Decreasing Absolute Risk Aversion Research Articles

Are annuities an inferior or normal good? Evidence from a less-developed country

One crucial decision made at retirement in Chile is whether to acquire an annuity or a phased withdrawal (PW) scheme. Annuities, unlike PW, do not allow for inheritance and provide smaller initial pension benefits while protecting against longevity and capital market risks. If preferences show decreasing absolute risk aversion (DARA), then an annuity (insurance) should be considered an inferior good. We test this hypothesis on Chilean data using a binary choice model. Our results reject the DARA hypothesis for the whole sample. However, after splitting the sample into low- and high-income groups, we find that the former have increasing absolute risk aversion (IARA) behavior, whereas the latter have DARA behavior. These findings suggest that policy programs encouraging retirement savings, such as tax breaks and subsidies, should be approached with caution depending on the balance of high and low-income individuals, particularly in less-developed economies.

Safety versus Compensation for Professional Athletes Who Face the Prospect of Career-Ending Injuries: An Economic Risk Analysis

The National Football League and National Hockey League have instituted several rule changes, equipment improvements and medical protocols in response to the frequency of serious career-ending injuries. These two professional leagues and others have litigated lawsuits by former players who have sought financial compensation. This paper constructs a simple economic model of a risk averse athlete who faces the uncertain prospect of a career-ending injury. Improving the athlete’s welfare can be accomplished by reducing the probability of a serious injury or providing increased compensation in the event of such an injury. The net marginal preference for safety is high in sports with moderate to high probabilities of serious injury. Compensation plans are favored in sports with moderate to low probabilities. Significant increases in player salaries have little effect on a players net marginal preference for safety. These results are robust to constant or decreasing absolute risk aversion.

The Impact of Health Risks on Individual Decision Making: Focusing on the Demand for Insurance and Risky Assets

This study examines the impact of health and health risks on individuals' decision-making using a bivariate utility function, where the level of utility depends on both wealth and health. The findings are as follows, first, partial insurance may be optimal even under an actuarially fair insurance premium. Conversely, full insurance or over insurance may be optimal, even under an actuarially unfavorable premium. Second, when the utility function exhibits cross-risk vulnerability toward health, the presence of unfair health risks, independent of losses, increases the demand for insurance. Third, correlation-loving individuals reduce their investment in risky assets as health deteriorates when their preference exhibits decreasing absolute risk aversion (DARA) in wealth and absolute risk aversion (ARA) in wealth is sufficiently large. Conversely, correlation-averse individuals reduce their investment in risky assets as health deteriorates when their preference for DARA and ARA in wealth is sufficiently small. Fourth, when the utility function exhibits cross-risk vulnerability toward health, the presence of unfair health risks independent of the returns of risky assets reduces the demand for those assets.

Risk aversion and entrepreneurship under uncertainty: Further results

The extant literature has shown that (i) the positive relation between assets and the rate of business startups and (ii) the increase in the relative return to risky entrepreneurship for the marginal individual when his assets increase are both driven by risk preferences that exhibit decreasing absolute risk aversion (DARA). In this paper, we contribute to the theory of entrepreneurship under uncertainty by proving that DARA is not only sufficient but also necessary for these two results. DARA as such plays an essential role for the understanding of the occupational choice between risky entrepreneurship (self-employment) and secure employment when uncertainty prevails.

Downside risk aversion vs decreasing absolute risk aversion: an intuitive exposition

Downside risk aversion (downside RA) and decreasing absolute risk aversion (DARA) are different concepts that describe preferences for which the harm from bearing risk is lessened by an increase in wealth. This note presents some intuitive explanations of the difference between the two concepts using simple lotteries and graphical analysis. All risk-averse utility functions exhibit downside risk aversion, except those that exhibit sufficiently strong increasing absolute risk aversion. In a sense, downside RA is to be expected: adding downside risk to a baseline lottery is analogous to increasing risk while adding upside risk is analogous to decreasing risk. The difference between the two concepts can be attributed to the use of different measures of the harm from risk bearing: downside RA measures harm using the utility premium and DARA measures harm using the risk premium. The two premia can change at different rates and even in different directions as wealth increases.

Market insurance and endogenous saving with multiple loss states

The standard one-period model for insurance demand does not consider the interaction between the present and the future. Reflecting this observation, we analyze intertemporal insurance demand and saving in a two-period model with multiple loss states. When an individual has no access to a capital market, we first find that an actuarially fair premium does not guarantee full insurance in general, unlike in the standard approach. Income stream and discount factors are also important in determining insurance demand. Second, insurance is neither an inferior good nor a Giffen good. Third, an increase in concavity of the utility function does not always lead to an increase in insurance demand. The current income level and changes in downside risk aversion affect insurance demand. When the individual has access to a capital market, we further have the following observations. Fourth, an actuarially fair premium leads to full insurance. Fifth, insurance is an inferior good and can be a Giffen good under decreasing absolute risk aversion (DARA). An increase in the interest rate leads to a lower insurance demand and a higher saving when the relative risk aversion is less than unity. Lastly, an increase in concavity of the utility function leads to an increase in insurance demand and a decrease in saving. In conjunction, our findings point to the fact that the standard results are not obtainable if insurance demand is considered in isolation from the capital market.

On the Change of Risk Aversion in Wealth: Evidence from a Closed Economic System

How does risk aversion change in wealth? To answer this question, we implemented a field experiment in the form of a free-to-play mobile game. Players made lottery choices at various points in the game and at different levels of in-game wealth. Since the game was designed as a closed economic system, that is, wealth could not be transferred into or out of the game, only in-game wealth was relevant for players’ choices. Analyzing the choices of over 2,000 players, we find robust evidence for decreasing absolute risk aversion (DARA) and decreasing relative risk aversion (DRRA). We also find evidence of an always safe heuristic in a subgroup of decisions and observe a tendency of players to act according to the hot hand fallacy. Our research design allows us to exclude inertia and lets us analyze lottery stakes of significant size relative to in-game wealth. Our results render implications for theoretical research, empirical studies, and for the optimal design of financial products.

Calculating a Giffen Good

This paper provides a simple example of the utility function with two consumption goods which can be calculated by hand to produce a Giffen good. It is based on the theoretical result by Kubler et al. (Am Econ Rev 103:1034–1053, 2013). Using a model of portfolio selection with a risk-free asset and a risky asset, they showed that there always exists a parameter set which assures that the risk-free asset becomes a Giffen good if the utility function belongs to the HARA (hyperbolic absolute risk aversion) family with decreasing absolute risk aversion (DARA) and decreasing relative risk aversion (DRRA). This paper investigates their result further in a usual microeconomic setting where the risk-free asset and the risky asset are changed to the first and second consumption goods, respectively. It is organized as follows. First, a standard utility maximization problem of a consumer is directly solved to obtain the conditions for the first good to be a Giffen good. Second, the same problem is analyzed by means of decompositions of the price effect due to Slutsky and Sasakura (Italian Econ J 2:258–280, 2016). As is well known, the former decomposition consists of the substitution effect and the income effect, while the latter implies the decomposition into the ratio effect and the unit-elasticity effect. Lastly these analyses are compared and summarized. It should be added that the utility function proposed in this paper can also be used for the analysis of a normal good mutatis mutandis.

Stochastic Interest Rate Model and Its Applications: A Case for India

In this dissertation the main focus area was to use one factor interest rate models in India to obtain the descriptive nature and risk profile of money markets in India. For the period of 2012-2020 we found that CIR (1985) model fits and describes the interest rate path for India much better than Vasicek model. Both of these models were calibrated to make each of their parameters pseudo time varying and maximum likelihood estimation (MLE) was used to find optimal model parameters. We used daily weighted average of call money market rates as input data for calibration. Under the assumptions of constant relative risk aversion (CRRA) and decreasing absolute risk aversion (DARA) of CIR model, we used the closed form solutions to obtain bond prices and yields on 3 month T-bill. Average 10 year yield curve for the period 2012-20 was also forecasted and it was observed that Indian yield curve has a hump shape, with higher yields on longer dated bonds. We find that there exists higher term premium for longer dated bonds, for example, term premium on 10 year G-Sec has increased at a faster rate, relative to shorter maturity bonds, with the trend getting stronger since 2016 with an exception in year 2019. For risk profiling, the paper uses Expected-shortfall (ES) and Value-at-Risk (VaR) on 3 month bonds. It was found that expected shortfall normalized for yield stood at 25% on average for the period 2012-20. This means that traders in the money market need to constantly look out for price risk, to hedge for this, we propose that the trader uses call options on bonds. We find that fair prices of call options for CIR distribution function under Blacks-Scholes model will be an expensive hedging strategy. But that said, the Greeks for these call options (Rho, Delta and Gamma) show that the call option will not be sensitive to interest rate and bond price changes and hence will be a stable hedging strategy. The paper concludes that this is because of very high speed of mean reversion and low volatility in interest rate paths. This result can be associated with credibility, transparency and clear policy decisions made by the Indian central bank and newly formed Monetary Policy Committee (MPC). It was also seen that MPC has been successful to lower volatility by 9 times since its inception while maintaining the same high levels of speed of reversion in interest rates.

A test of risk vulnerability in the wider population

Panel data from the German SOEP is used to test for risk vulnerability (RV) in the wider population. Two different survey responses are analysed: the response to the question about willingness-to-take risk in general and the chosen investment in a hypothetical lottery. A convenient indicator of background risk is the VDAX index, an established measure of volatility in the German stock market. This is used as an explanatory variable in conjunction with HDAX, the stock market index, which proxies wealth. The impacts of these measures on risk attitude are identifiable by exploiting the time dimension of the panel and matching survey months with corresponding observations from these time-varying factors. Both of the survey responses allow us to test for decreasing absolute risk aversion (DARA); in one case, we find strong evidence of DARA, while in the other, we do not. Both survey responses also allow us to test for RV, and in both cases we find strong evidence. In the case of the hypothetical lottery response, we are also able to estimate a “coefficient of risk vulnerability” (CRV). This is defined as the absolute amount by which absolute risk aversion rises in response to a doubling of background risk. We estimate CRV to be between 1.03 and 1.27.

SOCIAL INSURANCE UNDER FRAUD AND REDISTRIBUTIVE TAXATION

This paper examines the equity and efficiency effects of social insurance in the presence of insurance fraud and linear income taxes and shows the following findings. (i) Under the commonly accepted assumption of decreasing absolute risk aversion (DARA), the social insurance benefit may increase insurance fraud, whereas raising the marginal tax rate (lumpsum transfer) of the linear income tax also causes insurance fraud to increase (decrease). (ii) Equity and efficiency effects of social insurance are conflicting rather than complementary with each other.

On Three Standard Results in the Theory of Insurance Demand

Abstract This article re-examines three standard results in the theory of insurance demand: (i) full coverage with a fair premium and partial coverage with an unfair premium; (ii) insurance is an inferior good under decreasing absolute risk aversion (DARA) and (iii) insurance may be a Giffen good under DARA. It has been shown recently that (i) holds for the class of insurance policies in which maximum coverage fully covers the potential loss. We show that whether (i) holds beyond this class of policies is indeterminate. In addition, we employ a unified framework to investigate the effects of changes in initial wealth and price. In particular, we show that both (ii) and (iii) hold for a certain class of insurance policies which include all commonly-used types of policies. The result also provides a unified treatment of several results in the extant literature.

On Three Standard Results in the Theory of Insurance Demand

This article re-examines three standard results in the theory of insurance demand: (i) full coverage with a fair premium and partial coverage with an unfair premium; (ii) insurance is an inferior good under decreasing absolute risk aversion (DARA) and (iii) insurance may be a Giffen good under DARA. It has been shown recently that (i) holds for the class of insurance policies whose maximum coverage fully covers the potential loss. We show that whether (i) holds beyond this class of policies is indeterminate. In addition, we employ a unified framework to investigate the effects of changes in initial wealth and price. In particular, we show that both (ii) and (iii) hold for a certain class of insurance policies which include all commonly-used types of policies. The result also provides a unified treatment of several results in the extant literature.

Modelling the effects of exposure to risk on junior faculty productivity incentives under the academic tenure system

This paper relies on modelling tools from probability theory and the economics of risk to analyze the ex-ante incentive properties of tenure from the perspective of junior faculty members. The theoretical results show that under publication value uncertainty and risk aversion, a junior faculty member publishes at a point where the expected value of publication exceeds the marginal cost of publication. In addition, under decreasing absolute risk aversion (DARA), increasing a junior faculty member's base salary reduces the implicit cost of private risk bearing thereby stimulating scientific productivity. However, increasing levels of uncertainty in the value of publication reduces faculty research incentives. These results have important implications for academic departments as they seek to enact effective policies to achieve and maintain their accreditation and reputation goals through maximum faculty productivity.

Climate-adaptive planning for the long-term resilience of transportation energy infrastructure

This paper investigates a long-term planning response to the climate-vulnerability of transportation energy infrastructure in the borough of Manhattan, NY. The proposed model, a two-stage stochastic optimization, features a hybrid utility-regret function with increasing relative and decreasing absolute risk aversion. Modeling results suggest (1) investment in early- and late-stage resilience-enhancing solutions as a complementary approach with significant weight on immediate actions, and (2) a decentralized supply chain formation through an early-stage deployment of reservoir tanks within the case study area.

Extensions on Stochastic Dominance Efficiency Tests

We consider second, third, fourth and fifth order stochastic dominance (SSD, TSD, FOSD and FISD, respectively) as well as decreasing absolute risk aversion (DARA) stochastic dominance (DSD). For comparison with DSD we also consider stochastic dominance (ESD) based on CARA utility functions. Their relevance in practice arises from empirical evidence on individual preferences fitting to preference models underlying such stochastic dominance relations. Assuming a known, discrete and finite probability distribution we derive necessary and sufficient efficiency tests under the six types of stochastic dominance. Simple arguments yield well-known SSD and TSD efficiency tests which are subsequently used to develop new FOSD, FISD, DSD and ESD efficiency tests. We provide numerical demonstration using stock market data of the US.

Input Demand Under Joint Energy and Output Prices Uncertainties

In this paper, we analyze the impacts of joint energy and output prices uncertainties on the input demands in a mean–variance framework. We find that an increase in expected output price will surely cause the risk-averse firm to increase the input demand, while an increase in expected energy price will surely cause the risk-averse firm to decrease the demand for energy, but increase the demand for the non-risky inputs. Furthermore, we investigate the two cases with only uncertain energy price and only uncertain output price. In the case with only uncertain energy price, we find that the uncertain energy price has no impact on the demands for the non-risky inputs. We also show that the concepts of elasticity and decreasing absolute risk aversion (DARA) play an important role in the comparative statics analysis.

Modeling the Effects of Exposure to Risk on Junior Faculty Scientific Productivity Incentives Under the Academic Tenure System

This paper provides an analytical investigation of the impact that tenure risks have on junior faculty publication incentives. It is motivated by the fact that untenured faculty often face the pressure to publish or lose their position in academic institutions where publication is the ultimate criteria for advancement. Faculty face risks during the probationary period for which risks markets are absent, and so must manage their risk exposure privately. The results show that under publication value uncertainty and risk aversion, a junior faculty member publishes at a point where the expected value exceeds the marginal cost of publication. Also, under decreasing absolute risk aversion (DARA), increasing a junior faculty member's base salary reduces the implicit cost of private risk bearing and stimulates scientific productivity. However, an increase in the level of uncertainty in the value of publication reduces faculty research productivity incentives. These results have important implications for academic departments as they seek to enact effective policies to achieve and maintain their accreditation and reputation goals through maximum faculty productivity.

Risky rents

We consider a strategic contest game in which risk-averse agents exert efforts to increase their share of a risky rent. We show that a unique symmetric equilibrium always exists under constant or decreasing absolute risk aversion. We also show that agents exert in general less efforts when they are more risk averse or when the rent is more risky.

Some new results about optimal insurance demand under uncertainty

The aim of this paper is to investigate the optimal insurance demand of a risk-averse agent who is faced with background uncertainty. The preferences of the agent are represented by two-moment, mean-standard deviation utility functions. By the comparative statics, we find that under the assumption of decreasing absolute risk aversion (DARA), the changes of background uncertainty have effects on optimal insurance demand.