Noise Tolerance under Risk Minimization

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results

Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a singleperiod, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.Aggregation, heterogeneous consumers, absolute risk tolerance, mutual fund theorem

Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Some consequences of these results and refinements of these results for the class of HARA utility functions are discussed

Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a singleperiod, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.Aggregation, heterogeneous consumers, absolute risk tolerance, mutual fund theorem.

Are Risk Averse Agents More Optimistic? A Bayesian Estimation Approach

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1,536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated. As a consequence, we conclude that the consensus belief is biased towards pessimism.Bayesian estimation, MCMC scheme, importance sampling, pessimism, risk tolerance, risk aversion, consensus belief

Are Risk-Averse Agents more Optimistic? A Bayesian Estimation Approach.

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. Its estimation leads to a non-trivial statistical problem. We start from a large lottery survey (1536 individuals). We assume that individuals have true unobservable characteristics. We adopt a Bayesian approach and use a hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We find that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated.Bayesian Estimation; MCMC Scheme; Importance Sampling; Pessimism; Risk Tolerance; Risk Aversion; Consensus Belief;

The Correlation of Welath Across Generations

This paper examines the similarity in wealth between parents and their children, and explores alternative explanations for this relationship. We find that the age-adjusted elasticity of child wealth with respect to parental wealth is 0.37, before the transfer of bequests. Lifetime income and ownership of particular assets, both of which exhibit strong intergeneration similarity, jointly explain nearly two-thirds of the wealth elasticity. Education, past parental transfers, and expected future bequests account for little of the remaining elasticity. Using new experimental evidence, we assess the importance of risk tolerance. The risk tolerance measures vary as theory would predict with the ownership of risky assets, and are highly correlated between parents and children. However, they explain little of the intergenerational correlation in the propensity to own different assets, suggesting that children's savings propensities are determined by mimicking their parents' behavior, or the inheritance of preferences not related to risk tolerance. Additionally, these risk tolerance measures explain only a small part of the remaining intergenerational wealth elasticity.

Sorting, Incentives and Risk Preferences: Evidence from a Field Experiment

The, often observed, positive correlation between incentive intensity and risk has been explained in two ways: the presence of transaction costs as determinants of contracts and the sorting of risk-tolerant individuals into firms using high-intensity incentive contracts. The empirical importance of sorting is perhaps best evaluated by directly measuring the risk tolerance of workers who have selected into incentive contracts under risky environments. We use experiments, conducted within a real firm, to measure the risk preferences of a sample of workers who are paid incentive contracts and face substantial daily income risk. Our experimental results indicate the presence of sorting; Workers in our sample are risk-tolerant. Moreover, their level of tolerance is considerably higher than levels observed for samples of individuals representing broader populations. Interestingly, the high level of risk tolerance suggests that both sorting and transaction costs are important determinants of contract choices when workers have heterogeneous preferences.Risk aversion, sorting, incentive contracts, field experiments

The Risk Tolerance of International Investors

Investor confidence and risk tolerance are important concepts that investors are constantly trying to gauge. Yet these concepts are notoriously hard to measure in practice. Most attempts rely on price or return data, but these run into trouble when trying to disentangle whether an observed price change is attributable to a shift in investor confidence or a change in fundamental value. In this paper, we take an alternative approach by looking at the world-wide holdings and trading of risky assets. We model global capital markets as the interaction between large global institutional investors and smaller domestic investors from each country. This permits separation of global price changes into two components, one that reflects changes in demand and fundamentals perceived by all investors, and a second that reflects changes in the relative risk tolerance of institutional investors over and above that of domestics. The latter component, changes in relative risk tolerance of global institutions, is driven by the willingness of these investors to acquire additional assets in each country in proportion to their current holdings. Using our model, we show how data on asset holdings and flows across countries can be used to identify changes in risk tolerance. We then apply this identification scheme to recent data on the global portfolio holdings of institutional investors. The resulting measure of risk tolerance impressionistically accords well with periods of market turbulence and quiescence. It also accounts for a considerable portion of the variation in portfolio holdings and is informative about future returns.