Ross risk vulnerability for introductions and changes in background risk

We present two theorems that provide necessary and sufficient conditions for an expected utility maximizer to become more risk averse in the sense of Ross with respect to bearing a foreground risk after the introduction of any independent fair or unfair additive background risk. We call these decision makers Ross risk vulnerable, and show that Ross decreasing absolute risk aversion and Ross decreasing absolute prudence are jointly sufficient for Ross risk vulnerability. Restrictions on utility necessary and sufficient for Ross risk vulnerability with respect to stochastic dominance deteriorations of an existing background risk are also presented. Our analysis concludes with applications of Ross risk vulnerability.     

Decreasing downside risk aversion and background risk

In this paper, we show that risk vulnerability can be associated with the concept of downside risk aversion (DRA) and an assumption about its behavior, namely that it is decreasing in wealth. Specifically, decreasing downside risk aversion in the Arrow–Pratt and Ross senses are respectively necessary and sufficient for a zero-mean background risk to raise the aversion to other independent risks.     

When Ross meets Bell: The linex utility function

At first glance, there would appear to be no relationship between Bell’s (1988) concept of one-switch utility functions and that of a stronger measure of risk aversion due to Ross (1981). We show however that specific assumptions about the behavior of the stronger measure of risk aversion also give rise to the linex utility function which belongs to the class of one-switch utility functions. In particular, this utility class is the only one that satisfies a stronger version of Kimball’s (1993) standard risk aversion over all levels of wealth. We apply our results to consider n$n$th-degree deteriorations in background risk and their effect on risk taking behavior.     

Intensity of preferences for bivariate risk apportionment

Bivariate risk apportionment is the preference for dispersing risks associated with two aspects of individuals’ well-being into different states of the world. In this paper, we propose an intensity measure of this preference by extending to the bivariate case the concept of marginal rate of substitution between risks of different orders introduced in the univariate case by Liu and Meyer (2013). We show that the intensity measure of the preference for bivariate risk apportionment is characterized by bivariate risk attitudes in the sense of Ross. The usefulness of our measures to understand economic choices is illustrated by the analysis of two specific decisions: savings under environmental risk and medical treatment in the presence of diagnostic risks.     

Risk aversion in RDEU

Various notions of risk aversion can be distinguished for the class of rank-dependent expected utility (RDEU) preferences. We discuss the relationships amongst five of these, and describe simple (testable) characterizations in terms of elementary probability transformations for all but the weakest notion. The paper also provides the first complete characterization of the RDEU orderings that are risk-averse in the sense of Jewitt [Jewitt, I., 1989. Choosing between risky prospects: the characterization of comparative static results and location independent risk. Management Science 35, 60–70]. We also extend Chew et al.’s [Chew, S.H., Karni, E., Safra, Z., 1987. Risk aversion in the theory of utility with rank-dependent probabilities. Journal of Economic Theory 42, 370–381] important characterization of strong risk aversion [Rothschild, M., Stiglitz, J.E., 1970. Increasing risk: I. A definition. Journal of Economic Theory 2, 225–243] by relaxing strict monotonicity and differentiability assumptions, and allowing for discontinuities in the probability transformation function. The important special case of maximin choice falls within this relaxed RDEU class. It is shown that any strongly risk-averse RDEU order is a convex combination of maximin and another RDEU order with concave utility and continuous, concave probability transformation. Our proof of the result on strong risk aversion is also simpler (as well as more general) than that of Chew et al. [Chew, S.H., Karni, E., Safra, Z., 1987. Risk aversion in the theory of utility with rank-dependent probabilities. Journal of Economic Theory 42, 370–381].     

引入风险厌恶偏好的供应链部分回购协调契约

研究了由一个风险中性的供应商和一个风险厌恶的零售商组成的供应链系统的部分回购契约。将部分回购契约建模讨论,并进行数值模拟分析。结果表明,当零售商为风险厌恶时,供应链系统仍能达到协调,且回购比例是零售商的风险厌恶程度的增函数,批发价格是零售商的风险厌恶程度的减函数。     

Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.     

Forecasting stock market volatility: Can the risk aversion measure exert an important role?

In this paper, we predict realized volatility of stock return by utilizing time-varying risk aversion based on a simple linear autoregressive model. Our in-sample results suggest that time-varying risk aversion have significant impact for stock return volatility. In terms of out-of-sample forecasting performance, the empirical results indicate that the incorporation of time-varying risk aversion in the benchmark model can yield more accurate stock return volatility forecasts. Notably, the out-of-sample forecasting results confirm that our conclusions are robust when we apply alternative lag orders and alternative prediction evaluation periods. Finally, we study links between the prediction ability of time-varying risk aversion and the volatility of other stock indices and two kinds of crude oil, and find that the new predictor can effectively strengthen forecasting performance in most case. In view of the importance of volatility risk in the asset pricing process, our research is of great significance for financial asset participants.     

Rationalizing investors’ choices

Assuming that agents’ preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.     

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.     

Financial risk taking in the presence of correlated non-financial background risk

This paper characterizes the stochastic deterioration resulting from taking a zero-mean financial risk in the presence of correlated non-financial background risk. We show in particular that it has an equivalent stochastic order as well as a necessary and sufficient “integral condition” that implies and is implied by a particular sense in which the stochastic deterioration can be decomposed into a “correlation increase” and a “marginal risk increase”. We further characterize a measure of aversion to the stochastic deterioration. These characterizations provide for a more general framework for formulating concepts of increases in risk and correlation and for better understanding risk management decisions governed by individuals’ attitudes to them.     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

An intertemporal CAPM with higher-order moments

We propose an intertemporal asset pricing model that incorporates both preference for higher-order moments and stochastic investment opportunities and encompasses a wide range of existing models. We provide supporting evidence from the U.S. stock market and find that, not only is systematic skewness negatively priced, an extra return premium is also required for accepting high systematic risk associated with a rise in risk aversion. Our findings suggest that considering both skewness preference and intertemporal hedging demands improves the estimated risk-return trade-off, and that cross-sectional anomalies such as value, momentum, and failure probability puzzles can be partially explained by our model.     

Aggregate stock market behavior and investors’ low risk aversion

This paper studies whether investors’ high risk aversion can be avoided in a representative-agent model that is able to explain aggregate stock market behavior in the US financial market. We present a consumption-based asset pricing model with a representative agent who has a ‘catching up with the Joneses’ preference to show that high risk aversion can be avoided in a representative-agent model that can help explain many of the empirically observed properties of the aggregate stock market return, including the equity premium and risk-free rate puzzles, the predictability of long-horizon stock returns, and the ‘leverage effect’ in return volatility.     

Relative risk aversion and the transmission of financial crises

We study how investor behavior affects the transmission of financial crises. If investors exhibit decreasing relative risk aversion, then negative wealth shocks increase the risk premium required to hold risky assets. We integrate this into a second generation model of currency crises which allows for contagion through changes in fundamentals. Investor behavior can be a transmission channel of financial crises, as changes in risk premia increase the coverage ratio and makes the defense of a peg less attractive for the policy maker. The feedback effect of the risk premia on the probability of devaluation also makes multiple equilibria more likely. The possible stabilization effects of capital controls and a Tobin tax on the international transmission of financial crises are also studied.     

Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection

In a mean variance framework, we analyse risk taking in the presence of a (possibly) dependent background risk, exemplified in a linear portfolio selection problem. We first characterise the comparative statics of changes in the distribution and dependence structure of the background risk. For unfair, undesirable and loss-aggravating increases in background risks (both dependent and independent), we then present necessary and sufficient restrictions on preferences such that greater background uncertainty leads to reduced risk taking. With mean-variance preferences, these restrictions boil down to simple conditions on the marginal rate of substitution between risk and return. They can be easily related to familiar notions such as risk vulnerability, properness or standardness.     

Calibrating the wealth effects of decoupled payments: Does decreasing absolute risk aversion matter?

Arrow’s hypotheses regarding the relationship between wealth and risk aversion measures have formed the basis for a large body of empirical research and theory. For example, many have suggested that decoupled farm subsidy payments may increase production as they decrease farmers’ risk aversion. This paper develops a new calibration technique designed to measure the minimum change in concavity of a utility of wealth function necessary to describe a particular change in production behavior for some discrete change in wealth. I conclude that measurable changes in production levels should not be produced by changing levels of risk aversion except when wealth changes are a substantial portion of wealth. This tool draws into question the usefulness of Arrow’s hypotheses in many current applications.     

Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model

In this paper, we investigate the relation between time-varying risk aversion and renminbi exchange rate volatility using the conditional autoregressive range-mixed-data sampling (CARR-MIDAS) model. The CARR-MIDAS model is a range-based volatility model, which exploits intraday information regarding the intraday trajectory of the price. Moreover, the model features a MIDAS structure allowing for time-varying risk aversion to drive the long-run volatility dynamics. Our empirical results show that time-varying risk aversion has a significantly negative effect on the long-run volatility of renminbi exchange rate. Moreover, we observe that both intraday ranges and time-varying risk aversion contain important information for forecasting renminbi exchange rate volatility. The range-based CARR-MIDAS model incorporating time-varying risk aversion provides more accurate out-of-sample forecasts of renminbi exchange rate volatility compared to a variety of competing models, including the return-based GARCH, GARCH-MIDAS and GARCH-MIDAS incorporating time-varying risk aversion as well as range-based CARR, CARR-MIDAS and heterogeneous autoregressive (HAR), for forecast horizons of 1 day up to 3 months. This result is robust to alternative risk aversion measure, alternative MIDAS lags as well as alternative out-of-sample periods. Overall, our findings highlight the value of incorporating intraday information and time-varying risk aversion for forecasting the renminbi exchange rate volatility.     

我国民办高校财务风险规避研究

我国民办高校普遍存在办学基础不牢固、筹资困难、经费来源渠道单一,社会捐赠落后等问题,需要采取风险识别、分析评价与分级、风险处置、规避和反馈等环节,使财务风险降到最低,风险成本降到最小,推进民办高校的健康发展。     

Impact of investor’s varying risk aversion on the dynamics of asset price fluctuations

While investors’ responses to price changes and their price forecast have been identified as one of the major factors contributing to large price fluctuations in financial markets, our study shows that investors’ heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in understanding the dynamics of asset price fluctuations. We allow an agent specific and time-dependent risk aversion index in a popular power utility function with constant relative risk aversion to construct our DRA model in which we made two key contributions. We developed an approximated closed-form price setting equation, providing a necessary framework for exploring the impact of various agents’ behaviors on the price dynamics. The dynamics of each agent’s risk aversion index is modeled by a bounded random walk with a constant variance, and such dynamics is incorporated in the price formula to form our DRA model. We show numerically that our model reproduces most of the “stylized” facts observed in the real data, suggesting that dynamic risk aversion is an important mechanism for understanding the dynamics of the financial market and the resultant financial time series.