Coefficient Of Relative Risk Aversion Research Articles

Farmers’ Attitudes towards Risk—An Empirical Study from Poland

Risk aversion is an important research area in the field of agricultural economics in the last years. Creating effective and efficient risk management tools in an increasingly volatile economic and natural environment requires proper recognition of farmers’ behavior and attitudes towards risk. In this context, the main aim of the paper was to estimate farmers’ attitudes towards risk and identification of farm’s and farmer’s characteristics in dependency on risk aversion level. The assessment of farmers’ preferences towards risk was based on hypothetical games in a representative sample of 600 Polish farms—participants of Farm Accountancy Data Network (FADN). Based on the interviews with farmers, a relative risk aversion coefficient has been estimated. Results revealed that on average Polish farmers have quite a strong risk aversion. Their attitudes towards risk are strongly linked with their self-assessment regarding their way of making decisions under risk. Some relations between farmers’ risk aversion and perception of selected risk factors could also be observed. The results revealed that the application of specified risk management tools by farmers and their potential reaction to a significant income drop are related to risk aversion level.

Ambiguity, long-run risks, and asset prices in continuous time

This paper extends the long-run risks (LRR) models coined by Bansal and Yaron (2004) and Bansal, Kiku, and Yaron (2012) with Epstein and Zin’s (1989) recursive preferences into the LRR models with Chen and Epstein’s (2002) recursive multiple-priors utility, which captures the investor’s ambiguity on uncertainties. Our empirical analysis shows that considering ambiguity on uncertainties, in particular, large ambiguity on the long-run risks, in the LRR models can significantly improve the fitting performance of the equity premium and the risk-free rate when using a low relative risk aversion coefficient.

A Critical Comparison of Three Notions of Fractional Stochastic Dominance

Two notions of fractional stochastic dominance are recently proposed by Muller et al. (2017) and Huang et al. (2020), respectively. Our main objective is to understand the comparative advantages of the two notions, as well as their suitability in different contexts, by establishing several new technical results. For a more comprehensive comparison, we further include a third natural notion of fractional stochastic dominance based on the coefficient of relative risk aversion. Among the three notions, it turns out that one can be seen as a logarithmic version of second-order stochastic dominance (SSD), another one can be seen as a power version of SSD, whereas there does not exist a transformation to associate the last one with SSD. We find that these notions of fractional stochastic dominance are naturally connected to five classes of risk measures, including Value-at-Risk, Expected Shortfall, expectiles, entropic risk measures, and loss certainty equivalents. The three notions are further characterized in the contexts of the rank-dependent utility model and the cumulative prospect theory. We make some recommendations on which notion to use in specific situations, as they all have their own merits.

Rare events and long-run risks

Rare events (RE) and long-run risks (LRR) are complementary approaches for characterizing macroeconomic variables and understanding asset pricing. We estimate a model with RE and LRR using long-term consumption data for 42 economies, identify these two types of risks simultaneously from the data, and reveal their distinctions. RE typically associates with major historical episodes, such as world wars and depressions and analogous country-specific events. LRR reflects gradual processes that influence long-run growth rates and volatility. A match between the model and observed average rates of return on equity and short-term bonds requires a coefficient of relative risk aversion, γ, around 6. Most of the explanation for the equity premium derives from RE, although LRR makes a moderate contribution. However, LRR helps in fitting the Sharpe ratio. Generating good matches to the equity premium and Sharpe ratio simultaneously is still challenging.

Life with habit and expectation: A new explanation of equity premium puzzle

AbstractPrevious writers have attempted to resolve the equity premium puzzle by employing a utility function that depends on current consumption minus (or relative to) past habit consumption. This paper points out that an individual's current utility may also depend upon how well off in the recent past he or she had expected to be today. Hence we add the concept “expectation formation” to the utility modification term in a model with a habit‐formation utility function. We apply the model to the equity premium puzzle and find that it is able to fit the data with a relatively low coefficient of relative risk aversion. Furthermore, we introduce an updated data sample and apply different values of discounting factors, and find that in all circumstances, the model is able to generate coefficients of risk aversion that are consistent with theory. Hence we conclude that the model is able to resolve the equity premium puzzle.

Habit Formation, Public Capital Congestion Effect and Economic Growth

This paper constructs an endogenous growth model including habit formation and public capital congestioneffect, and analyzes the influence of fiscal policy and public capital congestion effect on economic growth under theframework of habit formation. It is found that under decentralized economy, there exists a unique equilibrium growthrate, and the growth rate increases with the improvement of private production efficiency, public capital productionefficiency and the reduction of public capital congestion effect. The influence of habit-forming parameters on theequilibrium growth rate depends on the relative risk aversion coefficient. In the social arrangement economy, habitformation and public capital jointly determine the problem of multiple equilibrium, similarly, the increase of publiccapital congestion effect will also reduce the equilibrium economic growth rate.

Is risk aversion related to occupational choice: evidence from 1996 PSID

ABSTRACT This paper investigates to what extent individuals’ risk aversion are correlated with the choice of occupation which differs from earnings risk by using 1996 PSID. Following Kimball et al. (2009), we first impute the individuals’ coefficient of relative risk aversion based on personal characteristics. Then, on the aggregate level, we find workers who are more risk averse will sort into occupations with low earnings risk. On the individual level, for one-unit increase in the coefficient of relative risk aversion, the probability of going to a more risky occupation decreases by 13.5%.

Mean-variance efficiency of optimal power and logarithmic utility portfolios

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal portfolios belong to the set of mean-variance feasible portfolios and establish necessary and sufficient conditions such that they are mean-variance efficient. Furthermore, we extend the derived theoretical finding to the general class of the log-skew-normal distributions. Finally, an application to the stock market is presented and the behaviour of the optimal portfolio is discussed for different values of the relative risk aversion coefficient. It turns out that the assumption of log-normality does not seem to be a strong restriction.

Disaggregation and the equity premium puzzle

Abstract Standard macroeconomic models cannot explain why stocks so greatly outperform bonds. However, this result depends on the use of aggregate consumption data. If markets are incomplete, then a representative agent might not exist and it is necessary to use consumption data at the household rather than aggregate level. In the household data, I fail to reject the Euler equation when the coefficient of relative risk aversion is as low as 2.7–3.8. This result is robust in a very general framework and I prove that many of the tests used in the literature are biased.

Risk Aversion and the Elasticity of Intertemporal Substitution among Australian Households

This paper explores the degree of risk aversion amonsg Australian households using panel data from the Household Income and Labour Dynamics in Australia (HILDA) Survey. Using households' share of risky assets, we test whether relative risk aversion is constant in wealth. After accounting for measurement error, we cannot reject the constant relative risk aversion (CRRA) assumption. Using a CRRA utility function, we estimate the elasticity of intertemporal substitution and infer a coefficient of relative risk aversion of 1.2 to 1.4. These findings can provide guidance for calibrating household preferences in macroeconomic models of the Australian economy.

Partnerships of Bidders with Constant Relative Risk Aversions

In this paper, we study a dynamic auction for allocating a single indivisible project while different participants have different bid values for the project. When the price rises continuously, the bidders can retreat the auction and obtain the compensation by the difference between the price at retreating time and the previous bid price. The final successful bidder achieves the project and pays compensations to others. We show that the auction of bidders with constant relative risk aversion (CRRA) has a unique equilibrium. While the relative risk aversion coefficient approaches to zero, the equilibrium with CRRA bidders would approach to the equilibrium with risk-neutral bidders.

Labor market search, endogenous disasters and the equity premium puzzle

The present paper investigates: (i) the endogenous disaster mechanism in a textbook search-and-matching model when calibrated with a constant flow value of unemployment that is close to average labor productivity and (ii) its contribution to solve the equity premium puzzle.I offer a simple explanation for the core of the disaster mechanism: the lower bound—say Xkink—on the annuitized costs the firm incurs from investing in a match lies sufficiently close to the body of productivity’s distribution. If labor productivity drops close to, or even below Xkink for consecutive periods, the firm’s annuitized share in expected future productivity of a worker can either only barely, or even no longer at all break even the annuitized lower bound of the costs the firm faces. Vacancies become unprofitable and the economy quickly enters a downward spiral. The core of the mechanism relies critically on an unreasonably high and constant flow value of unemployment. Disasters disappear entirely for slightly smaller or procyclical values and the effects cannot be compensated by empirically plausible adjustments of the model’s remaining parameters.While the model can generate a sizeable equity premium combined with a small risk-free rate if the flow value of unemployment is large and constant and if the coefficient of relative risk aversion and the elasticity of intertemporal substitution are both high, premia again collapse by an order of magnitude in the versions of the model without disasters.

Optimal retirement and portfolio selection with consumption ratcheting

The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in his/her consumption throughout his/her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent’s optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the von Neumann–Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent’s felicity utility function and depends only on the subjective discount rate and market parameters.

Ambiguity on uncertainty and the equity premium

This paper considers an asset pricing model with a multiple-priors recursive utility incorporating decision makers’ concern with ambiguity on drift and jumps of driving process. Based on our empirical evidence, given a small relative risk aversion (RRA) coefficient (e.g., RRA = 2), the model can well explain the equity premium puzzle, since the ambiguity aversion, as a complementary aversion of the risk aversion, can increase the equity premium and decrease the risk-free rate. This paper documents that ambiguity on uncertainty is a resolution of the equity premium puzzle.

Solution to the Equity Premium Puzzle

This study provides a solution of the equity premium puzzle. Questioning the validity of the Arrow-Pratt measure of relative risk aversion for detecting the risk behavior of investors under all conditions, a new tool, that is, the sufficiency factor of the model was developed to analyze the risk behavior of investors. The calculations of this newly tested model show that the value of the coefficient of relative risk aversion is 1.033526 by assuming the value of the subjective time discount factor as 0.99. Since these values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides a solution to the equity premium puzzle.

Present-Bias and the Value of Sophistication

This paper develops a dynamic wealth management model for risk-averse investors displaying present-bias in the form of hyperbolic discounting. The investor chooses an optimal consumption policy and allocates her funds between a risk-free asset, a traded liquid asset, and a non-traded illiquid asset. We characterize these policies for both sophisticated and naive present-biased investors. There are three results. First, sophisticated investors over-consume more than their naive counterparts if and only if their coefficient of relative risk-aversion is smaller than one. As a result, sophistication is welfare reducing (increasing) when risk-aversion is low (high). Second, increasing asset illiquidity always benefits the sophisticated investor more than the naive investor. Thus, the welfare gap between sophisticated and naive investors is increasing in the proxy for asset illiquidity. Finally, present-biased investors accumulate a larger share of their wealth in the non-traded illiquid asset than in the traded risky stock compared to the neoclassical exponential discounter investor. As a consequence, from the perspective of present-biased investors, the equity premium puzzle (1985) and the private equity puzzle (2002) are two sides of the same coin.

Risk, ambiguity, and Giffen assets

We provide necessary and sufficient conditions for the demand for financial assets to satisfy the law of demand (prices and quantity demanded move in opposite directions) when preferences take the expected utility, multiplier preferences, Choquet expected utility, and the maxmin expected utility forms. For the first three models the law of demand holds when the variation in the coefficient of relative risk aversion stays within a specified bound. Ensuring the law of demand holds in the maxmin expected utility model requires constant relative risk aversion.

Optimal Retirement and Portfolio Selection with Consumption Ratcheting

The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in his/her consumption throughout his/her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent’s optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the von-Neumann-Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent's felicity utility function and depends only on the subjective discount rate and market parameters.

The welfare cost of uncertainty in policy outcomes

This paper proposes a simple index of the welfare significance of uncertainty in the public goods resulting as policy outcomes. Our measure is the ex ante compensation an individual would require to accept an uncertain level of service compared to receiving the expected value of the distribution of possible values for that service. Our compensation measure is a function of the coefficient of relative risk aversion, the variance in the measure of environmental service associated with policy and relevant for the individual, and a set of conventional parameters that describe the properties of nonmarket benefit measures under conditions of certainty. We would expect that the inverse virtual price elasticity of the for the environmental service and the square of the coefficient of relative variation are the primary factors influencing the size of our compensation index.

The Intertemporal Risk-Return Relation is Alive and Well, It's Interpretation? Not So Much

Using data from 1980 through 2005, and implementations of the Intertemporal Capital Asset Pricing Model (ICAPM), this study consistently generates positive intertemporal risk-return relations within venture capital markets. During the first five years of business, venture capitalists (VCs) are shown to be risk averse, and are characterized by a Coefficient of Relative Risk Aversion (CRRA) estimated at about 2.75. From the sixth year of business onwards, VCs are characterized by CRRAs that are no higher than 1.91. Combination of rigorous theoretical and empirical evidence establishes that CRRAs less than or equal to 2.00 are evidence for risk seeking preferences. The CRRA for the representative risk bearing agent who aggregates preferences of risk averse and risk seeking agents is shown to aggregate to 3.59. This outcome, to wit, a higher CRRA (3.59) for an agent who aggregates risk averse and risk seeking preferences, in relation to the CRRA for the embedded representative risk averse agent (2.75) is formally and theoretically shown to be outcome that subsists in equilibrium. Totality of the formal theoretical and empirical evidence demonstrates interpretations of CRRAs that are higher than 2.75 as evidence for stock markets that consist in entirety of risk averse agents is not robust.