Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

Progressive taxation and the equal sacrifice principle

A classical problem in public finance is: when does equal sacrifice imply progressive taxation? Suppose that a tax schedule imposes equal sacrifice on all taxpayers in loss of utility, and that this property is preserved under re-indexing of the schedule. Then the utility function must exhibit constant relative risk aversion, i.e. it must be logarithmic or a power function. If equal sacrifice relative to such a utility function holds for all taxable incomes, and if tax rates do not exceed 100 percent, then the degree of relative risk aversion must be at least unity, and the tax must be nonregressive.     

Risk Appetite,Home Bias and the Unstable Demand for Emerging Market Assets

Home bias arises when the actual portfolio of an investor consists of a smaller proportion of foreign assets than that predicted by standard portfolio theory for the observed set of risks and returns on available assets. The existence and persistence of home bias undermines the theoretical case for the efficiency of international capital markets. In this paper we use data on UK pension fund portfolios to measure home bias, and find that this is doubly acute in the case of emerging market equity—a bias against overseas assets as a whole being further magnified by a bias against emerging markets within the foreign equity class as a whole. Moreover, contrary to the conventional assumption that risk aversion is both relatively low and stable over time (canonised in neoclassical theory by the derivation of constant relative risk aversion from the utility function itself) our finding that home bias fluctuates over time suggests that risk aversion is in fact time‐variant and path‐dependent. We sketch an alternative Keynesian approach in conclusion.     

On the stability of the constant relative risk aversion (CRRA) utility under high degrees of uncertainty

Growth models under uncertainty and constant relative risk aversion (CRRA) utility are fragile in explaining consumers’ choice, as equilibrium consumption is dependent on distributional assumptions. We show that, under semi-nonparametric distributions, general equilibrium models are stable, as the existence of expected utility is guaranteed.     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

Endogenous time-varying risk aversion and asset returns

Stylized facts about statistical properties for short horizon returns in financial markets have been identified in the literature, but a satisfactory understanding for their manifestation is yet to be achieved. In this work, we show that a simple asset pricing model with representative agent is able to generate time series of returns that replicate such stylized facts if the risk aversion coefficient is allowed to change endogenously over time in response to unexpected excess returns under evolutionary forces. The same model, under constant risk aversion, would instead generate returns that are essentially Gaussian. We conclude that an endogenous time-varying risk aversion represents a very parsimonious way to make the model match real data on key statistical properties, and therefore deserves careful consideration from economists and practitioners alike.     

The role of risk aversion in public goods dilemmas with environmental uncertainty: an experimental analysis

The purpose of this study is to extend earlier research on environmental uncertainty in public goods dilemmas. The present paper reports the results of an experiment designed to examine the effect of risk aversion on public goods provision. A von Neumann–Morgenstern utility function with constant coefficient of relative risk aversion is used to investigate the impact of risk attitudes within a threshold public goods environment. The outcome of the threshold public goods experiment shows that subjects are indifferent to the changes in environmental conditions. Additionally, the analysis indicates that risk aversion is a significant determinant of voluntary public goods contribution level.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Modeling non-monotone risk aversion using SAHARA utility functions

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.     

Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences.     

On the Value of Life in Rich and Poor Countries and Distributional Weights Beyond Utilitarianism

This paper discusses the use ofdistributional weights in CBA based on a generalBergson-Samuelson SWF. In particular it illustratessome consequences of applying a SWF characterized byconstant inequality aversion (which includes classicalutilitarianism as a special case), together with aconstant relative risk aversion utility function, whencalculating the damage costs of global warming. Itextends and clarifies earlier unintuitive results, andemphasizes that utility must be seen as fully cardinalin terms of levels in this context. In the specialcase of utilitarianism, on the other hand, it issufficient to be able to make interpersonalcomparisons of utility changes.     

Relative risk aversion around the world

In this letter the hypothesis of constant relative risk aversion is examined for 15 countries, using property/liability insurance data. For more than half the cases it is shown that CRRA can not be rejected. Following that, the degree of relative risk aversion is estimated, and found to usually lie between one and two.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences

From the expected‐utility approach, relative risk aversion being smaller than one and relative prudence being smaller than two emerge as preference restrictions that fully determine the optimal responses of decisions under uncertainty to certain shifts in probability distributions. We characterize the magnitudes of relative risk aversion and relative prudence in terms of the two‐parameter, mean‐standard deviation approach. We demonstrate that this characterization is instrumental in obtaining comparative static results in the two‐parameter setting. We further relate our findings to the results in the expected‐utility framework.     

Diversification versus optimality: is there really a diversification puzzle?

In this paper, we provide a general valuation of the diversification attitude of investors. First, we empirically examine the diversification of mean-variance optimal choices in the US stock market during the 11-year period 2003–2013. We then analyze the diversification problem from the perspective of risk-averse investors and risk-seeking investors. Second, we prove that investors’ optimal choices will be similar if their utility functions are not too distant, independent of their tolerance (or aversion) to risk. Finally, we discuss investors’ attitude towards diversification when the choices available to investors depend on several parameters.     

Utility functions of equivalent form and the effect of parameter changes on optimum decision making

We derive a class of utility functions that are equivalent with respect to a well-defined functional form. We study the case of constant relative risk aversion (of some order) to investigate on different equivalence relations in order to determine the, possibly infinite, number of equivalence classes when utility functions satisfy a specific form. Then we apply our results to standard applications in economics and finance, for example, to the effect of price volatility on optimum hedging. We would like to thank Bernhard Eckwert and Itzhak Zilcha for constructive comments and suggestions.     

Risk preference and indirect utility in portfolio-choice problems

We consider a portfolio-choice problem with one risky and one safe asset, where the utility function exhibits decreasing absolute risk aversion (DARA). We show that the indirect utility function of the portfolio-choice problem need not exhibit DARA. However, if the (optimal) marginal propensity to invest is positive for both assets, which is true when the utility function exhibits nondecreasing relative risk aversion, then the DARA property is carried over from the direct to the indirect utility function.     

Probabilistic risk aversion with an arbitrary outcome set

This paper analyzes risk aversion when outcomes/consequences may not be measurable in monetary terms and people have fuzzy preferences over lotteries, i.e. they choose in a probabilistic manner. The paper shows that comparative risk aversion is well defined in a constant error/tremble model but not in a strong utility model.     

From sure to strong diversification

This paper presents a characterization of weak risk aversion in terms of preference for sure diversification. Similarly, we show that strong risk aversion can be characterized by weakening preference for diversification,as introduced by Dekel (Econometrica 57:163,1989), in what we call preference for strong diversification. We are grateful to Jean-Yves Jaffray, Peter Wakker and anonymous reference for very helpful suggestions and comments.     

Consumption and precautionary saving: An empirical analysis under both financial and environmental risks

This paper studies the empirical relationship between consumption and saving under two different sources of uncertainty: financial risk and environmental risk. The analysis is carried out using time series data for six advanced economies in the period 1965–2007.The results support the theoretical conclusions that both financial risk alone and the interaction between financial and environmental risks influence consumption. Moreover, we suggest a solution to some shortcomings which affect the empirical analysis performed with one-argument utility functions. Finally, we provide new estimates of indexes of relative risk aversion and relative prudence, as well as relative preference of environmental quality.