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. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.     

The tradeoff between risk sharing and information production in financial markets

The production of information in financial markets is limited by the extent of risk sharing. The wider a stock's investor base, the smaller the risk borne by each shareholder and the less valuable information. A firm which expands its investor base without raising capital affects its information environment through three channels: (i) it induces incumbent shareholders to reduce their research effort as a result of improved risk sharing, (ii) it attracts potentially informed investors, and (iii) it may modify the composition of the base in terms of risk tolerance or liquidity trading. Implications for individual firms and the market as a whole are derived.     

Consequences, opportunities, and generalized consequentialism and non-consequentialism

In a recent paper published in Journal of Economic Theory (101 (2001) 423-436), by Suzumura and Xu, an analytical framework was developed, which allowed us to characterize the concept of consequentialism and non-consequentialism. To simplify matters, however, the treatment in that paper was confined only to the cases where no trade-off exists between consequential considerations, which reflect the individual's preferences over alternatives, and non-consequential considerations, which reflect the individual's concern over richness of opportunities from which alternatives are chosen. The present paper represents a generalization of our previous framework, which can now accommodate the situations where consequential considerations and non-consequential considerations actively interact. The analysis covers both the cases of finite and infinite number of alternatives.     

HETEROGENEOUS RISK ATTITUDES IN A CONTINUOUS‐TIME MODEL*

We prove that every continuous‐time model in which all consumers have time‐homogeneous and time‐additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results of the representative consumer and risk‐sharing rules in static models to continuous‐time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than in the absence of uncertainty.     

“Fair go” for all? Wealth and Risk Aversion of Australian Households*

A mean‐variance framework is applied to Australian household financial portfolios in order to provide estimates of relative risk aversion in the economy. Controlling for various socio‐economic characteristics, we explore whether risk aversion heterogeneity is a function of wealth heterogeneity. In contrast to most studies, we find evidence of very high risk aversion amongst the majority of households of poor households but vastly lower risk aversion amongst the high percentiles in the wealth distribution. Applying a first differences model across three survey waves spanning 2002 to 2010, we find that risk tolerance increases significantly with wealth. Risk tolerance is positively associated with mortgage payments, but rental payments have no relationship. In addition, we found no evidence that holding a university education has any discernible impact on risk aversion. Lastly, we present some preliminary findings as to the impact of financial advice on observed risk aversion. Financial advice is found to accentuating risk aversion, particularly amongst the wealthiest households. The findings have potential implications for the distribution of wealth in Australia that has received renewed interest recently.     

Production and insurance under regret aversion

This paper examines the behavior of a regret-averse producer facing revenue risk. To insure against the revenue risk, the producer can purchase a coinsurance contract with an endogenously chosen coinsurance rate. Regret-averse preferences are characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the regret-averse producer never fully insures against the revenue risk even though the coinsurance contract is actuarially fair. When the producer is sufficiently regret averse and the loss probability is high, we further show that the regret-averse producer chooses not to purchase the actuarially fair coinsurance contract. Even when purchasing the actuarially fair coinsurance contract is optimal, we derive sufficient conditions under which the regret-averse producer reduces the optimal output level as compared to that without the coinsurance contract. These results are distinct from those under pure risk aversion, thereby making the consideration of regret aversion crucial.     

When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?

In a standard incomplete markets model with a continuum of households that have constant relative risk aversion (CRRA) preferences, the absence of insurance markets for idiosyncratic labor income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks and aggregate consumption growth is independent over time. In equilibrium, households only use the stock market to smooth consumption; the bond market is inoperative. Furthermore, the cross-sectional distributions of wealth and consumption are not affected by aggregate shocks. These results hold regardless of the persistence of idiosyncratic shocks, even when households face tight solvency constraints. A weaker irrelevance result survives when we allow for predictability in aggregate consumption growth.     

Direct versus intermediated finance: An old question and a new answer

We consider a closed economy where a risk neutral bank competes with a competitive bond market. Firms can finance a risky project either by a bank credit or by issuing a bond which is directly sold to risk averse investors who also hold safe deposits at the bank. We show that the bank tends to allocate more capital to lower quality projects but there are some interesting qualifications. If the asymmetric information concerns only the success probability, then we observe adverse selection while if it concerns only the expected return, bad types are driven out of the market.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Some recent developments in capital market theory: A survey

This paper surveys some recent developments in the theory of capital markets. Particular emphasis is given to two strands of the literature. The first covers some recent and fundamental extensions to the theory of risk aversion and the demand for risky assets. These papers are concerned with the effect of non-hedgeable background risk on risk attitudes. The important implications for finance are for the size of the risk premium (the equity premium puzzle) and for the demand for and pricing of contingent claims. For example, background risk may help to explain the apparent over-pricing of options on equity indices. The second topic is interest rate term structure models. Stochastic term structure models try to capture the possible future shapes of the term structure of interest rates. This is relevant for the pricing of contingent claims, in particular for the pricing of interest rate derivatives such as American-style swaptions. The paper will survey the most important recent models in the literature, each of which satisfies the fundamental no-arbitrage property. It will discuss the implications of the models for the pricing of both European-style and American-style options.     

Between liberalism and democracy

We study and characterize axiomatically a class of voting rules, called consent rules, that incorporate aspects of majoritarianism and liberalism. An outcome of the vote specifies who among the voters are eligible to a certain right or qualification. Each outcome serves also as a permissible ballot. Consent rules are parameterized by the weights given to individuals in determining their own qualification. In one of these rules, the liberal rule, each individual's qualification is determined by her. In other rules, an individual's qualification requires social consent in various degrees. We also show the relation between self-determination and the liberal rule.     

Optimal risk sharing with background risk

This paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk-averse expected utility maximizers, the concept of “stochastic increasingness” is used. Different assumptions on the stochastic dependence between the insurable and uninsurable risk lead to different qualitative properties of the efficient contracts. The new results obtained under hypotheses of dependent risks are compared to classical results in the absence of background risk or to the case of independent risks. The theory is further generalized to nonexpected utility maximizers.     

Efficient allocations under ambiguity

Important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief, then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the consumption plans are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications.     

Asset return dynamics and the FX risk premium in a decentralized dealer market

The paper proposes a continuous time model of an FX market organized as a multiple dealership. The dealers have costly access to best available quotes. They interpret signals from the joint dealer-customer order flow and decide upon their own quotes and trades in the inter-dealer market. Each dealer uses the observed order flow to improve the subjective estimates of relevant aggregate variables, which are the sources of uncertainty. The risk factors are returns on domestic and foreign assets and the size of the cross-border dealer transactions in the FX market. These uncertainties have diffusion form and are dealt with according to the principles of portfolio optimization in continuous time. The model is used to explain the country, or risk, premium in the uncovered national return parity equation for the exchange rate. The two country premium terms that I identify in excess of the usual covariance term (consequence of the “Jensen inequality effect”) are: the dealer heterogeneity-induced inter-dealer market order flow component and the dealer Bayesian learning component. As a result, an “order flow-adjusted total return parity” formula links the excess FX return to both the “fundamental” factors represented by the differential of the national asset returns, and the microstructural factors represented by heterogeneous dealer knowledge of the aggregate order flow and the fundamentals.     

Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the inexistence of mutually compatible trades, with non-negative expectation with respect to any risk adjusted prior. These conditions are necessary when agents are not risk neutral at extreme levels of wealths. It is shown that the more uncertainty averse or risk averse the agents, the more likely are efficient allocations and equilibria to exist.     

Fundamentals, information, and international capital flows: A welfare analysis

In the recent discussion surrounding the design of a new international financial architecture, enhancing transparency has widely been proposed as a policy essential for increasing the efficiency of international capital markets. This paper uses a simple two-country (two-agent) general equilibrium model with incomplete markets and production to explore the welfare consequences of an increase in public information about country-specific fundamentals (increase in transparency). An improvement in the quality of information has two effects on the ex ante welfare of individual countries: A direct effect that increases the efficiency of global capital allocation and welfare, and an indirect general equilibrium effect that increases asset price volatility and may decrease welfare. When the degree of risk-aversion is low, at least one country will gain from an increase in information quality. If the degree of risk-aversion is high, then there are robust examples of economies for which an increase in information hurts all countries. The paper also discusses how certain institutional arrangements (international derivative markets, international agency) could ensure that all countries gain from better information by providing insurance against information-induced asset price risk.     

Financial opening, deposit insurance, and risk in a model of banking competition

We study the impact of competition on banks’ risk-taking behavior under different assumptions about deposit insurance and the dissemination of information. While financial opening increases banks’ riskiness, a risk-based deposit insurance or, alternatively, the public disclosure of financial information, are likely to mitigate this effect. Moreover, the limiting cases of uninsured but fully informed depositors, and risk-based full deposit insurance, yield the same equilibrium risk level. Although the welfare consequences of increased competition depend on its impact on risk, financial opening unambiguously improves welfare as we approach the limiting cases.     

Models of Capital Requirements in Static and Dynamic Settings

The aim of this paper is twofold. First, we generalize the notion of capital requirement, originally formulated in a regulatory framework, in order to unify other apparently diverse financial concepts. Second, we stress the interpretation of a capital requirement as a measure of risk, providing a link with the theory of coherent risk measures. We define a capital requirement as the minimal initial cost of a hedging action that makes the original position acceptable. Three basic elements are involved in such a methodology: a system of prices, a class of permitted hedging actions and a criterion of acceptability. Our approach is very general, because we construct capital requirements on vector spaces. However, we will give some concrete applications related, in particular, to the availability of a financial market, to the presence of different business units in an institution or to the fact that pay-offs are spread over different dates.     

Lifetime consumption and investment: Retirement and constrained borrowing

Retirement flexibility and inability to borrow against future labor income can significantly affect optimal consumption and investment. With voluntary retirement, there exists an optimal wealth-to-wage ratio threshold for retirement and human capital correlates negatively with the stock market even when wages have zero or slightly positive market risk exposure. Consequently, investors optimally invest more in the stock market than without retirement flexibility. Both consumption and portfolio choice jump at the endogenous retirement date. The inability to borrow limits hedging and reduces the value of labor income, the wealth-to-wage ratio threshold for retirement, and the stock investment.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997