Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences.     

The Risk and Incentives Trade-off in the Presence of Heterogeneous Managers

Agency theory predicts a negative relationship between risk and incentives, yet recent empirical evidence has not consistently found such a relationship. In fact, some researchers have found a positive relationship. By introducing competition for heterogeneous managers, who differ in their degrees of risk aversion, into a standard agency model, this paper demonstrates that a negative or positive relationship is theoretically possible. Which arises depends on the relative risk aversion parameters of the managers and the absolute and relative riskiness of the environments.Acknowledgement I thank two anonymous referees for helpful comments.     

Estimating risk aversion coefficients for dry land wheat,irrigated corn and dairy producers in Kansas

The risk attitudes of dry land wheat, irrigated corn, and dairy producers in Kansas are examined using the nonlinear mean–standard deviation approach. Results of analyses indicated that dryland wheat and dairy producers are characterized by increasing absolute and increasing relative risk aversion while irrigated corn producers are characterized by constant absolute and increasing relative risk aversion. Both crop enterprises exhibited constant returns to scale technology while the dairy enterprise exhibited decreasing returns to scale. Gross farm income was significant and positively related to relative risk aversion.     

Covered Call Investing in a Loss Aversion Framework

In a mean-variance framework, the covered call investment strategy has been seen as an inefficient method of allocating wealth. Covered calls reduce the riskiness of the portfolio and therefore lead to lower portfolio returns. Recent debate has focused on the shortcomings of mean-variance efficiency as an accurate depiction of investor utility. Using alternative utility functions, we find mixed support for the use of the covered call investing strategy. Using loss aversion, however, we reexamine the covered call investment decision and find it significantly enhances investor utility relative to an index portfolio investment strategy. We conclude that loss aversion's more accurate depiction of investor preferences and behavior helps to explain the popularity of the covered call investment strategy.     

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.     

Increasing returns and unsynchronized wage adjustment in sunspot models of the business cycle

A challenge to models of equilibrium indeterminacy based on increasing returns is that required increasing returns for generating indeterminacy can be implausibly large and rise quickly with the relative risk aversion in labor. We show that unsynchronized wage adjustment via a relative wage effect can both lower the required degree of increasing returns for indeterminacy to a plausible level and make it invariant to the relative risk aversion in labor. Consequently, indeterminacy and sunspot-driven fluctuations can emerge for plausible increasing returns regardless of the relative risk aversion in labor. Our model generates reasonable dynamics in terms of matching the business cycle, and sunspot shocks become more important with labor market friction.     

Vulnerability Orderings for Expected Poverty Indices

Vulnerability to poverty refers to the risk of an individual or household falling below the poverty line. A partial vulnerability to poverty ordering is defined to indicate when a situation characterized by uncertainty means that people are more vulnerable to poverty than in another situation. The family of expected poverty indices used in this context contains versions under vulnerability of many well‐known poverty indices. The ordering resembles the Hardy et al. result on the Lorenz partial ordering. A separate ordering for the expected income gap ratio is also investigated. First‐order stochastic dominance is used to indicate when the expected value of the censored returns from the states increases.     

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.     

Another Look at the Equity Risk Premium Puzzle

The model of Mehra and Prescott (1985, J. Econometrics, 22, 145–161) implies that reasonable coefficients of risk‐aversion of economic agents cannot explain the equity risk premium generated by financial markets. This discrepancy is hitherto regarded as a major financial puzzle. We propose an alternative model to explain the equity premium. For normally distributed returns and for returns far away from normality (but still light tailed), realistic equity risk premia do not imply puzzlingly high risk aversions. Following our approach, the ‘equity premium puzzle’ does not exist. We also consider fat‐tailed return distributions and show that Pareto tails are incompatible with constant relative risk aversion.     

On the robustness of the Arrow-Pratt risk aversion measure

For portfolio problems with joint normally distributed asset returns, the risk aversion measure R = -w₀(Eu″(w)/Eu′(w)), where w₀ is initial wealth can be used to characterize optimality. Comparisons between the global measure R and local measures based on R_A = -u″(w)/u′(w) are explored. Simulations for several utility function classes are described.     

Absolute and Relative Deprivation and the Measurement of Poverty

This paper develops the link between poverty and inequality by focussing on a class of poverty indices (some of them well–known) which aggregate normative concerns for absolute and relative deprivation. The indices are distinguished by a parameter value that captures the ethical sensitivity of poverty measurement to "exclusion" or "relative–deprivation" aversion. The indices can be readily used to predict the impact of growth on poverty. An illustration using LIS data finds that the United States show more relative deprivation than Denmark and Belgium whatever the percentiles considered, but that overall deprivation comparisons of the four countries considered will generally depend on the intensity of the ethical concern for relative deprivation. The impact of growth on poverty also depends on the presence of and on the attention granted to concerns over relative deprivation.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Trust,risk and time preferences: evidence from survey data

The paper shows that time preferences and risk preferences are key covariates of self-reported trust. They both predict negatively a measure of generalized trust; however, risk aversion is positively correlated with an index of particularized trusting behaviour (which refers to the circle of known people).     

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.     

Estimation of relative risk aversion across time

This article examines relative risk aversion in the framework of a three-moment asset pricing model that accounts for skewness. Accounting for skewness in calculating risk aversion gives a more accurate series of estimates of risk aversion and helps to reconcile the wide disparity in risk coefficients found in past literature. Risk aversion coefficients are calculated from 1926 to 2014 using stock market returns. This procedure results in a time series of data that can be related to other variables such as real interest rates and changes in demand for various asset classes.     

On the Economic Meaning of Machina's Fréchet Differentiability Assumption

This note shows that M. J. Machina's (1982, Econometrica50, 277-323) assumption that preferences over lotteries are smooth has some economic implications. We show that Fréchet differentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We also show that with constant absolute and relative risk aversion, expected value maximization, second order risk aversion, and Fréchet differentiability are equivalent. Journal of Economic Literature Classification Number: D81.     

Are momentum traders different? Implications for the momentum puzzle

This article examines the puzzlingly high unexploited momentum returns from a new perspective. We analyse characteristics of momentum traders in a sample of 692 fund managers. We find that momentum traders are ‘defined’ by their short-term horizon, by a behavioural view on the market and by a somewhat lower degree of risk aversion, whereas they are like other fund managers with respect to sophistication. This is consistent with the interpretation that momentum returns may compensate for the risk of momentum trading on short-term horizons and that the short-term oriented momentum traders are not in a position to perform long-term arbitrage.     

Price expectations,disequilibrium adjustments,and macroeconomic price stability

This paper examines the possibility of extending the basic theorems of the risk-free, two-sector, two-factor, constant returns to scale model of production to cover situations with price uncertainty. It is shown that the Rybczynski and Stolper-Samuelson theorems may fail to hold for certain cases while the factor price equalization theorem cannot carry over to the stochastic world, provided firms in the uncertainty sector exhibit decreasing absolute risk aversion. The implications of uniform (relative) changes in both factor endowments and in both (expected) commodity prices are also explored.     

Asset pricing in a production economy with Chew–Dekel preferences

In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with Chew–Dekel risk preferences and convex capital adjustment costs. When households display levels of disappointment aversion consistent with the experimental evidence, a version of the model parameterized to match the volatility of output and consumption growth generates unconditional expected asset returns and price of risk in line with the historical data. For the model with Epstein–Zin preferences to generate similar statistics, the relative risk aversion coefficient needs to be about 55, two orders of magnitude higher than the available estimates. We argue that this is not surprising, given the limited risk imposed on agents by a reasonably calibrated stochastic growth model.