Risk aversion for variational and multiple-prior preferences

The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents’ choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.     

Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors

Using the measure of risk aversion suggested by Kihlstrom and Mirman [Kihlstrom, R., Mirman, L., 1974. Risk aversion with many commodities. Journal of Economic Theory 8, 361–388; Kihlstrom, R., Mirman, L., 1981. Constant, increasing and decreasing risk aversion with many commodities. Review of Economic Studies 48, 271–280], we propose a dynamic consumption-savings–portfolio choice model in which the consumer-investor maximizes the expected value of a non-additively separable utility function of current and future consumption. Preferences for consumption streams are CES and the elasticity of substitution can be chosen independently of the risk aversion measure. The additively separable case is a special case. Because choices are not dynamically consistent, we follow the “consistent planning” approach of Strotz [Strotz, R., 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies 23, 165–180] and also interpret our analysis from the game theoretic perspective taken by Peleg and Yaari [Peleg, B., Yaari, M., 1973. On the existence of a consistent course of action when tastes are changing. Review of Economic Studies 40, 391–401]. The equilibrium of the Lucas asset pricing model with i.i.d. consumption growth is obtained and the equity premium is shown to depend on the elasticity of substitution as well as the risk aversion measure. The nature of the dependence is examined. Our results are contrasted with those of the non-expected utility recursive approach of Epstein–Zin and Weil.     

Can baby-boomers’ retirement increase stock prices?

In a dynamic asset-pricing model with Hyperbolic Absolute Risk Aversion preferences, investors who have Decreasing Relative Risk Aversion have an age dependent component in their optimal asset allocation rule. Unlike conventional models, this component affects equilibrium equity returns due to demographic trends in the same direction suggested by (Poterba, J. M. (2001). Demographic Structure and Asset Returns.The Review of Economics and Statistics, 83 (4) 565–584; Poterba, J. M. (2004). The Impact of Population Aging on Financial Markets, NBER Working Paper No. 10851). Calibration to US data between 1950 and 2050 reveals that between 1950 and 1970 this effect potentially added 0.15% to the 7.79% post-war long-term return (actual was 8.39%). As boomers joined the labor market (1970–2004) this positive effect turned negative (0.17–0.34%). Ignoring consumption and wealth effects, the model implies that this effect will draw 0.06% annually between 2005 and 2015 but add 0.22% between 2016 and 2050.     

‘Stochastically more risk averse:’ A contextual theory of stochastic discrete choice under risk

Microeconometric treatments of discrete choice under risk are typically homoscedastic latent variable models. Specifically, choice probabilities are given by preference functional differences (given by expected utility, rank-dependent utility, etc.) embedded in cumulative distribution functions. This approach has a problem: Estimated utility function parameters meant to represent agents’ degree of risk aversion in the sense of Pratt (1964) do not imply a suggested “stochastically more risk averse” relation within such models. A new heteroscedastic model called “contextual utility” remedies this, and estimates in one data set suggest it explains (and especially predicts) as well as or better than other stochastic models.     

Rational plunging and the option value of sequential investment: The case of petroleum exploration

The potential to invest sequentially in related assets creates a tradeoff between diversification and concentration. Loading a portfolio with correlated assets has the potential to inflate variance, but also creates information spillovers and real options that may augment total return and mitigate variance. We examine this tradeoff in the context of petroleum exploration. Using a simple model of geological dependence, we show that the value of learning options creates incentives for investors to plunge into dependence; i.e., to assemble portfolios of highly correlated exploration prospects. Risk-neutral and risk-averse investors are distinguished not by the plunging phenomenon, but by the threshold level of dependence that triggers such behavior. Aversion to risk does not imply aversion to dependence. Indeed the potential to plunge should be larger for risk-averse investors than for risk-neutral investors. We test the empirical validity of our theory by examining bidding activity in petroleum lease sales. We find significant plunging behavior across a broad sample of oil companies. We also find that privately-held firms pursue even more concentrated (less diversified) prospect portfolios than publicly-held firms—which we attribute to risk aversion rather than size.     

Risk aversion in a model of endogenous growth

Despite the evidence on incomplete financial markets and substantial risk being borne by innovators, current models of growth through creative destruction predominantly model innovators’ as risk neutral. Risk aversion is expected to reduce the incentive to innovate and we might fear that without insurance innovation completely disappears in the long run. The present paper introduces risk averse agents into an occupational choice model of endogenous growth in which insurance against failure to innovate is not available. We derive a clear negative relationship between the level of risk aversion and long run growth. Surprisingly, we show that in an equilibrium there exists a cut-off value of risk aversion below which the growth rate of the mass of innovators tends to a strictly positive constant. In this case, innovation persists on the long run and consumption per capita grows at a strictly positive rate. On the other hand, for levels of risk aversion above the cut-off value, the economy eventually stagnates.     

Estimation of market power in the presence of firm level inefficiencies

“The quiet life hypothesis” (QLH) by Hicks (1935) argues that, due to management’s subjective cost of reaching optimal profits, firms use their market power to allow inefficient allocation of resources. Increasing competitive pressure is therefore likely to force management to work harder to reach optimal profits. Another hypothesis, which also relates market power to efficiency is “the efficient structure hypothesis” (ESH) by Demsetz (1973). ESH argues that firms with superior efficiencies or technologies have lower costs and therefore higher profits. These firms are assumed to gain larger market shares which lead to higher concentration. Ignoring the efficiency levels of the firms in a market power model might cause both estimation and interpretation problems. Unfortunately, the literature on market power measurement largely ignores this relationship. In the context of a dynamic setting, we estimate the market power of US airlines in two city-pairs by both allowing inefficiencies of the firms and not allowing inefficiencies of the firms. Using industry level cost data, we estimate the cost function parameters and time-varying efficiencies. An instrumental variables version of the square root Kalman filter is used to estimate time-varying conduct parameters.     

A preference foundation for constant loss aversion

Following prospect theory and in particular the concept of loss aversion, introduced by Kahneman and Tversky (1979), we consider decision making under risk in which the decision maker’s preferences depend on a reference outcome. An outcome below this reference outcome is regarded as resulting from a loss: a loss decreases the decision maker’s basic utility more than a comparable gain increases this utility. An elegant and simple way to model this phenomenon was proposed by Shalev (2002): the utility of an outcome below the reference outcome is obtained from the basic utility by subtracting a multiple of the loss in basic utility: this multiple, the loss aversion coefficient, is constant across different reference outcomes. We provide a preference foundation for this loss aversion model.     

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.     

Robust firm pricing with panel data

Firms often have imperfect information about demand for their products. We develop an integrated econometric and theoretical framework to model firm demand assessment and subsequent pricing decisions with limited information. We introduce a panel data discrete choice model whose realistic assumptions about consumer behavior deliver partially identified preferences and thus generate ambiguity in the firm pricing problem. We use the minimax-regret criterion as a decision-making rule for firms facing this ambiguity. We illustrate the framework’s benefits relative to the most common discrete choice analysis approach through simulations and empirical examples with field data.     

Uncertain dynamics,correlation effects,and robust investment decisions

We analyze a firm׳s investment problem when the dynamics of project value and investment cost are uncertain. We provide an explicit solution using a robust method for an ambiguity averse firm taking this into account. Ambiguity aversion regarding a common risk factor impacts differently than ambiguity aversion regarding investment cost residual risk. Correlation between project value and investment cost matters; ambiguity aversion regarding common risk can decrease the investment probability only if correlation is positive. Ambiguity aversion regarding residual risk always increases the investment probability. When only project value is risky, volatility can monotonically decrease the investment threshold; this does not hold with the multiple prior method.     

Risk aversion and business cycles: An empirical analysis

Unlike investors, who tend to maintain highly-diversified portfolios, private entrepreneurs usually lack access to complete risk-pooling for idiosyncratic risks, thus more directly internalize the cost of volatility. Risk aversion, however, modifies the optimal contract between entrepreneurs and lenders by incorporating the risk premium that entrepreneurs demand for the uninsurable risk: the private equity premium. Consequently, real shocks tend to be amplified as changes in entrepreneurs’ net worth affect the private equity premium and so the rental rate of capital, investment and output. This theoretical framework suggests that economies where the private entrepreneurial sector is a relatively larger, and therefore more vulnerable to uninsurable risk, all else equal, should present higher volatility. I test this prediction by (1) conducting a simple reduced-form analysis that shows that output volatility is negatively associated with the relative importance of the corporate vs. the privately-held sector; and (2) estimating the model's structural parameters. Intuitively, countries where private entrepreneurs are predominant and so risk aversion is likely to impose stronger impacts, positive risk aversion coefficients should be found. Results suggest that risk aversion is empirically more relevant for economies like Argentina, Brazil, Chile, Korea, Mexico and Thailand than for Canada, France, Germany, the U.K. and the U.S.     

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].     

Are CEOs expected utility maximizers?

Are individuals expected utility maximizers? This question represents much more than academic curiosity. In a normative sense, at stake are the fundamental underpinnings of the bulk of the last half-century’s models of choice under uncertainty. From a positive perspective, the ubiquitous use of benefit-cost analysis across government agencies renders the expected utility maximization paradigm literally the only game in town. In this study, we advance the literature by exploring CEO’s preferences over small probability, high loss lotteries. Using undergraduate students as our experimental control group, we find that both our CEO and student subject pools exhibit frequent and large departures from expected utility theory. In addition, as the extreme payoffs become more likely CEOs exhibit greater aversion to risk. Our results suggest that use of the expected utility paradigm in decision making substantially underestimates society’s willingness to pay to reduce risk in small probability, high loss events.     

基于风险规避的供应链弹性塑造

本文试图从弹性管理的思想中找到一条规避供应链风险的途径,并且通过对供应链弹性的分析,分别从弹性生产,在供应链设计时"预嵌"弹性,提高供应链敏捷性,构建环境弹性等四个方面进行基于风险规避的供应链弹性的塑造。     

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.     

Demand and supply estimation biases due to omission of durability

We build a dynamic equilibrium model of a durable goods oligopoly with a competitive secondary market to evaluate the bias in estimating the structural parameters of demand and supply when durability is omitted. We simulate data from our dynamic model and use them to estimate the model’s static counterpart. We find that the static estimate of the elasticity of demand is an overestimate of the true elasticity and that the static estimate of the markup is an underestimate. Our results provide a benchmark on the magnitude and sign of the bias when static models are used for economic inference.     

CEO贫困出身、薪酬激励与企业风险承担

本文利用2007—2017年沪深A股上市公司数据,考察CEO的贫困出身对企业风险承担的影响,并基于薪酬异质性和薪酬公平性两个维度进一步探究薪酬激励在其中的调节作用,研究发现：（1）CEO的贫困出身显著抑制企业风险承担,表现出风险规避型性格特征;（2）将薪酬激励细化为股权激励和货币薪酬,非国有企业中,股权激励显著提高贫困出身CEO的风险承担意愿,而高额的货币薪酬则显著加剧贫困出身CEO的风险规避倾向,但国有企业贫困出身CEO的风险承担意愿与薪酬激励不存在显著相关关系;（3）基于薪酬公平性视角,非国有企业中,贫困出身CEO的薪酬总额低于行业平均水平越多,其风险承担意愿提升越显著,但若其薪酬总额高于行业平均越多,则会显著加剧其风险规避倾向,并且这种效应不存在于国有企业样本中。上述结论在考虑内生性影响后依然稳健。     

Probabilistic forecasts of volatility and its risk premia

The object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non-linear state space approach. Option and spot market information on the latent variance process is captured by using dual ‘model-free’ variance measures to define a bivariate observation equation in the state space model. The premium for variance diffusive risk is defined as linear in the latent variance (in the usual fashion) whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process, driven by a function of past measurements. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and for the bivariate measure. The method is applied to spot and option price data on the S&P500 index from 1999 to 2008, with conclusions drawn about investors’ required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by alternative methods. To illustrate the benefits of the approach, it is used to produce forecasts of prices of derivatives on volatility itself. In addition, the posterior distribution is augmented by information on daily returns to produce value at risk predictions. Linking the variance risk premia to the risk aversion parameter in a representative agent model, probabilistic forecasts of (approximate) relative risk aversion are also produced.     

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.