

Risk aversion in symmetric and asymmetric contests

We analyze existence, uniqueness and properties of equilibria in incompletely discriminating Tullock contests with logistic contest success functions, when contestants are risk averse. We prove that a Nash equilibrium for such a contest exists, but give an example of a symmetric contest with both symmetric and asymmetric equilibria, showing that risk aversion may lead to multiple equilibria. Symmetric contests have unique symmetric equilibria but additional conditions are necessary for general uniqueness. We also study the effects on incumbents of additional competitors entering the contest under these conditions and examine the effects of risk aversion on rent dissipation in symmetric and asymmetric contests.     

Risk aversion,order strategy and price formation

Since goods classified as non-durable may, in fact, have a durable component, random-walk tests of the permanent income hypothesis using non-durable data series may yield incorrect results. This paper investigates this problem by first simulating a model of consumption to show the effects of durability on statistical tests of non-durable consumption models, and then by applying these tests to various disaggregated consumption series to determine the effect in practice. The paper finds that there are significant differences in the behaviour of the series within the non-durables and services catagories, and that these differences may be related to durability. The effect of this on standard tests of consumption is discussed.     

Risk aversion,innovation and performance in family firms

An analysis of the effect of family governance on the relationships among risk aversion, innovation and performance is the purpose of this study. Beyond the level of risk and innovation, we are interested in analysing the relationship between them and their influence on performance in family firms. Traditionally, risk-seeking has been associated with innovation and performance. Our results confirm both components to be independent and, furthermore, show relationships with opposite signs as expected in the literature. In a sample of 500 firms, the results confirm an idiosyncratic behaviour in family firms; innovation contributes to performance to a higher extent in family firms, and at the same time, risk aversion is positively associated with performance only in non-family firms.     

Risk aversion and portfolio allocation to mutual fund classes

The major factors affecting fund flows allocated to a range of mutual fund classes bearing different risk–return profiles are studied. The flexible functional form of the Almost Ideal Demand System (AIDS) is applied to identify the major drivers of Greek investors' demand patterns for equity, bond, balanced and money market funds, given the strong growth rates of the domestic fund market and the economy's latest entry into the EMU. An increase in household expenditure is shown to have a positive impact on mutual fund flows. An adverse price impact, however, may erode budget benefits towards a fund class, as the price factor appears to be important. The cross-price effects provide insight on complementarity and substitutability among the mutual fund classes. Variations in investors' risk aversion attitudes affect demand for mutual funds and can result in asset reallocation between the asset classes. The conclusions have useful policy implications particularly to asset fund management and portfolio allocation strategies and can be compared with established mutual fund markets.     

Risk aversion,impatience, and optimal timing decisions

In this paper, a theory measuring a decision maker's aversion to temporal risks is developed in the context of a simple choice framework that admits the interpretation “time varying utility of wealth.” A relation “more temporally risk averse” is defined and characterized in terms of instantaneous risk aversion (the usual single variable case) and impatience. A further characterization of this relation is obtained in the context of a class of action timing problems known as optimal stopping problems and is applied to preference based investigations of information production, incentives to innovate, and job search.     

Risk and risk aversion when states of nature matter

When uncertainty is associated with some intrinsically relevant states of nature, there is no reason for an agent to base his or her preferences only on probability distribution of claims. We propose a new concept of risk for state-contingent claims that, unlike the standard concept of Rothschild–Stiglitz, does not identify state-contingent claims with their probability distribution. This concept is called mean-independent risk, and we provide a simple characterization in terms of marginal utilities of (non-expected) utility functions that exhibit aversion to mean-independent risk. We study implications of aversion to mean-independent risk on agents’ choices under uncertainty. This research has been supported by the NSF under Grant SES-0099206. I have benefited from numerous conversations with Rose-Anne Dana and illuminating discussions with Tadeusz Miłosz about the theory of subgradients.     

Risk aversion and the earnings of US immigrants and natives

The literature on the earnings of natives and immigrants has heretofore ignored differences in compensating wages for job risks. It is possible that the risk involved in migration may indicate a greater willingness on the part of immigrants to accept riskier jobs than natives. Alternatively, immigrants may attempt to protect their migration investment by choosing occupations with less risk, indicating a higher degree of risk aversion. This paper examines differences in risk aversion between US immigrants and natives, and corresponding differentials in wage premiums for job risk. Our analysis suggests that on average immigrants are exposed to 21% less risk than natives, but receive a 25% higher risk premium. The higher degree of risk aversion of immigrants and their lower exposure to risk, and thus lower earnings, explains 5% of the higher observed earnings of natives. We also find that earlier immigrant cohorts (pre-1970) are employed in riskier jobs than are recent cohorts, but the difference accounts for only a small portion of the observed earnings differential. Finally, we estimate statistical values of life of $3.6 million for US natives and $4.6 million for immigrants, well within the range of previous studies.     

On bidding with securities: Risk aversion and positive dependence

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Risk aversion, moral hazard, and the principal's loss

Summary. In their seminal paper on the principal-agent model with moral hazard, Grossman and Hart (1983) show that if the agent's utility function is , then the loss to the principal from being unable to observe the agent's action is increasing in the agent's degree of absolute risk aversion. Their proof is restricted to the case where the number of observable outcomes is equal to two, and it uses an argument that is specific to that case. In this note, we provide an alternative proof that generalizes their result to any (finite) number of outcomes. Received: March 21, 2001; revised version: June 21, 2001