Measures of Risk Aversion: Some Clarifying Comments

This paper develops a matrix-measure of multivariate risk aversion which is related to a notion of risk premium and states the restrictions that must be imposed upon the matrix-measures of two utility functions in order that one require a higher risk premium than another for every small multivariate risk. A necessary and sufficient condition for comparability of global attitude towards risk is that the local restrictions hold over the entire domain. The usefulness of the measures of risk aversion is discussed within the context of a multivariate risk-sharing problem. UNIVARIATE MEASURES OF ABSOLUTE and relative risk aversion were introduced in the seminal works of Pratt [8] and Arrow [1], and have since become indispensable tools for the analysis of risk bearing in situations involving unidimensional risks. Recent years witnessed numerous attempts to generalize various aspects of the Pratt-Arrow notions to the case of multivariate risk (Kihlstrom and Mirman [6], Keeney [5], Duncan [2], Paroush [7], and Stiglitz [9]). The univariate case is qualitatively different from the multivariate case in that the ordinal preferences of all decision makers are identical, whereas in the multivariate case the preference orderings may differ among decision makers. This fact has two important consequences. First, while the analysis of risk bearing in situations involving univariate risks turns out to depend solely upon the cardinal properties of the function representing the ordinal preferences of the decision makers involved, in situations involving multivariate risks, the ordinal preferences themselves play an important role in addition to that of the function representing them. Second, in the univariate case the local measure of absolute risk aversion permits a complete ordering of individuals according to the relation least as risk averse as, whereas in the multivariate case such ordering is not in general independent of the specific risk under consideration. Pratt [8] has shown that the univariate measure of absolute risk aversion satisfies a formal relation to a number which has the interpretation of risk premium. In this study I introduce a matrix measure of absolute multivariate risk aversion which satisfies a similar formal criterion. It should be noted at the outset, however, that in the multivariate case the risk premium may be regarded as a vector of commodities (see, for example, Duncan [2, 3]), and interpersonal comparison of risk aversion is not directional independent. I.e., the ranking of risk

Inert atmosphere system

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).

Chapter 2This chapter examines the extent to which gender differences in risk aversion explain why women have a lower entrepreneurship rate, earn less, and work fewer hours than men. Data from the NLSY79 confirms previous findings that women are more risk averse than men. However, while less risk averse men tend to become self-employed, there is no significant effect of risk aversion on women's entrepreneurship decisions. Similarly, greater risk aversion increases earnings for male entrepreneurs, but it has no effect on female entrepreneurial earnings. More risk aversion lowers female wages, but the effects are of modest magnitude. On the contrary, more risk aversion raises male wages. Risk aversion does not explain variation in hours of work for either men or women. These findings and standard decomposition suggest that widely reported differences in risk aversion across genders play only a trivial role in explaining gender gaps in labor market outcomes.Chapter 3While more risk averse individuals are less likely to become entrepreneurs, theory predicts that more risk averse entrepreneurs pick ventures with higher expected returns and so they should survive in business longer than their less risk averse counterparts. Using successive entry cohorts of young entrepreneurs in the NLSY79, we find contrary to theory that the most successful entrepreneurs are the least risk averse. This surprising finding suggests that commonly used measures of risk aversion are not indicators of taste toward risk. Instead, measured risk aversion signals weak entrepreneurial ability--the least risk averse are apparently those who can best assess and manage risks. Indeed, our interpretation is consistent with recent experimental evidence linking cognitive ability with a greater willingness to accept risk.Chapter 4The fourth chapter investigates the stability of measured risk attitudes over time, using a 13-year longitudinal sample of individuals in the NLSY79. A variance decomposition shows that 57% of the total variance in measured risk aversion is attributable to variation in measured risk aversion within individuals and only 43% to variation across individuals. After removing variation attributable to socioeconomic factors, the proportion of within variance drops to 54%, strongly rejecting the presumption that measured risk attitudes are stable over time. We find that an individual's measured risk aversion changes systematically responding to personal economic circumstances. Measured risk aversion responds to fluctuations in employment: duration of employment spells and out of labor force increases risk aversion whereas length of unemployment spells decreases risk aversion. Previous labor market experience also increases risk aversion. Finally, risk aversion is quadratic in age and net family income with an inverted U-shape. Our analysis shows that measured risk aversion cannot be treated as a fixed attitude toward risk but rather a changing attitude that reflects changes in personal economic circumstances.Chapter 5In Lazear (2005)'s model of entrepreneurship, individuals with more diverse academic and occupational training are more likely to become entrepreneurs, while more narrowly trained individuals become employees. This chapter examines whether Lazear's model can also explain which individuals become nonprofit entrepreneurs. Information on successive cohorts of college graduates from a single university from 1982-2006 show that observed diversity of academic and occupational skills increases the probability of nonprofit sector entrepreneurship, consistent with previous findings of for-profit entrepreneurs. In addition, unobservable talents that increase probability of for-profit startups are positively correlated with the unobservable skills that lead to nonprofit start-ups, consistent with a presumed entrepreneurial skill that underlies the Lazear Jack-of-All-Trades model.

The Choice between a Stock and a Corporate Bond: Risk Aversion or Downside Risk Aversion?

Chapter 4 - Measuring Risk and Risk Aversion

Risk Aversion and Trade Union Membership

This paper develops the requisite conditions for interpersonal comparisons of attitudes toward risk in the presence of uncertain lifetime. For comparable individuals measures of absolute risk aversion are presented. Using the notion of actuarial notes the paper applies the measures of risk aversion to a comparative static analysis of the demand for term life insurance coverage.

Researchers have commonly used financial gambles to assess risk preferences, though attitudes regarding monetary gambles may differ from those concerning health risks. Moreover, the conventional measure of risk preference—the Pratt-Arrow coefficient of relative risk aversion—is a point-elasticity suitable only for trivial risks, whereas the risks pertaining to medical treatment—often involving life-ordeath decisions—are quite substantial. Our objective is to examine attitudes toward health risks and the variables that influence those attitudes. In addition to the conventional metric, we employ an alternative measure of risk aversion designed for large-scale risks; the latter is calculated as an arc-elasticity of marginal utility. Both measures are applied to responses from a health preference survey, which incorporates a standard gamble over longevity. Measured risk aversion is then related to health and demographic variables using multiple linear regressions. Our research suggests that tolerance of health risks may be influenced by an endowment effect reflecting the asymmetry of medical information between patients and providers. We also find that the arc-elasticity measure captures more of the significant differences and has a stronger correlation to demographic and socio-economic variables than does the more traditional point-elasticity measure, indicating that the conventional measures of risk aversion are indeed ill suited to large-scale risks such as those involving health. In addition, our results suggest that health-related risk preferences may differ from financial risk attitudes. Although our sample is relatively small and largely homogeneous, these results collectively provide a basis for replication and a justification for additional study on the measurement of risk aversion with regard to health.

Labour on the family farm: A theory under uncertainty - an extension

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks.

The economic literature has focused on the role of uncertainty in the real economy, employing both measures of risk aversion and ambiguity aversion in structural models. In this connection, concerns about the measures for VIX and EPU, have been raised about whether or not they both measure and identify similar type of uncertainty. Using a structural vector autoregressive (SVAR) approach, we examine the relationship between VIX and EPU, their impact on the real economy and whether, and under which conditions, they can be distinguished between measures of risk aversion and ambiguity aversion. Specifically, we analyse the impact of uncertainty shocks of VIX and EPU on the industrial production, unemployment, and consumer credit in the US. Our main finding is that given their fundamental differences, the two measures are capturing different dimensions of uncertainty, VIX is a measure of risk aversion and EPU is a measure of ambiguity aversion. As such, our results are very important in terms of trading decision strategies to be implemented by investors and portfolio managers as it may help explain the two central behavioral traits affecting economic lifecycle problems, such as production, unemployment and consummation.

Kenneth Arrow posed the hypotheses that investors reveal decreasing absolute risk aversion (DARA) and increasing relative risk aversion (IRRA). It is very difficult to empirically test these two hypotheses since one needs to analyze an investor's investment decisions at various points in his/her economic life cycle as the investor's wealth varies. An experimental study is conducted to test these two hypotheses when the subject's wealth varies depending on his/her investment performance. The experiment involves an actual money gain or loss which is indexed to the individual's investment performance. It is found that DARA is indeed strongly supported, but IRRA is rejected.

Since Sandmo's seminal paper on the theory of the competitive firm under output price uncertainty, there has been considerable research on this topic [2; 5; 6; 10; 11; 14]. In all these studies, it is assumed that, in the absence of complete contingent markets, output price risk is the only source of uncertainty for the firm. However, this may not be a realistic assumption. In particular, as argued by Kihlstrom et al. [7], it appears reasonable to consider the case where some of the initial wealth of the firm is held in risky assets. In that case, initial wealth is uncertain and should be modelled as a random variable. The objective of this paper is to investigate the introduction of random initial wealth in Sandmo's theory of the firm under price uncertainty. In Sandmo's model, a number of important comparative static results (e.g., the conditions under which the supply function is upward sloping [14, 69], or under which increased price uncertainty reduces supply [5] depends critically on the sign of a particular expression' stated in Lemma 2 in Ishii [5]. While Sandmo [14, 69] shows this expression is non-negative under Arrow-Pratt decreasing absolute risk aversion, it can be verified that his proof no longer holds when initial wealth is random. Therefore, the comparative static analysis conducted by Sandmo [14], Batra and Ullah [2] and Ishii [5] is no longer valid and gives ambiguous results under initial wealth uncertainty. The reason is that the Arrow-Pratt measures of risk aversion [1; 12] are too weak for making comparisons in situations where there is more than one source of uncertainty [13]. Then, what can be deduced from the theory of the competitive firm in the (realistic) case where both initial wealth and output price are uncertain? We will show here that meaningful results on the behavior of the competitiv firm under uncertainty can be obtained provided that the Arrow-Pratt measures of risk aversion [1; 12] are replaced by the Ross measures of risk aversion [13]. In particular, a comparative static analysis of the production decisions using Ross characterization of risk behavior is presented. A number of new results are derived on the properties of risk responsive supply and input demand functions under both price and initial wealth uncertainty.

Fake or substandard fertiliser is a growing concern in many countries. Even in places not affected by fertiliser quality problems, uncertainty could arise due to weather variability, soil quality, or doubts about the effectiveness of fertiliser in general. Past literature has shown that risk aversion leads to lower fertiliser use and farmers become less risk averse as they become wealthier. We build upon this literature by showing that the marginal effect itself might not be the same for farmers of different wealth levels either. In our study, the measures of risk aversion were elicited from two different techniques: a self-assessment question and a lottery game. Results from regression analysis show that the marginal effect of risk aversion on fertiliser use depends on the wealth levels of farmers. Low-wealth farmers reduce their fertiliser intensity when their risk aversion increases. The marginal effect for high-wealth farmers is insignificant.