A dual theory approach to estimating risk preferences in the parimutuel betting market

This paper introduces an alternative empirical approach to estimating risk preferences in the parimutuel betting market using a dual theory model which is amended to include bettors’ misperceptions of probabilities. We replicate previous empirical results and test our alternative empirical approach using parimutuel horse race betting data. Our results suggest that while bettors are risk-averse, they are also prone to misperceiving probabilities by overweighting low probabilities and underweighting high probabilities. As an application, these results replicate the choice patterns consistent with the Allais paradox.     

On the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences

This paper establishes the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences. It shows that the prerequisite for comparability of risk aversion in the multivariate case, namely, identical ordinal preferences on the commodity space, corresponds to identical, properly defined, reference sets in the case of state-dependent preferences. For comparable decision makers the condition that the utility function of one is a concave transformation of that of the other on the commodity space corresponds to the condition that the expected utility of one is a concave transformation of that of the other on the reference set.     

A note on risk aversion and multivariate,state-dependent preferences

Within the multivariate, state-dependent utility framework, a full insurance specification of risk aversion places severe restrictions on preferences. In particular, the von Neumann-Morgenstern utility function must be separable, and state-dependent only for consumption of the insured good.     

Real estate and relative risk aversion with generalized recursive preferences

This paper investigates how real estate wealth affects the household’s attitude toward risk, and derives the closed-form expressions for risk aversion with generalized recursive preferences. We find three channels through which real estate wealth affects risk aversion, and these channels are absent in the traditional measure of relative risk aversion as in Arrow (1965) and Pratt (1964). First, illiquidity and fluctuations in real estate value increase consumption risk, thereby increasing risk aversion. Second, real estate as an asset provides a cushion for absorbing negative shocks to households, reducing risk aversion. Third, an increase in real estate prices lowers the profit of the firm that uses real estate as a factor of production, induces a decline in the real wage, and causes a rise in consumption risk. This channel increases risk aversion. We study how these channels as a whole determine relative risk aversion using a basic real business cycle model with generalized recursive preferences and compare the results with the case of expected utility preferences. Finally, we explore the implications of the firm’s and the household’s real estate holdings and illiquidity of real estate on the risk premiums for equity and real estate.     

Jointly radial and translation homothetic preferences: generalized constant risk aversion

Summary. The paper identifies the structural restrictions on preferences required for them to exhibit both translation homotheticity in particular direction and radial homotheticity. The results are illustrated by an application to an asset allocation problem in the absence of riskless asset.Received: 22 January 2002, Revised: 31 March 2003, JEL Classification Numbers: D8, D2. Correspondence to: Robert G. Chambers     

Inequality aversion and risk aversion

This note shows that for two social welfare functions which are inequality averse with respect to certainty equivalents, if one is more inequality averse for certainty equivalents than the other, the household preference induced by optimally allocating aggregate bundles according to this social welfare function is more risk averse than the other. We present examples showing that this comparative static can be reversed if absolute inequality aversion is dropped. We show that the utilitarian rule always induces the least risk averse household preference among all social welfare functions (this corresponds to the sum of certainty equivalents).     

Social preferences and lying aversion in children

While previous research has shown that social preferences develop in childhood, we study whether this development is accompanied by reduced use of deception when lies would harm others, and increased use of deception to benefit others. In a sample of children aged between 7 and 14, we find strong aversion to lying at all ages. Lying is driven mainly by selfish motives and envy. Children with stronger social preferences are less prone to deception, even when lying would benefit others at no monetary cost. Older children lie less than younger children and use self-justification to lie.     

State-uncertainty preferences and the risk premium in the exchange rate market

This paper shows that state-uncertainty preferences help to explain the observed exchange rate risk premium. In the framework of Lucas (1982) economy, state-uncertainty preferences amount to assuming that a given level of consumption will yield a higher level of utility the lower is the level of uncertainty perceived by consumers. Under these preferences we can distinguish between two factors driving the exchange rate risk premium: “macroeconomic risk” and “the risk associated with variation in the private agents' perception on the level of uncertainty”. Empirical evidence from three main European economies in the transition period to the euro provides empirical support for the model. The model is more successful in accounting for the observed currency risk premium than models with more standard preferences, and the general perception of risk by private agents is shown to be a more important determinant of risk premium than macroeconomic uncertainty.     

Momentum and betting market perceptions of momentum in college football

Past research has demonstrated that bettors believe positive momentum carries over from contest to contest. This article examines whether there is any empirical support for this belief by testing for the presence of across-contest momentum effects in college football. We characterize momentum in multiple fashions and after controlling for between-team heterogeneity find no evidence that systematic relationships exist between the degree of momentum a team enters a contest with and the outcome of that contest. From a wagering market perspective, this indicates that there is no statistically significant advantage to betting on teams perceived to possess positive momentum. Our results also suggest that the combination of the opening betting line set by odds makers and the subsequent market movement of that line does not systematically overreact to teams on streaks.     

Loss aversion and market crashes

This study proposes a rational expectation equilibrium model of stock market crashes with information asymmetry and loss averse speculators. We obtain a state-dependent linear optimal trading strategy, which makes the equilibrium price tractable. The model predicts nonlinear market depth and the result that small shocks to fundamentals (e.g., supply or informational shocks) can cause abrupt price movements. We demonstrate that short-sale constraints intensify asset price collapses relative to upward movements. The model also generates contagion between uncorrelated assets. These results are consistent with the main puzzling features observed during market crashes, namely abrupt and asymmetric price movements that are not driven by major news events but coupled with a spillover effect between unrelated markets.     

Mean-dispersion preferences and constant absolute uncertainty aversion

We axiomatize, in an Anscombe–Aumann framework, the class of preferences that admit a representation of the form V(f)=μ−ρ(d)$V(f)=\mu -\rho (d)$, where μ is the mean utility of the act f with respect to a given probability, d   is the vector of state-by-state utility deviations from the mean, and ρ(d)$\rho (d)$ is a measure of (aversion to) dispersion that corresponds to an uncertainty premium. The key feature of these mean-dispersion   preferences is that they exhibit constant absolute uncertainty aversion. This class includes many well-known models of preferences from the literature on ambiguity. We show what properties of the dispersion function ρ(⋅)$\rho (\cdot )$ correspond to known models, to probabilistic sophistication, and to some new notions of uncertainty aversion.     

Information and efficiency: an empirical study of a fixed odds betting market

The efficiency of the fixed odds betting market for football in England is investigated. It is the efficiency of how market participants utilize available information that is tested. A model of bookmaker behaviour is presented in which the bookmaker maximizes their expected share of the total amount bet. It is found that an expected profit maximizing bookmaker could set market inefficient odds. Several empirical tests using the ordered probit model with data on prices and publicly available information are carried out. Evidence of market inefficiency is identified offering profitable betting opportunities.     

Comparing risk aversion in a probability triangle

An agent's acceptance set consists of the probability distributions preferred to the status quo. One agent is more risk averse than another if the more risk averse agent's acceptance set is a proper subset of the less risk averse agent's acceptance set. An agent's odds premium expresses the odds in favor of winning the largest cash prize in a lottery over the best and worst alternatives that is indifferent to the the agent's initial wealth. Comparisons of two agents odds premia completely characterizes the risk aversion relations between them when facing lotteries in a probability triangle. The result applies to expected utility and some non-expected utility theories. Received: December 30, 1998; revised version: February 10, 1999     

Intertemporal substitution, risk aversion and ambiguity aversion

Summary. This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.Received: 5 August 2003, Revised: 12 March 2004, JEL Classification Numbers: D80, D81, D90.I am grateful to Larry Epstein for his guidance and invaluable advice, and to a referee for helpful comments and suggestions.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Efficiency in the NFL betting market: modifying and consolidating research methods

Modifying and consolidating previous research methods to generate more reliable estimates, some fairly weak evidence is found of inefficiency in the NFL betting market resulting from a bias favouring home underdog (against away favourite) teams. In contrast to previous research, no evidence is found that ‘momentum strategies’ generate significant returns in this market.     

Endogenous factor market distortion, risk aversion, and international trade under input uncertainty

In the context of non-diversifiable and sector-specific risks in labour markets, we show that the resulting factor market distortion – attributable to an endogenous intersectoral wage differential – can provide a possible rationale that explains why larger wage dispersion prevails in developing nations. We also demonstrate how endogenous wage distortions spill over to capital markets, with capital-poor economies offering lower rates of returns. In addition, we show that inequality in the distribution of wealth further deviates factor allocation away from first-best and impairs intersectoral mobility of the poor.
Ce mémoire montre que la distorsion dans le marché des facteurs qui résulte de risques non diversifiables et spécifiques à certains secteurs (et qui se traduit par un différentiel de salaire endogène entre secteurs) peut expliquer pourquoi on observe une dispersion plus grande des salaires dans les pays en voie de développement.On montre aussi comment des distorsions endogènes de salaires débordent vers les marchés de capitaux,ce qui fait que les pays pauvres en capital ont des rendements plus faibles.De plus, on montre que l'inégalité dans la distribution de la richesse contribue à faire dévier l'allocation des ressources de son optimum de premier ordre et nuit à la mobilité inter-sectorielle des pauvres.     

Repetitive risk aversion

We propose a reasonable condition, which we call repetitive risk aversion (RRA), to be imposed on any utility function to account for the observed data on the relationship between the degree of absolute risk aversion and wealth. We deduce this condition from the concept of the fear of ruin (Aumann and Kurz 1977) and show it to be equivalent to the behaviorally meaningful condition that the risk premium is increasing at a non-increasing rate with the size of the bet. We drive mixed risk aversion, which is known to be stronger than standard and thus proper risk aversion, from RRA. We present several economic applications of RRA to demonstrate that it delivers better comparative static results.I am thankful to Jacques Drèze and Louis Eeckhoudt for their comments. I greatly appreciate the comments of an anonymous reviewer of this journal which have resulted in substantial improvement to both the content and presentation of the paper. An earlier version of this paper was presented at seminars at Brown, CORE, Hopkins, HKUST, Yale, and IMS     

First-order risk aversion and non-differentiability

Summary First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery , is proportional, for smallt, tot. Equivalently, 0$$ " align="middle" border="0"> . We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).We are grateful to the Social Sciences and Humanities Research Council of Canada for financial support and to Kim Border, Larry Epstein, Mark Machina and Joe Ostroy for helpful discussions and suggestions.