Pricing risk and ambiguity: the effect of perspective taking (original) (raw)
Related papers
Attitudes towards risk and ambiguity across gains and losses.
Theory and Decision
We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to elicit attitudes to risky and ambiguous prospects. In particular we wish to investigate if there are differences in agent behaviour under uncertainty over gain amounts vis a vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gain and risk seeking over losses, displaying a "reflection effect" as documented in Amos Tversky and Daniel Kahneman (1992) and (ii) they are mildly ambiguity averse over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of reflection effects where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Finally, our results suggest that reflection across gains and losses is not an individual trait but depends upon whether the form of uncertainty is precise or ambiguous since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects.
Ambiguity and asset prices: an experimental perspective
2006
Most of the economics and finance literature assumes that individual agents obey the Savage axioms; that is, they maximize expected utility according to subjective priors. However, Knight, Ellsberg and others argue that individual agents distinguish between risk (known probabilities) and uncertainty, or ambiguity (unknown probabilities), and that individual agents may display aversion to ambiguity, just as they display aversion to risk. This paper studies the impact of ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitude toward ambiguity is heterogeneous in the population, just as attitude toward risk is heterogeneous in the population, but that heterogeneity in attitude toward ambiguity has different implications than heterogeneity in attitude toward risk: agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This leads to a wider range of state price densities and to potential reversals of ranking of state price densities. Experiments confirm the theoretical predictions.
Ambiguity in Individual Choice and Market Environments: On the Importance of Comparative Ignorance
After Ellsberg's thought experiments brought focus to the relevance of missing information for choice, extensive efforts have been made to understand ambiguity theoretically and empirically (Ellsberg 1961). Fox and Tversky (1995) make an important contribution to understanding behavioral responses to ambiguity. In an individual choice setting they demonstrate that an aversion to ambiguous lotteries arises only when a comparison to unambiguous lotteries is available. The current study advances this literature by exploring the importance of Fox and Tversky's finding for market outcomes and finds support for their Comparative Ignorance Hypothesis in the market setting. Experiments in both individual choice and market settings examine behavior under risk and ambiguity. A sizeable effect of ambiguity on prices is observed-but only when the experimental treatment makes the risky and ambiguous assets easily comparable. Further, when ambiguity is salient, individual attitudes towards ambiguity and behavior in the marketplace are linked; ambiguity-averse subjects tend to avoid ambiguous assets in the marketplace. However, a simple experimental manipulation that makes the distinction between risk and ambiguity less apparent changes outcomes dramatically; the correlation between individual ambiguity attitudes and market allocations disappears, as do differences in market prices between risky and ambiguous assets.
Ambiguity aversion: experimental modeling, evidence, and implications for pricing∗
2013
This paper provides a systematic analysis of individual attitudes towards ambiguity, based on laboratory experiments. The design of the analysis captures different degrees of ambiguity in various settings, and it allows to disentangle attitudes towards risk and attitudes towards ambiguity. In addition to individual attitudes, the experiments also elicit expectations about other participants’ attitudes, allowing us to relate own behavior to expectations about others. New measures are introduced for both, the degree of ambiguity in a situation and ambiguity aversion. Ambiguity is embedded in standard utility theory and a parameter of ambiguity aversion is estimated and contrasted to the parameter of risk aversion. The analysis provides a test of theoretical models of ambiguity aversion. The main findings are that ambiguity aversion on average is much more pronounced than human aversion against risk and that it is very different across individuals. Moreover, while most theoretical work...
A Case-Based Model of Probability and Pricing Judgments: Biases in Buying and Selling Uncertainty
Management Science, 2012
W e integrate a case-based model of probability judgment with prospect theory to explore asset pricing under uncertainty. Research within the "heuristics and biases" tradition suggests that probability judgments respond primarily to case-specific evidence and disregard aggregate characteristics of the class to which the case belongs, resulting in predictable biases. The dual-system framework presented here distinguishes heuristic assessments of value and evidence strength from deliberative assessments that incorporate prior odds and likelihood ratios following Bayes' rule. Hypotheses are derived regarding the relative sensitivity of judged probabilities, buying prices, and selling prices to case-versus class-based evidence. We test these hypotheses using a simulated stock market in which participants can learn from experience and have incentives for accuracy. Valuation of uncertain assets is found to be largely case based even in this economic setting; however, consistent with the framework's predictions, distinct patterns of miscalibration are found for buying prices, selling prices, and probability judgments.
The impact of ambiguity on prices and allocations in competitive financial markets
2003
This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In particular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross-section of portfolio choices, a wider range of state price/probability ratios and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are infra-marginal: ambiguity averse investors have an indirect effect on prices because they change the per-capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the "value effect" in historical data.
Risk, ambiguity, and the separation of utility and beliefs
Mathematics of Operations Research, 2001
We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization.
Ambiguity in asset markets: theory and experiment
Review of Financial …, 2010
This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In particular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross-section of portfolio choices, a wider range of state price/probability ratios and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are infra-marginal: ambiguity averse investors have an indirect effect on prices because they change the per-capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the "value effect" in historical data.
Theory and decision, 2009
We use the multiple price list method and a recursive expected utilitytheory of smooth ambiguity to separate out attitude towards risk from that towardsambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts.On an aggregate level,we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on anindividual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual char-acteristic, but depends upon whether the form of uncertainty is precise or ambiguous,since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.