Coefficient Of Relative Risk Aversion Research Articles

The Bitcoin Premium: A Persistent Puzzle

Abstract On average, stocks have a much higher rate of return than bonds; this has led to research on the equity premium puzzle. Similarly, Bitcoin outperforms stocks; I call this the Bitcoin premium puzzle. I show that standard macroeconomic models predict a low or negative Bitcoin premium. Though Bitcoin is extremely volatile, the model is rejected even when the coefficient of relative risk aversion is above 10. The Bitcoin premium declined after a structural break in late 2013. However, the puzzle is persistent; there has been no downward trend in the premium since.

Risk preferences over health: Empirical estimates and implications for medical decision-making

Mainstream health economic theory implies that an expected gain in health-related quality of life (HRQoL) produces the same value for consumers, regardless of baseline health. Several strands of recent research call this implication into question. Generalized Risk-Adjusted Cost-Effectiveness (GRACE) demonstrates theoretically that baseline health status influences value, so long as consumers are not risk-neutral over health. Prior empirical literature casts doubt on risk-neutral expected utility-maximization in the health domain. We estimate utility over HRQoL in a nationally representative U.S. population and use our estimates to measure risk preferences over health. We find that individuals are risk-seeking at low levels of health, become risk-averse at health equal to 0.485 (measured on a 0–1 scale), and are most risk-averse at perfect health (coefficient of relative risk aversion = 4.51). We develop the resulting implications for medical decision making, cost-effectiveness analyses, and the proper theory of health-related decision making under uncertainty.

A formula for the elasticity of substitution of a large class of smooth utility functions

We derive a general formula for the elasticity of substitution of a large class of smooth utility functions. This formula depends critically on two terms: the marginal rate of substitution and the elasticity of marginal utility, which may be interpreted according to the context either as the coefficient of relative risk aversion or as the intertemporal elasticity of substitution. This formula works for homothetic and non-homothetic utility functions. Besides, it holds for two important class utility functions often used in both empirical and theoretical works: the quasi-linear utility and the Stone-Geary utility functions.

Optimal energy portfolio method for regulable hydropower plants under the spot market

The energy allocation method for regulable hydropower plants under the spot market significantly impacts their income. The available studies generally draw on the Conditional Value-at-Risk (CVaR) approach, which typically assumes a fixed risk aversion coefficient for generators. This assumption is based on the assumption that the total energy the power plant can allocate is constant during the decision period. However, the amount of energy that the regulable hydropower plant can generate will be affected by inflow and water level during the decision period, and the assumption of the fixed risk aversion coefficient is only partially consistent with the actual decision behavior of the hydropower plant. In this regard, the time-varying relative risk aversion (TVRRA) based method is proposed for the energy allocation of regulable hydropower plants. That method takes the change value of the hydropower plant’s energy generation as the basis for adjusting the time-varying relative risk aversion coefficient to make the energy allocation results more consistent with the actual decision-making needs of the hydropower plant. A two-layer optimal method is proposed to obtain the income-maximizing energy portfolio based on regulable hydropower plants’ time-varying relative risk aversion coefficient. The inner point method solves the optimal energy portfolio of income and risk in the upper layer. The time-varying relative risk aversion coefficient in the lower layer accurately describes the dynamic risk preference of hydropower plants for each period. The results and comparison show that the proposed method increases the income of the energy portfolio by 31%, and water disposal of regulated hydropower plants is reduced by 2%. The energy portfolio optimization method for regulable hydropower plants proposed in this paper not only improves the economic income of hydropower plants but also improves the utilization rate of hydro energy resources and enhances the market competitiveness of regulable hydropower plants.

Weak Instruments, Degree of Risk Aversion and Equity Premium: Evidence from Singapore, South Korea and Taiwan

AbstractUsing data from Singapore, South Korea, and Taiwan, we estimate the coefficient of relative risk aversion (RRA) in the constant relative risk aversion utility specification of the consumption‐based capital asset pricing model. Conventional instrumental variables methods find that the coefficient of RRA is low but the inverse of it—the elasticity of intertemporal substitution in consumption—is also low. Such contradictory findings could be attributed to instruments being weak. Using weak‐instrument robust tests, we find from the equity market data that the coefficient of RRA is rather high, which could potentially explain the high equity premiums in these three East Asian economies.

Evolutionary foundation for heterogeneity in risk aversion

We examine the evolutionary basis for risk aversion with respect to aggregate risk. We study populations in which agents face choices between alternatives with different levels of aggregate risk. We show that the choices that maximize the long-run growth rate are induced by a heterogeneous population in which the least and most risk-averse agents are indifferent between facing an aggregate risk and obtaining its linear and harmonic mean for sure, respectively. Moreover, approximately optimal behavior can be induced by a simple distribution according to which all agents have constant relative risk aversion, and the coefficient of relative risk aversion is uniformly distributed between zero and two.

Optimal portfolio selection with life insurance under subjective survival belief and habit formation

<p style='text-indent:20px;'>This paper studies the optimal consumption, investment, and life insurance choices for a wage earner with subjective survival beliefs and habit formation types. The wage-earner has access to a risk-free asset, an index bond, and a stock in a financial market. Introducing subjective survival beliefs describes the wage earner's optimistic or pessimistic attitude towards the longevity risk. Two types of habit formation are considered: one depends on real past consumption; the other is incited by money illusion and depends on nominal past consumption. The aim is to maximize the expected utility of real consumption, total legacy, and terminal wealth, where the utility of consumption comes from the part of real consumption that exceeds real habit level. Using the dynamic programming method, we provide and prove a verification theorem and obtain the closed-form solution of the optimization problem. Numerical results reveal that subjective survival beliefs and habit formation types play important roles in the financial behaviors of the wage-earner. Detailed results are exhibited. Especially, subjective survival beliefs, the existence of habit formation, and the relative risk aversion coefficient affect the demand for life insurance.</p>

HİSSE SENEDİ PRİMİ BULMACASININ ÇÖZÜMÜ

This study provides the solution to the equity premium puzzle. The new model was developed by including the behavior of investors toward risk in financial markets in prior studies. 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 to be 0.99. Furthermore, investors investing in risk-free asset allocate negative utility for an uncertain wealth value, while those investing in equity allocate positive utility for an uncertain wealth value in 1977 that is automatically selected as the year for the determination of the behavior of investors toward risk. Since the above mentioned values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides the solution to the equity premium puzzle.

The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations

The goal of this article is to provide a detailed introduction to infinite-horizon investment–consumption problems for agents with preferences described by Epstein–Zin (EZ) stochastic differential utility (SDU). In the setting of a Black–Scholes–Merton market, we seek to describe all parameter combinations that lead to a well-founded problem in the sense that the problem is not just mathematically well posed, but the solution is also economically meaningful. The key idea is to consider a novel and slightly different description of EZ SDU under which the aggregator has only one sign. This new formulation clearly highlights the necessity for the coefficients of relative risk aversion and of elasticity of intertemporal complementarity (the reciprocal of the coefficient of intertemporal substitution) to lie on the same side of unity.

CRRA utility and the sustainability of cooperation in infinitely-repeated games

In a symmetric infinitely-repeated game, where players have constant relative risk aversion (CRRA), or constant elasticity of intertemporal substitution, utility functions, it is shown that the critical discount factor required to sustain full cooperation is decreasing in the coefficient of relative risk aversion (increasing in the elasticity of intertemporal substitution). An application to cooperation in international environmental agreements (IEA) is presented and it is shown that the limit of the critical discount factor as the number of countries goes to infinity is equal to one (zero) if the coefficient of intertemporal inequality aversion is less (greater) than one. • Analyses infinitely-repeated game when players have CRRA utility functions. • Cooperation in infinitely-repeated games is easier the more risk-averse are players. • Application to International Environmental Agreement with many countries.

Factors affecting attitude towards risk: The case of small-scale fishers in Guimaras

The presence of risk and uncertainty in the field of capture fisheries warrants an understanding of how small-scale fishers respond to these uncertainties. Previous studies showed that fishers’ decision-making process is influenced by various factors, including their risk preference. Studies on this subject are scarce despite the relative importance of risk preference in explaining small-scale fisher’s behavior. This study used a multiple price list experiment to elicit small-scale fisher’s risk preference in Guimaras province and employed multinomial logit regression to determine socioeconomic factors influencing risk preference. The results showed that small-scale fishers are slightly risk-averse given the mean Constant Relative Risk Aversion (CRRA) coefficient of 0.20. This risk-averse attitude is significantly influenced by monthly household income, being a Pantawid Pamilyang Pilipino Program (4P’s) beneficiary, and having outstanding credit. Therefore, the risk-averse attitude of small-scale fishers is an essential consideration in implementing fishery regulations and poverty alleviation programs.

Are risk preferences explaining gender differences in investment behavior?

We analyze individual investment behavior among 822 young men and women that are members of 111 formal business groups in northern Ethiopia. We collected baseline data and investment data one year later combined with incentivized field experiments to obtain dis-aggregated risk preference data. We find that businesswomen on average invest significantly less at individual level than businessmen but Cohen’s d values for the gender difference are moderate in size. Women are found to have higher Constant Relative Risk Aversion (CRRA-r) coefficients (more concave utility function), to be more loss averse, but also to be more optimistic in their expectations (lower Prelec β) than men. Women were also poorer in non-land assets, came from more land-poor parents, and had lower incomes. The gender differences in risk attitudes and baseline endowments could explain some of but not all of the gender differences in investment behavior.

An analytical solution for the robust investment-reinsurance strategy with general utilities

In financial markets, different investors have different attitudes or preferences on the investment policies and reinsurance problems. For investors with different investment utilities, how to provide an optimal investment strategy is not only a very hard problem, but also an urgent problem to be solved. In this paper, we derive an analytical solution for the optimal allocation problem of investment-reinsurance with general-form utility function. The general utility function allows for varying relative risk aversion coefficient, which is an important feature in finance theory. However, obtaining analytical solutions for general utility function has been difficult or impossible. The solution presented in this paper is constructed through the homotopy analysis method (HAM) and written in the form of a Taylor series expansion. The fully nonlinear Hamilton–Jacobi–Bellman (HJB) equation is decomposed into an infinite series of linear PDEs, which can be solved analytically. In the end, three examples are presented to illustrate the convergence and accuracy of the method, it also demonstrates that different risk reference investors have different investment-reinsurance strategies.

Risk aversion when preferences are altruistic

We link risk preferences, as measured by the coefficient of relative risk aversion, with the prevalence and intensity of altruism, which we operationalize by the propensity of a person to voluntarily transfer part of his wealth to another person. To quantify the intensity of altruism, we incorporate a coefficient αi∈(0,1) in the utility function of an altruistic person i. This coefficient measures the extent to which the altruistic person derives utility from the wellbeing of another person. We show that an altruistic person who is an active donor (benefactor) is more risk averse than a non-altruistic person, and that the relative risk aversion of altruistic person i is an increasing function of αi. In addition, we show, in line with intuition, that person j who is the beneficiary of an altruistic transfer is less risk averse than a comparable person who is not a beneficiary of an altruistic transfer, and that the relative risk aversion of person j is a decreasing function of αi. When we analyze a setting in which two persons are altruistic towards each other, we find that, in essence, the risk aversion consequences of mutual altruism do not differ from the risk aversion consequences of unilateral altruism.

A Study on Dynamic Asset Allocation Strategy for Optimal Portfolio Selection

We use iterative numerical procedures combined with analytical methods due to Rapach and Wohar (2009) to solve for the dynamic asset allocation strategy for optimal portfolio demand. We compare different optimal portfolio demands when investors in each country have different access to overseas and domestic investment opportunities. The optimal dynamic asset allocation strategy without foreign investment opportunities leads domestic investors in Korea, Hong Kong, and Singapore to allocate more funds to domestic bonds than to domestic stocks. However, the U.S. investors allocate more wealth to domestic stocks than to domestic bonds. Investors in all countries short bills at a low level of risk aversion. Next, we investigate dynamic asset allocation strategy when domestic investors in Korea have access to foreign markets. The optimal portfolio demand leads investors in Korea to allocate most resources to domestic bonds and foreign stocks. On the other hand, the portfolio weights on foreign bonds and domestic stocks are relatively low. We also analyze dynamic asset allocation strategy for the investors in the U.S., Hong Kong, and Singapore when they have access to the Korean markets as overseas investment opportunities. Compared to the results when the investors only have access to domestic markets, the investors in the U.S. and Singapore increase the portfolio weights on domestic stocks in spite of the overseas investment opportunities in the Korean markets. The investors in the U.S., Hong Kong, and Singapore short domestic bills to invest more than initial funds in risky assets with a varying degree of relative risk aversion coefficients without exception.

Real(istic) Time-Varying Probability of Consumption Disasters

We model the time-varying probability of consumption disasters with international risk interactions and estimate the model using national accounts data of 42 countries back to 1833. The estimated world and country-specific disaster probabilities accord well with historical macroeconomic disasters. A match of equity premium requires a relative risk aversion coefficient around 5, substantively smaller than the previous estimates. Also, the model delivers a significantly better match for the equity volatility than alternative rare disaster models. Finally, the disaster probability index estimated from the model can predict equity returns in the very long term---up to 50 years.

Free boundary problem for an optimal investment problem with a borrowing constraint

<p style="text-indent:20px;">This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.</p>

Welfare Effects of Unemployment Benefits When Informality is High

We analyze for the first time the welfare effects of unemployment benefits (UBs) in a context of high informality, exploiting matched administrative and survey data with individual-level information on UB receipt, formal and informal employment, wages and consumption. Using a difference-in-differences approach, we find that dismissal from a formal job causes a large drop in consumption, which is between three to six times larger than estimates for developed economies. This is generated by a permanent shift of UB recipients towards informal employment, where they earn substantially lower wages. We then exploit a kink in benefits and show that more generous UBs delay program exit through a substitution of formal with informal employment. However, the disincentive effects are small and short-lived. Because of the high insurance value and the low efficiency costs, welfare effects from increasing UBs are positive for a range of values of the coefficient of relative risk aversion.

Evolutionary Foundation for Heterogeneity in Risk Aversion

We examine evolutionary basis for risk aversion with respect to aggregate risk. We study populations in which agents face choices between aggregate risk and idiosyncratic risk. We show that the choices that maximize the long-run growth rate are induced by a heterogeneous population in which the least and most risk averse agents are indifferent between aggregate risk and obtaining its linear and harmonic mean for sure, respectively. Moreover, an approximately optimal behavior can be induced by a simple distribution according to which all agents have constant relative risk aversion, and the coefficient of relative risk aversion is uniformly distributed between zero and two.

The hedging-based utility risk measure

FinTech makes numerous financial products accessible to common investors but up to now, there is no risk measure method specially customized for common investors instead of financial institutions which are generally too big to fail. This paper develops a hedging-based utility risk measure (HBU) theory. We show that HBU is a convex risk measure and if the utility has a constant relative risk aversion coefficient, HBU is also coherent. Roughly speaking, HBU is the opposite of a generalized utility indifference price. HBU depends on claimants' utility and the hedging instruments accessible to them and thus it is a personal (subjective) risk measure especially suitable for common investors who need to have a comprehensive risk evaluation of a financial product.