Risk Aversion,Downside Risk Aversion and Paying for Stochastic Improvements

This paper considers the relationship between risk preferences and the willingness to pay for stochastic improvements. We show that if the stochastic improvement satisfies a double-crossing condition, then a decision maker with utility v is willing to pay more than a decision maker with utility u, if v is both more risk averse and less downside risk averse than u. As the condition always holds in the case of self-protection, the result implies novel characterizations of individuals’ willingness to pay to reduce the probability of loss. By establishing a general result on the correspondence between an individual's willingness to pay, and his optimal purchase of stochastic improvement when there is a given relationship between stochastic improvements and the amount paid for them, we further show that all results on the willingness to pay can be applied directly to characterize the conditions under which a more risk averse individual will optimally choose to buy more stochastic improvement. Generalizations of existing results on optimal choice of self-protection can be obtained as corollaries.     

Downside Risk

Economists have long recognized that investors care differentlyabout downside losses versus upside gains. Agents who placegreater weight on downside risk demand additional compensationfor holding stocks with high sensitivities to downside marketmovements. We show that the cross section of stock returns reflectsa downside risk premium of approximately 6% per annum. Stocksthat covary strongly with the market during market declineshave high average returns. The reward for beasring downsiderisk is not simply compensation for regular market beta, noris it explained by coskewness or liquidity risk, or by size,value, and momentum characteristics. (JEL C12, C15, C32, G12)     

Downside Risk in Practice

Although investors associate risk with negative outcomes and downside fluctuations, modern portfolio theory does not. For investors, volatility per se is not necessarily bad; volatility below a benchmark is. A stock that magnifies the market's fluctuations is not necessarily bad; one that magnifies the market's downside swings is. Even Harry Mar‐kowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the “mean‐variance” framework that he ultimately proposed and that has since become the standard. This article highlights the shortcomings of traditional measures of risk (the standard deviation and beta), introduces the concept of downside risk, and discusses two measures of it—the “semideviation” and “downside beta.” It also discusses the use of such measures in asset pricing models to estimate required returns on equity. Data from a few well‐known companies are used to illustrate that the cost of equity based on downside risk can be substantially different from that based on the CAPM. The article concludes with a brief discussion of risk‐adjusted returns and a comparison of the traditional method of calculating such returns with both the Sharpe ratio and its counterpart in a downside risk framework, the Sortino ratio. The appendix demonstrates how to calculate these risk measures in Excel.     

Downside Risk in Emerging Markets

This paper investigates the relation between downside risk and expected returns on the aggregate stock market in an international context. Nonparametric and parametric value at risk are used as measures of downside risk to determine the existence of a risk-return trade-off. For emerging markets, fixed effects panel data regressions provide evidence for a significantly positive relationship between monthly expected market returns and downside risk. This result is robust after controlling for aggregate dividend yield and price-to-fundamental ratios. The relationship between expected returns and downside risk is weaker for developed markets and vanishes when control variables are included in the specification.     

Downside Risk and Investment Choice

This paper develops an optimal investment strategy for individuals concerned with avoiding the possibility of realizing returns below a predetermined target level within a prescribed period of time. Assuming a Brownian motion process, a model is developed which allows computation of the exact probability of failure. The algorithm and associated comparative statics with respect to the mean and standard deviation of returns, target return, time horizon, and risk-free rate of return are likely to have many useful practical applications.     

Risk Aversion Revisited

In order to supply additional empirical evidence of the effect of wealth on relative risk aversion, this study investigates households' demand for risky assets, using analysis of covariance techniques applied to the asset holdings of Canadian individual households. The extent and pattern of life-cycle effects are also examined. Results generally point to decreasing relative risk aversion when housing is either excluded from the definition of wealth or treated as a riskless asset. The investor's life-cycle plays a prominent role in portfolio selection behavior, with risk aversion increasing uniformly with age. Tax differentials do not seem to be an important element in investment decisions with respect to risk. When the sample and wealth definitions are censored in order to approximate those of previous empirical studies, their findings on relative risk aversion are generally corroborated.     

Portfolio Diversification Effects of Downside Risk

Risk managers use portfolios to diversify away the unpricedrisk of individual securities. In this article we compare thebenefits of portfolio diversification for downside risk in casereturns are normally distributed with the case of fat-taileddistributed returns. The downside risk of a security is decomposedinto a part which is attributable to the market risk, an idiosyncraticpart, and a second independent factor. We show that the fat-tailed-baseddownside risk, measured as value-at-risk (VaR), should declinemore rapidly than the normal-based VaR. This result is confirmedempirically.     

Risk Aversion and Arbitrage

This paper characterizes conditions under which asset returns and consumption are consistent with risk-averse preferences. It is shown that risk aversion is equivalent to “zero arbitrage” on a transformation of the payoff space. The implicit state prices which are dual to this no-arbitrage condition can be interpreted as prices of “pure consumption hedges.” This zero-arbitrage restriction implies the usual restrictions associated with nonsatiation. The analysis holds in both complete and incomplete market settings.     

Option-Implied Risk Aversion Estimates

Using a utility function to adjust the risk‐neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential‐utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.     

风险厌恶、失望厌恶和期货套期保值

本文考察失望厌恶对期货套期保值的影响。我们把一个不变的绝对风险厌恶（CARA）效用函数放进Gul（1991）的失望厌恶框架之内。它显示出，一个更厌恶失望的套期保值者会比一个厌恶失望程度较低的套期保值者选择一个更接近于最小方差套期保值的最优期货头寸。当套期保值者厌恶风险的程度较低时，失望厌恶的效应更强。对失望很小程度的厌恶会使一个接近于风险中性的套期保值者持有一个截然不同的头寸。此外，一个更厌恶风险或失望的套期保值者会有一个较低的参考点reference point。数字上的结果显示，厌恶失望的套期保值者的参考点往往会低于传统的厌恶损失的套期保值者的参考点。于是，厌恶失望的套期保值者的行动会更加保守，利用机会牟利的行为会少于传统的厌恶损失的套期保值者。     

Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk

To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.     

Risk Aversion and the Value of Risk to Life

The standard literature on the value of life relies on Yaari’s (1965) model, which includes an implicit assumption of risk neutrality with respect to life duration. To overpass this limitation, we extend the theory to a simple variety of preferences that are not necessarily additively separable. The enlargement we propose is relevant for the evaluation of life‐saving programs: current practice, we estimate, puts too little weight on mortality risk reduction of the young. Our correction exceeds in magnitude that introduced by the switch from the notion of number of lives saved to the notion of years of life saved.     

中国个人消费信贷状况及风险防范研究

随着个人信用消费的不断扩大,消费信贷的比重不断提高,在整个市场个人信用制度不完善的情况下,个人信贷风险凸现,银行个人信贷中的不良资产率上升。本文从中国消费信贷的总量状况出发,对于银行消费信贷内部结构展开探讨,继而分析消费信贷的客户风险、制度风险及法律政策风险,并以此为基础提出了建立个人信用管理制度、充分利用客户信用分析法、逐步试点个人破产制度、建立银行内控体系及风险转嫁渠道以及完善个人消费信贷的相关法律保障等防范措施。     

证券监管中行政诉讼风险防范的法律思考

强化依法行政的意识，提高防范行政诉讼风险的能力，是近年来中国证券监管系统愈显紧迫的任务与课题。本文从司法受案和审理这一独特视角，结合证券监管实践，对几类可诉行政违法行为和相关疑难问题进行了深入探讨，廓清了理论和实践中存在的模糊认识，有针对性地提出了防范诉讼风险的有效对策。     

经济下行、PPP风险来源与机制设计

自金融危机之后,PPP模式在全球范围内遭到了广泛的质疑,曾经被视为发展公共基础设施建设重要手段的PPP模式沦为各国地方政府沉重的财政负担.为此,我们通过分析经济下行情境下PPP模式在欧盟国家的风险来源,研究了中国现行PPP模式机制设计中的风险识别与分配机制.结果 显示,现阶段物有所值定性评价、地方财政压力测算与风险分配框架受到地方政府强大内生性需求的影响,在经济下行情境中一部分潜在的风险就很容易被忽视:(1)物有所值定性评价结果高度一致,政府官员背景评审专家影响了最终评价结果;(2)地方财政承受能力论证测算以经济繁荣时期的财政增长率为基准,低估了经济下行情境中PPP项目财政支出对于财政预算的压力;(3)风险分配框架不合理,倾向于由政府与社会资本共同承担,将前期风险识别与谈判成本转嫁到了后期再协商阶段.上述发现有助于揭示我国PPP模式推广过程中的机制缺陷,为提高PPP项目抵御未来不确定性的能力,进一步规范中国PPP模式在公共基础设施领域中的应用提供了指引.     

行业趋同度、投资者情绪与股市下跌风险

行业趋同度及投资者情绪可以反映市场交易热度.用格兰杰因果网络计算市场的行业趋同度,指数换手率、波动率及BEYR代表投资者情绪,研究这些指标对指数收益及股市下跌风险的影响发现:4个指标对指数收益的预测能力并不稳健,但是对股市下跌风险却有显著的预测能力;用4个指标构造合成因子,发现合成因子对股市下跌风险的预测能力更为显著;利用合成因子进行择时,可以有效避免市场极端的下跌行情,因子择时策略的夏普比率达到0.53,远超指数买入持有策略的0.14.综合来看,行业趋同度及投资者情绪代表的交易热度能够对股市下跌风险提前预警,从而带来投资收益的显著提高.     

过度自信、风险厌恶与我国上市公司经理薪酬激励

经理风险厌恶会增加股东使用业绩薪酬激励的成本,然而通过对我国上市公司高管的经验研究发现,如果经理过度自信,则会减弱风险厌恶带来的负面影响,表现为其薪酬中的报酬业绩敏感度更高,且其与风险之间的负相关关系减弱。同时研究还发现,非系统风险所占总风险比重较大的公司,相比系统风险所占比重较大的公司,会给予过度自信的高管更高的报酬业绩敏感度,这意味着高管的过度自信主要源于其对公司非系统风险认知的偏差。     

Relative Risk Aversion as an Arc Elasticity

Risk aversion is the central reason why individuals purchase insurance and undertake other forms of risk management. But deriving the Pratt–Arrow coefficient of relative risk aversion from a utility function requires familiarity with differential calculus—a level of mathematics beyond the prerequisites for most introductory risk management courses. Thus, students are not exposed to one of the most important and fundamental concepts in the field unless and until they take more advanced courses. The present article demonstrates that relative risk aversion can be obtained as an arc elasticity using only elementary mathematics. This approach highlights the relationship between risk aversion and the demand for insurance, and integrates concepts from the principles of economics course, helping to unify the business curriculum. Numerical examples are easily computed and graphed using electronic spreadsheets, providing students with a hands-on learning experience. For sufficiently small risks, the arc elasticity measure reduces to the Pratt–Arrow coefficient, providing a platform for discussing the difference between large-scale and small-scale risk aversion in upper-level courses.     

Implied Risk Aversion Parameter from Option Prices

This paper estimates the representative investor's coefficient of relative risk aversion using option price data. Estimation is carried out using the method of simulated moments. Employing the following assumptions: a) agents have constant proportional risk averse preferences, b) complete markets exist, and c) asset returns are distributed lognormally, an objective function is constructed within the equivalent martingale measure framework. Unlike the case of equity markets, the implied risk aversion parameter from option prices is quite low and stays between zero and one.