Aggregation of Heterogeneous Beliefs and Asset Pricing Theory: A Mean-Variance Analysis

Within the standard mean-variance framework, this paper provides a procedure to aggregate the heterogeneous beliefs in not only risk preferences and expected payoffs but also variances/covariances into a market consensus belief. Consequently, an asset equilibrium price under heterogeneous beliefs is derived. We show that the market aggregate behavior is in principle a weighted average of heterogeneous individual behaviors. The CAPM-like equilibrium price and return relationships under heterogeneous beliefs are obtained. The impact of diversity of heterogeneous beliefs on the market aggregate risk preference, asset volatility, equilibrium price and optimal demands of investors is examined. As a special case, our result provides a simple explanation for the empirical relation between cross-sectional volatility and expected returns.

Optimality of linearity with collusion and renegotiation

This study analyzes a continuous-time N-agent Brownian hidden-action model with exponential utilities, in which agents' actions jointly determine the mean and the variance of the outcome process. In order to give a theoretical justification for the use of linear contracts, as in Holmstrom and Milgrom (1987), we consider a variant of its generalization given by Sung (1995), into which collusion and renegotiation possibilities among agents are incorporated. In this model, we prove that there exists a linear and stationary optimal compensation scheme which is also immune to collusion and renegotiation

Discounting, Inequalities and Economic Convergence

The aim of this paper is to examine the impact of inequalities and economic convergence on the efficient discount rate, in the absence of any risk-sharing scheme. We consider an economy in which the initial consumption level and the distribution of consumption growth are heterogeneous. The benchmark case is when inequalities are permanent and relative risk aversion is constant. The discount rate is not affected by inequalities in that case. We first relax the assumption on risk aversion, and we derive conditions under which permanent inequalities reduce the discount rate. If relative prudence is larger than unity, an increase in economic convergence always raises the efficient discount rate. In a realistic calibration exercise, we show that the effect of economic convergence is to triple the discount rate, from less 2% to more than 6%.prudence, temperance, concordance, discount rate

The Behavior of Savings and Asset Prices When Preferences and Beliefs Are Heterogeneous

Movements in asset prices are a major risk confronting individuals. This paper establishes new asset pricing results when agents differ in risk preference, time preference and/or expectations. It shows that risk tolerance is a critical concept driving savings decisions, consumption allocations, prices and return volatilities. Surprisingly, due to the equilibrium risk sharing, the precautionary savings motive in the aggregate can vastly exceed that of even the most prudent actual agent in the economy. Consequently, a low real interest rate, resulting from large aggregate savings, can prevail with reasonable risk aversions for all agents. One downside of a large aggregate savings motive is that savings rates become extremely sensitive to output fluctuation. Thus, the same mechanism that produces realistically low interest rates tends to make them unrealistically volatile. A powerful isomorphism allows differences in time preference and expectations to be swept away in the analysis, yielding an equivalent economy whose agents differ merely in risk aversion. These results hold great potential to simplify the analysis of heterogeneous-agent economies, as we demonstrate in quantifying how asset prices move and bounding their volatilities. All results are obtained in closed form for any number of agents possessing additively separable preferences in an endowment economy.

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

Empirical Pricing Kernels and Investor Preferences

This paper analyzes empirical market utility functions and pricing kernels derived from the DAX and DAX option data for three market regimes. A consistent parametric framework of stochastic volatility is used. All empirical market utility functions show a region of risk proclivity that is reproduced by adopting the hypothesis of heterogeneous individual investors whose utility functions have a switching point between bullish and bearish attitudes. The inverse problem of finding the distribution of individual switching points is formulated in the space of stock returns by discretization as a quadratic optimization problem. The resulting distributions vary over time and correspond to different market regimes.Utility function, Pricing Kernel, Behavioral Finance, Risk Aversion, Risk Proclivity, Heston model.

Adventures in Time and Space: What Shapes Behavioural Decisions in Drosophila melanogaster?

Variation in behaviour can be observed both between individuals, based on their condition and experience as well as between populations due to sources of heterogeneity in the environment. These behavioural differences have evolved as a result of natural and sexual selection where different strategies may be favoured depending on the costs and benefits associated with those behaviours. In this thesis I examine two sources of heterogeneity within the environment and their behavioural consequences: how spatial complexity mediates sexual selection over time, and how inter and intraspecific signals and individual condition influence social oviposition behaviour. By increasing spatial complexity, we were able to manipulate male-female interaction rate which in turn influenced courtship behaviour and male-induced harm, the consequence of this was an increase in female fecundity especially in the later days of the assay and no change in offspring fitness. These results supported the idea that spatial complexity is able to mediate sexual selection through decreased harm to females. Oviposition decisions are of high consequence to an individual’s fitness and can be shaped by many environmental conditions. Instead of expending energy to evaluate all their different costs and benefits of the conditions of potential oviposition sites females can chose to rely on the signals left by others, in this case it would be beneficial for females to identify signals most like themselves. While we found females oviposited with individuals of the same species and diet, when given the option they showed more interest in and laid more eggs on media that previously held virgin males, bringing into question many assumptions of copying behaviour. In Drosophila melanogaster the only control females have over their offspring is who they mate with and where they oviposit their eggs, thus, these two factors can have a long-lasting impact on individual fitness for future generations. It is also important to consider how the standard lab environment may be shaping these behaviours, and the consequences this has for the evolutionary trajectory of lab populations

Optimality of linearity with collusion and renegotiation

This study analyzes a continuous-time N-agent Brownian hidden-action model with exponential utilities, in which agents' actions jointly determine the mean and the variance of the outcome process. In order to give a theoretical justi¯cation for the use of linear contracts, as in Holmstrom and Milgrom (1987), we consider a variant of its generalization given by Sung (1995), into which collusion and renegotiation possibilities among agents are incorporated. In this model, we prove that there exists a linear and stationary optimal compensation scheme which is also immune to collusion and renegotiation.Principal-agent problems; moral hazard; linear contracts; continuous-time model; Brownian motion martingale method; collusion,; renegotiation; team

A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation or Cross-sectional Heterogeneity?

In this paper we study the asset pricing implications of a parsimonious two-agent macroeconomic model with two key features: limited participation in the stock market and heterogeneity in the elasticity of intertemporal substitution. The parameter values for the model are taken from the real business cycle literature and are not calibrated to match any financial statistic. Yet, with a risk aversion of two, the model is able to explain a large number of asset pricing phenomena including all the facts matched by the external habit model of Campbell and Cochrane (1999). Examples in this list include a high equity premium and a low risk-free rate; a counter-cyclical risk premium, volatility and Sharpe ratio; predictable stock returns with coe?cients and R2 values of long-horizon regressions matching their empirical counterparts, among others. In addition the model generates a risk-free rate with low volatility (5.7 percent annually) and with high persistence. We also show that the similarity of our results to those from an external habit model is not a coincidence: the model has a reduced form representation which is extremely similar to Campbell and Cochrane’s framework for asset pricing. However, the macroeconomic implications of the two models are very different, favoring the limited participation model. Moreover, we show that policy analysis yields dramatically different conclusions in each framework.Limited stock market participation, asset pricing, the equity premium puzzle, incomplete markets, habit formation, elasticity of intertemporal substitution.

An Empirical Analysis of the Role of Risk Aversion in Executive Compensation Contracts

This paper empirically tests the principal-agent model prediction that the use of performance measures for incentive purposes is affected by the agent’s risk aversion. We find that the use of both accounting and market performance measures in executive compensation contracts decreases as the level of risk aversions increases. We further find that agent-specific characteristics, i.e., risk aversion, become more important in designing executive compensation contracts when performance measures are less useful due to measure-specific characteristics.Economics ;