A Survey Measure of Risk Aversion

We Use Survey Data on the Well-Being of Individuals to Measure Attitude Toward Risk. Risk Neutrality Cannot Be Rejected by the Data.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.

Empirical test of an agricultural landscape model: the importance of farmer preference for risk aversion and crop complexity

Developing models to predict the effects of social and economic change on agricultural landscapes is an important challenge. Model development often involves making decisions about which aspects of the system require detailed description and which are reasonably insensitive to the assumptions. However, important components of the system are often left out because parameter estimates are unavailable. In particular, measurements of the relative influence of different objectives, such as risk, environmental management, on farmer decision making, have proven difficult to quantify. We describe a model that can make predictions of land use on the basis of profit alone or with the inclusion of explicit additional objectives. Importantly, our model is specifically designed to use parameter estimates for additional objectives obtained via farmer interviews. By statistically comparing the outputs of this model with a large farm-level land-use data set, we show that cropping patterns in the United Kingdom contain a significant contribution from farmer’s preference for objectives other than profit. In particular, we found that risk aversion had an effect on the accuracy of model predictions, whereas preference for a particular number of crops grown was less important. While nonprofit objectives have frequently been identified as factors in farmers’ decision making, our results take this analysis further by demonstrating the relationship between these preferences and actual cropping patterns.

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

Risk aversion, overconfidence and private information as determinants of majority thresholds

We present and experimentally test a theoretical model of majority threshold determination as a function of voters’ risk preferences. The experimental results confirm the theoretical prediction of a positive correlation between the voter's risk aversion and the corresponding preferred majority threshold. Furthermore, the experimental results show that a voter's preferred majority threshold negatively relates to the voter's confidence about how others will vote. Moreover, in a treatment in which individuals receive a private signal about others’ voting behaviour, the confidence-related motivation of behaviour loses ground to the signal's strength.

Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. And market expectations on financial variables may influence macroeconomic policy decisions. It can be useful also for corporate and financial institutions decision making. This paper uses the Liu et all (2007) approach to estimate the option-implied Risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a Real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied Real World Density for an emerging market currency. Our empirical application uses a sample of Brazilian Real/US Dollar options traded at BM&F-Bovespa from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risktransformations. The relative risk aversion is calculated for the full sample. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy, such as Araújo (2005) and Issler and Piqueira (2000). Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results in the out-of-sample analysis of the RND forecast ability for exchange rate options. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the out-of-sample performance improves substantially, with satisfactory results in both Kolmogorov and Berkowitz tests. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

The role of consumer's risk aversion on price rigidity

This paper aims at contributing to the research agenda on the sources of price stickiness, showing that the adoption of nominal price rigidity may be an optimal firms' reaction to the consumers' behavior, even if firms have no adjustment costs. With regular broadly accepted assumptions on economic agents behavior, we show that firms' competition can lead to the adoption of sticky prices as an (sub-game perfect) equilibrium strategy. We introduce the concept of a consumption centers model economy in which there are several complete markets. Moreover, we weaken some traditional assumptions used in standard monetary policy models, by assuming that households have imperfect information about the ineflicient time-varying cost shocks faced by the firms, e.g. the ones regarding to inefficient equilibrium output leveIs under fiexible prices. Moreover, the timing of events are assumed in such a way that, at every period, consumers have access to the actual prices prevailing in the market only after choosing a particular consumption center. Since such choices under uncertainty may decrease the expected utilities of risk averse consumers, competitive firms adopt some degree of price stickiness in order to minimize the price uncertainty and fi attract more customers fi.'

Labor supply, risk aversion and economic refrom in China

Economic reform in China has created a small, but fast-growing private sector that has spurred rapid productivity growth. Growth of the private sector is predicated upon continued labor movements away from state-run industries and into private firms. This paper presents a theory of labor market sectoral choice demonstrating that three factors determine private sector labor supply-the difference in wages between the state and private sectors, private sector wage risk and risk aversion. Estimation of the model using survey data provides strong support for the theory. We find that the riskiness of private sector earnings has a greater effect in discouraging workers from taking jobs in private firms than the wage premi um has in attracting workers.

Asymmetric auctions and risk aversion within independent private valoues

We study tournaments with many ex-ante asymmetric (heterogeneous) contestants as an independent-private-values all-pay auction. The asymmetry is either with respect to the distribution of valuations for the prize or the risk preferences. By characterizing equilibria in tnonotone strategies we show that tournaments \:vith man~y heterogenous contestants are qualitatively distinct. First, with two (or many ex-ante identical) participants, a contestant always exerts some effort with positive probability. In contrast, with many asymmetric participants, one 1night not exert any effort at all, even if there is a positive probability that he has the highest valuation among ali. Second, in tournan1ents with t'wo (o r n1any ex-ante h01nogenous) contestants, equilibrium effort densities are decreasing. This prediction is at odds with experimental evidence that shows the empírica! density might be increasing at high effort levels. V\.lith rnany heterogeneous contestants, however. the increasing bid density is consistent with an equilibrium behavior.