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on Utility Models and Prospect Theory |
| By: | Drichoutis, Andreas; Lusk, Jayson |
| Abstract: | In this paper we show that the wildly popular Holt and Laury (2002) risk preference elicitation method confounds estimates of the curvature of the utility function, the traditional notion of risk preference, with an estimate of the extent to which an individual weights probabilities non-linearly. We show that a slight modification to their approach can remove the confound while preserving the simplicity of the method which has made it so popular. Data from a laboratory experiment shows that our new method yields significantly different levels of implied risk aversion than the Holt and Laury task even after econometrically controlling for probability weighting in the latter. Implied risk aversion from the traditional Holt and Laury task is relatively insensitive to payout amount, but our new method reveals increasing relative risk aversion and risk neutrality at low payout amounts. |
| Keywords: | expected utility theory, experiment, probability weighting, rank dependent utility, risk |
| JEL: | D81 C91 |
| Date: | 2012–03–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:37762&r=upt |
| By: | Uzi Segal (Boston College) |
| Abstract: | Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. We show that when the choice set consists of pairwise statistically independent lotteries, transitive regret-based behavior is consistent with betweenness preferences and with a family of preferences that is characterized by a consistency property. Examples of consistent preferences include CARA, CRRA, and anticipated utility. |
| Keywords: | Regret, transitivity, non-expected utility |
| Date: | 2012–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:796&r=upt |
| By: | Pierre Chaigneau |
| Abstract: | It is established that the standard principal-agent model cannot explain the structure of commonly used CEO compensation contracts if CRRA preferences are postulated. However, we demonstrate that this model has potentially a high explanatory power with preferences with decreasing relative risk aversion, in the sense that a typical CEO contract is approximately optimal for plausible preference parameters. |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:fmg:fmgdps:dp693&r=upt |
| By: | Hamza Bahaji (DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris IX - Paris Dauphine) |
| Abstract: | This paper examines the incentives from stock options for loss-averse employees subject to probability weighting. Employing the certainty equivalence principle, I built on insights from Cumulative Prospect Theory (CPT) to derive a continuous time model to value options from the perspective of a representative employee. Consistent with a growing body of empirical and experimental studies (Lambert and Larcker, 2001; Hodge et al., 2006), the model predicts that the employee may overestimate the value of his options in-excess of their risk-neutral value. This is nevertheless in stark contrast with a common finding of standard models based on the Expected Utility Theory (EUT) framework that options value to a risk-averse undiversified employee is strictly lower than the value to risk-neutral outside investors. In particular, I proved that loss aversion and probability weighting have countervailing effects on the option subjective value. In addition, for typical setting of preferences parameters around the experimental estimates (Tversky and Kahneman, 1992; Abdellaoui, 2000), and assuming the company is allowed to adjust existing compensation when making new stock option grants, the model predicts that incentives are maximized for strike prices set around the stock price at inception. This finding is consistent with companies' actual compensation practices that standard EUT-based models have difficulties accommodating their existence. The paper also examines the relationship between risk taking incentives and stock options and finds that an executive who is subject to probability weighting may be more prompted than a risk-neutral executive to act in order to increase the firm's assets volatility. |
| Keywords: | Stock options, Cumulative Prospect Theory, Incentives, Subjective value. |
| Date: | 2011–05–13 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00681607&r=upt |
| By: | Kenneth Kasa (Simon Fraser University); |
| Abstract: | This paper studies decision making by agents who value optimism, but are unsure of their environment. As in Brunnermeier and Parker (2005), an agent’s optimism is assumed to be tempered by the decision costs it imposes. As in Hansen and Sargent (2008), an agent’s uncertainty about his environment leads him to formulate ‘robust’ decision rules. It is shown that when combined, these two considerations can lead agents to adhere to the Rational Expectations Hypothesis. Rather than being the outcome of the sophisticated statistical calculations of an impassive expected utility maximizer, Rational Expectations can instead be viewed as a useful approximation in environments where agents struggle to strike a balance between doubt and hope. |
| Keywords: | Rational expectations; robustness |
| JEL: | D81 D84 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:sfu:sfudps:dp12-05&r=upt |
| By: | Emmanouil Mentzakis; Jingjing Zhang |
| Abstract: | This study compares individual preferences across incentives (i.e., hypothetical vs. real incentives) and over time (i.e. elicitation at two different points in time) in a choice experiment involving charitable donating decisions. We provide evidence of hypothetical bias but little evidence of instability of individual giving. There is significant heterogeneity in individual preferences, with real incentives either dampening or pronouncing the observed donating behaviour. Neither hypothetical bias nor instability is observed when we examine the propensity of individuals to make internally consistent decisions over identical choices. |
| Keywords: | Individual preference, hypothetical bias, time inconsistency, discrete choice experiments, charitable donations |
| JEL: | C91 D11 D91 H40 |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:070&r=upt |
| By: | Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University); William A. Masters (Department of Food and Nutrition Policy, Tufts University); Timothy N. Cason (Department of Economics, Krannert School of Management, Purdue University) |
| Abstract: | This study provides a unified theoretical and experimental framework in which to compare three canonical types of competition: winner-take-all contests won by the best performer, winner-take-all lotteries where probability of success is proportional to performance, and proportional-prize contests in which rewards are shared in proportion to performance. We introduce random noise to reflect imperfect information, and collect independent measures of risk aversion, other-regarding preferences, and the utility of winning a contest. The main finding is that efforts are consistently higher with winner-take-all contests. The lottery contests have the same Nash equilibrium as proportional prizes, but induce contestants to choose higher efforts and receive lower, more unequal payoffs. This result may explain why contest designers who seek only to elicit effort offer lump-sum prizes, even though contestants would be better off with proportional rewards. |
| Keywords: | contests, rent-seeking, lotteries, incentives in experiments, risk aversion |
| JEL: | C72 D72 D74 J33 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:12-04&r=upt |
| By: | Pierre Chaigneau |
| Abstract: | We use a comparative approach to study the incentives provided by dierent types of compensation contracts, and their valuation by risk averse managers, in a fairly general setting. We show that concave contracts tend to provide more incentives to risk averse managers, while convex contracts tend to be more valued by prudent managers. Thus, prudence can contribute to explain the prevalence of stock-options in executive compen- sation. We also present a condition on the utility function which enables to compare the structure of optimal contracts associated with dierent risk preferences. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:fmg:fmgdps:dp697&r=upt |
| By: | Moti Michaeli |
| Abstract: | Aumann--Serrano (2008) and Foster--Hart (2009) suggest two new riskiness measures, each of which enables one to elicit a complete and objective ranking of gambles according to their riskiness. Hart (2011) shows that both measures can be obtained by looking at a large set of utility functions and applying "uniform rejection criteria" to rank the gambles in accordance with this set of utilities. We use the same "uniform rejection criteria" to extend these two riskiness measures to the realm of uncertainty and develop complete and objective rankings of sets of gambles, which arise naturally in models of decision making under uncertainty. |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp603&r=upt |
| By: | Daniel L. McFadden; Mogens Fosgerau |
| Abstract: | We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints. |
| JEL: | C25 D11 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17953&r=upt |
| By: | Amnon Schreiber |
| Abstract: | In their seminal works, Arrow (1965) and Pratt (1964) defined two aspects of risk aversion: absolute risk aversion and relative risk aversion. Based on their definitions, we define two aspects of risk: absolute risk and relative risk. We consider situations in which, by making an investment, an agent exchanges a certain amount of wealth w by a random distributed level of wealth W. In such situations, we define absolute risk as the riskiness of a gamble that is distributed as W-w, and relative risk as the riskiness of a security that is distributed as W/w. We measure absolute risk by the Aumann and Serrano (2008) index of riskiness and relative risk by an equivalent index that we develop in this paper. The two concepts of risk do not necessarily agree on which one of two investments is riskier, and hence they capture two different aspects of risk. |
| Date: | 2012–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp597&r=upt |
| By: | Philippe Mueller; Andrea Vedolin; Hao Zhou |
| Abstract: | In the short-run, bond risk premia exhibit pronounced spikes around major economic and financial crises. In contrast, long-term bond risk premia feature cyclical swings. We empirically examine the predictability of the market variance risk premium—a proxy of economic uncertainty—for bond risk premia and we show the strong predictive power for the one month horizon that almost entirely disappears for horizons above one year. The variance risk premium is largely orthogonal to well-established bond return predictors—forward rates, jumps, yield curve factors, and macro variables. We rationalize our empirical findings in an equilibrium model of uncertainty about consumption and inflation which is coupled with recursive preferences. We show that the model can quantitatively explain the levels of bond and variance risk premia as well as the predictive power of the variance risk premium while jointly matching salient features of other asset prices. |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:fmg:fmgdps:dp686&r=upt |
| By: | Philippe Mueller; Andrea Vedolin; Yu-min Yen |
| Abstract: | Using data from 1983 to 2010, we propose a new fear measure for Treasury markets, akin to the VIX for equities, labeled TIV. We show that TIV explains one third of the time variation in fund- ing liquidity and that the spread between the VIX and TIV captures flight to quality. We then construct Treasury bond variance risk premia as the difference between the implied variance and an expected variance estimate using autoregressive models. Bond variance risk premia display pronounced spikes during crisis periods. We show that variance risk premia encompass a broad spectrum of macroeconomic uncertainty. Uncertainty about the nominal and the real side of the economy increase variance risk premia but uncertainty about monetary policy has a strongly neg- ative effect. We document that bond variance risk premia predict excess returns on Treasuries, stocks, corporate bonds and mortgage-backed securities, both in-sample and out-of-sample. Fur- thermore, this predictability is not subsumed by other standard predictors. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:fmg:fmgdps:dp699&r=upt |
| By: | Vladimir Danilov (Central Economics and Mathematics Institute, Russian Academy of Sciences); Gleb Koshevoy (Central Economics and Mathematics Institute, Russian Academy of Sciences); Frank Page (Department of Economics, Indiana University); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange economies, all papers known to us stating conditions for existence of equilibrium with unbounded short sales place conditions on recession cones of agents' preferred sets or, more recently, require compactness of the utility possibilities set. In contrast, in this paper, we place conditions on the preferred sets themselves. Roughly, our condition is that the sum of the weakly preferred sets is a closed set. We demonstrate that our condition implies existence of equilibrium. In addition to our main theorem, we present two theorems showing cases to which our main theorem can we applied. We also relate our condition to the classic condition of Hart (1974). |
| Keywords: | arbitrage, unbounded short sales, asset market models, sum of weakly preferred sets, existence of equilibrium |
| JEL: | D50 D53 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:1203&r=upt |
| By: | Sylvain Barde |
| Abstract: | An information-theoretic thought experiment is developed to clarify why the maximum entropy methodology is appropriate for predicting the equilibrium state of economic systems. As a first step, object allocation problems, modeled as knapsack problems, are shown to be equivalent to congestion games under weak assumptions. This proves the existence of finite improvement paths linking initial conditions and Nash equilibria. The existence of these improvement paths is precisely what enables the use of maximum entropy to make predictions concerning the equilibrium state. Finally an illustration of this predictive power is provided through an application to the Schelling model of segregation. |
| Keywords: | Information entropy; knapsack problem; potential function; Schelling segregation. |
| JEL: | C02 C11 C63 D80 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:1202&r=upt |
| By: | Andersson, Ola (Research Institute of Industrial Economics (IFN)); Argenton, Cédric (CentER & TILEC); Weibull, Jörgen W. (Stockholm School of Economics) |
| Abstract: | In games with continuum strategy sets, we model a player’s uncertainty about another player’s strategy, as an atomless probability distribution over the other player’s strategy set. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles in which every player’s strategy is optimal under his or her uncertainty about the others. General properties of this robustness criterion are derived and it is shown that it is a refinement of Nash equilibrium when payoff functions are continuous. We apply the criterion to a class of Bertrand competition games. These are discontinuous games that admit a continuum of Nash equilibria. Our robustness criterion selects a unique Nash equilibrium, and this selection agrees with recent experimental findings. |
| Keywords: | Nash equilibrium; Refinement; Strategic uncertainty; Bertrand competition; Log-concavity |
| JEL: | C72 D43 L13 |
| Date: | 2012–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:0910&r=upt |
| By: | Masaaki Fukasawa |
| Abstract: | Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization. |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1204.0637&r=upt |