On Multivariate Risk Aversion

Two prominent views pertaining to measures of risk aversion can be found in the literature. First, Arrow [2] and Pratt [3]developed risk aversion measures based on the curvature characteristics of the individual investor's utility for wealth function. If the investor's utility for wealth function is given by V(W), then are the Arrow-Pratt measures of absolute and relative risk aversion, respectively. The investor is risk averse or a risk lover as r(W) and r* (W) are positive or negative. The investor exhibits increasing, constant, or decreasing absolute risk aversion as while he exhibits increasing, constant, or decreasing relative risk aversion as .

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.

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.

Rent Seeking Contest and Indirect Risk Preference

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 4 - Measuring Risk and 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.

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.

The absolute and relative risk aversion characteristics of a large sample of farm operators were estimated from the observed portfolio responses to changes in wealth. Regression estimates suggest that farm operators display decreasing absolute risk aversion. Relative risk aversion varies by type of farm. However, the definition of risky assets has an important bearing on relative risk aversion characteristics. Non-wealth variables are also important in explaining the holding of risky assets by farm operators.

Risk Aversion and Trade Union Membership

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

The risk premium and the probability premium are used to determine appropriate coefficients of absolute risk aversion under CARA utility. A defensible range of risk aversion coefficients is defined by the coefficients that correspond to risk premiums falling between 1 and 99% of the amount at risk or to probability premiums falling between .005 and .49 for a lottery that pays or loses a given sum. The consequences of ignoring risk premiums when selecting risk-aversion coefficients for representative decision makers are illustrated by calculation of the implied risk premium associated with the levels of absolute risk aversion assumed in six selected studies.

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

Individual patients’ values and preferences are critical to patient-centered decisions. When dealing with health outcomes on an interval scale, where many intermediate outcomes must be considered, it can be helpful to encourage the patient decision maker to consider what functional form may be specified and parameterized for a given outcome attribute. This assessment problem is described in Keeney and Raiffa’s classic book. 1 For simplicity, let us restrict ourselves to unidimensional settings. We are asked first to specify an attitude toward risk (risk neutral, risk averse, or risk seeking) and then subclassify attitudes depending on whether the risk attitude is constant, absolutely decreasing, or relatively decreasing, in the case of the most common attitude, risk aversion. These questions then often specifyafunctionalformforthepatient’sutilityfunction,whichcanbeparameterizedonthebasisofalimited number of responses from the patient decision maker. This approach tends to consider just risk aversion, the curvature of the utility function as determined by the ratio of its second to its first derivative. That curvature can be quantified by the Pratt-Arrow measure of risk aversion, 2 u 2 /u 1 , although other measures, such as the stronger Ross measure of risk aversion, 3–6 are sometimes used. We use the notation u i to denote the ith derivative of u(x), d i u(x)/dx i . For utilitydistribution functions,onecanconsider either utility density functions (udfs) or their integrals, cumulative utility functions (cufs), analogous toprobabilitydensity functions (pdfs) and cumulative distribution functions (cdfs). For density functions, shape can be described by the function’s moments (e.g., 0-mean, 1-slope, 2-variance, 3-skewness, 4-kurotosis,andhigherunnamedmoments).Normatively, utilities with positive skewness are preferred by individuals whose utility function has u 3 . 0, whereas low kurtosis should be preferred by individuals whose utility function has u 4 \0. 7