RISK AVERSION,WEALTH, AND BACKGROUND RISK

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks. (JEL: D1, D8)     

基于通货膨胀和风险偏好视角的资产配置研究

不确定条件下的资产配置问题无论对于学术研究还是投资行为都具有重大的理论和实际意义。本文选取广义范围上的现金、股票、债券作为投资者进行资产配置的产品,在CRRA(Constant Relative Risk Aversion)和HARA(Hyperbolic Absolute Risk Aversion)两种偏好假设下,分别求出了投资者效用最大化时的最优财富以及最优资产组合中各资产的权重,并比较分析了两种偏好假设下通货膨胀、风险偏好、投资期限三种因素对资产配置的影响。研究结论表明:通货膨胀会影响股票和债券的风险溢价,进而影响最优资产组合中各资产的权重;股票的权重不会受投资期限的影响,在通货膨胀率和风险偏好不变时,其值始终为一常数,但债券和现金的权重则由投资期限、通货膨胀和风险偏好共同决定;此外,在CRRA和HARA偏好假设下,以上三种因素对资产配置的影响存在较大差异,特别是在HARA框架下存在买空行为。     

RISK AVERSION AND PLANNING HORIZONS

A number of empirical studies seem to reject the additive separability of preferences that is assumed in most theoretical models of the life cycle. We show that, when additive separability is abandoned and interactions between consumptions at different dates are taken into account, an interesting relation emerges between risk aversion and length of the planning horizon. Specifically, we show that when consumptions at different dates are specific substitutes, risk aversion increases with horizon length. This may explain the surprising empirical finding that individuals seem to increase the share of wealth held in risky assets as they become older. (JEL: D11, D91, G11)     

基于信息更新的动态资产组合选择

本文研究了不完全信息下风险资产收益前两阶矩的参数不确定性对动态资产组合选择的影响。首先,在连续时间下假设资产价格服从随机扩散过程,引入参数不确定性,运用随机控制方法推导出风险资产最优选择的封闭解,给出定性分析。其次,在离散时间下用一阶自回归模型描述风险资产收益动态,基于贝叶斯分析框架,以上证综合指数不同区间段的两个样本做实证研究。结果表明,当投资者的风险规避程度大于(小于)对数效用时,参数不确定性将导致负(正)的投资期效应;当投资者在估计过程中运用较多的历史数据、或者风险规避程度增加时,参数不确定性的影响将减弱;参数不确定性下的资产组合选择可解释风险溢价之迷。研究说明了在动态资产组合选择过程中应考虑参数不确定性问题。     

Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis

We derive the analogue of the classic Arrow–Pratt approximation of the certainty equivalent under model uncertainty as described by the smooth model of decision making under ambiguity of Klibanoff, Marinacci, and Mukerji (2005). We study its scope by deriving a tractable mean‐variance model adjusted for ambiguity and solving the corresponding portfolio allocation problem. In the problem with a risk‐free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher ambiguity aversion only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In particular, a positive alpha corresponds to a long position in the ambiguous asset, a negative alpha corresponds to a short position in the ambiguous asset, and greater ambiguity aversion reduces optimal exposure to ambiguity. The analytical tractability of the enhanced Arrow–Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of model uncertainty on equilibrium asset prices.     

考虑损失规避的期望效用投资组合模型

投资者行为的本质特征会影响投资者对不同风险资产的投资决策。本文从期望效用最大化的角度研究不同风险资产的配置问题,并将人的心理活动引入了投资组合模型之中。论文借鉴了损失规避这个重要的概念,将投资者的效用函数表示为期末财富和财富变化的函数;建立了基于损失规避的最优投资组合模型;并对我国上海股票市场进行了实证分析,得到了在财富变化的不同关心程度下的组合前沿。     

Robust portfolio planning in the presence of market anomalies

In this study, a short-term portfolio modeling formulation is developed using existing anomalies as a single determinant for daily Istanbul Stock Exchange National 100 Composite Index (ISE) and US dollars (USD) returns in a Robust optimization (RO) framework. Using anomalies in planning within an RO framework establishes a balance between risk seeking and risk averse behaviors, as generating profit from anomalies is risky and RO enables to settle down the extreme risk seeking behavior. Applications of the model using various data sets result in real profit generation such that terminal wealth figures increase considerably more than Wholesale Price Index (WPI). This study demonstrates that RO is a viable approach to make use of anomaly information for short-term profits.     

Predicting Cancer‐Prevention Behavior: Disentangling the Effects of Risk Aversion and Risk Perceptions

Experimental and survey research spanning the last two decades concludes that people who are more risk tolerant are more likely to engage in risky health activities such as smoking and heavy alcohol consumption, and are more likely to be obese. Subjective perceptions of the risk associated with different activities have also been found to be associated with health behaviors. While there are numerous studies that link risk perceptions with risky behavior, it is notable that none of these controls for risk aversion. Similarly, studies that control for risk aversion fail to control for risk misperceptions. We use a survey of 474 men and women to investigate the influence of risk aversion, risk misperceptions, and cognitive ability on the choice to engage in behaviors that either increase or mitigate cancer risk. We measure optimism in two dimensions: baseline optimists are those who inaccurately believe their cancer risk to be below its expert‐assessed level, while control optimists are those who believe they can reduce their risk of cancer (by changing their lifestyle choices) to a greater extent than is actually the case. Our results indicate that baseline optimism is significantly and negatively correlated with subjects′ tendencies to engage in cancer‐risk‐reducing behaviors, and positively correlated with risky behaviors. Subjects’ control misperceptions also appear to play a role in their tendency to engage in risky and prevention behaviors. When controlling for both of these types of risk misperception, risk aversion plays a much smaller role in determining health behaviors than found in past studies.     

参数不确定性和效用最大化下的动态投资组合选择

标准投资组合选择理论假设投资者准确地知道与资产收益率相关的各种参数(例如均值和方差),忽视了参数不确定性引致的估计风险给投资决策带来的影响.本文研究引入参数不确定和学习时的连续时间动态投资组合选择问题,使用鞅方法求导出了具有CRRA型效用函数的投资者的最优投资策略的显式表达式.在此基础上,我们结合中国证券市场中的实际数据深入分析了参数不确定性以及投资者初始信念对最优投资策略的影响.     

WHO IS ‘BEHAVIORAL’? COGNITIVE ABILITY AND ANOMALOUS PREFERENCES

In this paper, we ask whether variation in preference anomalies is related to variation in cognitive ability. Evidence from a new laboratory study of Chilean high‐school students with similar schooling backgrounds shows that small‐stakes risk aversion and short‐run discounting are less common among those with higher standardized test scores. The relationship with test scores survives controls for parental education and wealth. We find some evidence that elementary‐school GPA is predictive of preferences measured at the end of high school. Two laboratory interventions provide suggestive evidence of a possible causal impact of cognitive resources on expressed preferences.     

Heston模型下DC型养老金等价管理费用问题研究

本文针对DC型养老金收费管理问题展开了系统研究,假定风险资产服从Heston模型,养老金管理者按资产财富比例和工资比例两种方式收取管理费用,试图在这两种方式中找到一个平衡点（等价管理费用）。运用随机最优控制理论得到了CARA和CRRA两种效用准则下等价管理费用的解析表达,从表达式中发现等价管理费用只与无风险利率、积累时间以及按工资比例收费的代表参数有关,而积累时间与参保人年龄有很强的相关性。最后,通过数值算例分析了参保人年龄对等价管理费用的影响以及等价管理费用对财富过程的影响,研究结果显示：在CARA效用下,等价管理费用随参保人年龄严格递增,而在CRRA效用下相反;无论在CARA效用还是CRRA效用下,等价管理费用对养老金账户财富都有正负两方面的影响。     

Workers’ Risk Tolerance and Occupational Injuries

This study explores the relationship between individuals’ risk tolerance and occupational injuries. We analyze data from a national representative survey of U.S. workers that includes information about injuries, risk tolerance, cognitive and noncognitive attributes, and risky behaviors. We measure risk tolerance through questions regarding individuals’ willingness to gamble on their lifetime income. We estimate zero‐inflated count models to assess the role played by such measures on workers’ recurrent injuries. We discuss some implications of our results for future research and occupational safety policies. Our results highlight the concurrent and changing role played by individual, work, and environmental factors in explaining recurrent incidents. They show that risk tolerance affects recurrent injuries, although not in the direction that proponents of the concept of proneness would expect. Our measure of risk aversion shows that individuals who are somewhat more risk tolerant have fewer recurrent injuries than those who are risk averse. But the estimated relationship is U‐shaped, not monotonic and, therefore, not easy to predict. At the same time, we find that individuals’ “revealed risk preferences”—specific risky behaviors—are related to higher injury probabilities. Demanding working conditions, measures of socioeconomic status, health, and safety problems experienced by workers during their youth remain among the most important factors explaining the phenomena of recurrent injuries. So our results contribute also to the important debate about the relationship between health and socioeconomic status.     

动态均值-方差资产组合的有效性:时变风险容忍度视角

尽管均值-方差模型在静态资产组合优化过程中得到广泛运用并证明是有效的,但在动态情景下,均值-方差模型运用于动态资产组合优化过程中的有效性问题引起人们的质疑：一是常风险规避系数的设定不符合事实;二是投资者偏好设定不符合动态情景下的主流效用函数族。鉴于此,本文假设投资者风险容忍度是资产组合投资期与投资者期望收益率的函数,研究动态均值-方差资产组合的有效性问题。基于均值-方差分析框架构建时变风险容忍度下的动态资产组合模型;运用伊藤定理和拉格朗日乘子法获得最优资产组合封闭解;基于二次效用偏好下的动态资产组合,从资产组合策略、夏普率、确定性等价收益率和有效前沿等视角验证动态均值-方差资产组合策略和业绩,并予以实证。结果表明：动态均值-方差资产组合不但具有同等业绩而且体现了其灵活性和风险对冲价值;尽管动态均值-方差资产组合表现出高杠杆性,但其确定性等价收益率较高,且随投资期的增加呈现倒U型趋势;动态均值-方差资产组合的投资期效应显著,强于投资者期望收益率。研究指出,时变风险容忍度下的动态均值-方差资产组合管理和优化策略有效,但在短投资期（低于12个月）和（或）低期望收益率下并不适用。研究不但拓展了均值-方差模型在动态情境下的应用,而且体现了投资者源于心理和（或）其财富变化的投资行为调整。     

模型不确定性条件下的Robust投资组合有效前沿与CAPM

本文提出了Robust投资组合有效前沿的概念,并研究了模型不确定性条件下的资本资产定价模型(CAPM)。研究发现,当市场上不存在无风险资产时,模型不确定性对风险资产投资比例的影响是非平等的,因此会导致投资组合的非分散化;而且此时的两基金分离定理以及零-βCAPM也不成立。但是当市场上存在无风险资产时,模型不确定性对风险资产投资比例的影响则是平等的,并且两基金分离定理仍然成立,因为任何Robust有效前沿组合都可以表示为市场组合与无风险资产的线性组合。而此时的CPAM仍然能够成立,只是在表达形式上增添了一个因子--不确定性因子;并且所有资产或资产组合的超额收益都可以分解为风险溢价与不确定性溢价两部分。     

时变损失厌恶下基于动态CVaR的ETF基金最优资产配置策略研究

首先对静态线性损失厌恶下的最优资产配置策略模型及其性质进行了分析,构建了基于TGARCH-EVT-POT-GPD的动态市场风险测度方法,提出了时变损失厌恶条件下基于动态条件风险约束的ETF基金最优资产配置策略模型,并基于遗传算法进行了求解。实证研究发现：当参考收益率及CVaR置信水平固定时,随着损失厌恶系数的增大,投资者采用大幅调整资产权重的方式来获得盈利的行为将逐渐减少;当参考收益率及损失厌恶系数固定且CVaR置信水平变化条件下,置信水平越高,损失厌恶投资者更偏好风险较低的资产,其对于投资风险的估计将更加敏感,投资策略更为保守;损失厌恶系数较高置信水平固定时,随着参考收益率的增加,单项资产的CVaR逐渐减小;在置信水平较高时,随着损失厌恶系数的增加,即使参考收益率增加,但投资组合的超额损失平均水平降低。     

基于幂风险谱和蒙特卡洛模拟的贷款优化配置模型

极端风险对于银行资产配置至关重要,尤其是次贷危机之后尾部风险以惨重的代价引起了金融机构的重视,传统条件风险价值CVaR、风险价值VaR不能有效度量尾部极端风险,因此本文基于幂风险谱和蒙特卡洛模拟构建了贷款组合优化配置模型,同时控制尾部极端风险和信用风险。本文一是通过损失-X_i越大、其风险权重φ_i也就越大的思路,构建幂风险谱PSR （Power Spectral Risk）最小的目标函数对极端风险进行控制,即弥补了CVaR同等看待尾部风险、忽略风险较大的损失应予以更大权重的不足,也同时弥补了VaR仅提供某一置信水平下资产损失的最大值、无法反映一旦超过这一数值的可能损失的弊端。二是通过蒙特卡洛模拟信用等级迁移引起贷款收益的变化情景,并以信用等级迁移后贷款组合损失越大、则风险厌恶权重越大的思路构建幂风险谱PSR最小为目标函数,以贷款组合的收益大于目标收益为约束,构建贷款优化配置模型,改变了现有研究贷款配置时没有同时控制信用风险和尾部风险的不足。对比分析结果表明：本文模型能够实现更高的收益风险比,即在单位幂风险谱PSR下能够实现较高的收益。     

通胀对高管的股权激励和工作努力策略的影响

股权激励能够使得公司与高管的共同利益最大化,并且解决由于信息不对称所产生的委托代理问题。高管不可观测的工作控制着公司股票价格。由于高管的真实财富受到市场通胀不确定性的影响,本文研究了通胀环境下,以风险厌恶和工作努力效率为特质的高管,在银行无风险资产账户、市场投资组合和公司股票间寻求最优配置以达到个人终端真实财富预期效用最大化。首先利用伊藤公式得到了高管的真实财富过程;其次利用动态规划原理构建了满足最优工作努力策略和股权激励问题的哈密尔顿-雅可比-贝尔曼（HJB）方程,并找到了解析解;最后对结果进行了数值模拟,并从经济学的角度分析了通胀风险对高管的股权激励和工作努力策略的影响。本文研究表明：由于通胀不确定性影响着高管财富的实际价值,当高管财富效用服从对数函数时,公司股票占高管个人财富的最优比例不受通胀风险影响,但是高管在市场投资组合的投资比例随通胀波动率的增加而下降,进而影响到高管对市场投资组合账户和银行无风险资产账户的投资比例。高管的财富效用服从幂函数时,对于长期契约,股权激励代表的长远共同利益引导着高管看好公司的发展前景,激励着高管付出更高水平的努力,此时通胀带来的货币贬值风险对高管的的影响较小;而对于短期契约,长远共同利益的缺乏和通胀风险的变大诱导着高管的短视行为,高管将减持公司股票并且减少努力。本文所得结论对公司的股权激励理论做了有益的补充。     

RISK AVERSION AND EXPECTED UTILITY THEORY: AN EXPERIMENT WITH LARGE AND SMALL STAKES

We employ a novel data set to estimate a structural econometric model of the decisions under risk of players in a game show where lotteries present payoffs in excess of half a million dollars. The decisions under risk of players in the presence of large payoffs allow us to estimate the parameters of the curvature of the von Neumann–Morgenstern utility function—not only locally, as in previous studies in the literature, but also globally. Our estimates of relative risk aversion indicate that a constant relative risk aversion parameter of about 1 captures the average of the sample population. We also find that individuals are practically risk neutral at small stakes and risk averse at large stakes—a necessary condition, according to Rabin’s calibration theorem, for expected utility to provide a unified account of individuals’ attitudes toward risk. Finally, we show that for lotteries characterized by substantial stakes, nonexpected utility theories fit the data equally as well as expected utility theory.     

Peer Effects in Risk Aversion

We estimate peer effects in risk attitudes in a sample of high school students. Relative risk aversion is elicited from surveys administered at school. Identification of peer effects is based on parents not being able to choose the class within the school of their choice, and on the use of instrumental variables conditional on school‐grade fixed effects. We find a significant and quantitatively large impact of peers’ risk attitudes on a male individual's coefficient of risk aversion. Specifically, a one standard deviation increase in the group's coefficient of risk aversion increases an individual's risk aversion by 43%. Our findings shed light on the origin and stability of risk attitudes and, more generally, on the determinants of economic preferences.     

稳健的动态资产组合模型研究

事件风险与参数的不确定性对金融决策有重大的影响,投资者担心股市上极端金融事件的出现,突然改变股票价格和波动率,造成较大的损失.通过引入风险规避的稳健投资者以及模型设定可能存在误差,投资者在最小化模型设定误差的前提下,制定风险资产收益跳跃情况下的动态资产组合战略,最大化投资者的效用.结果表明,当投资者是风险规避和不确定性规避者时,稳健的投资准则会显著降低他们对风险资产的需求.