Risk Aversion, the Labor Margin, and Asset Pricing in DSGE Models (original) (raw)

Risk Aversion and the Labor Margin in Dynamic Equilibrium Models

2012

The household's labor margin has a substantial effect on risk aversion, and hence asset prices, in dynamic equilibrium models even when utility is additively separable between consumption and labor. This paper derives simple, closed-form expressions for risk aversion that take into account the household's labor margin. Ignoring this margin can dramatically overstate the household's true aversion to risk. Risk premia on assets priced with the stochastic discount factor increase essentially linearly with risk aversion, so measuring risk aversion correctly is crucial for asset pricing in the model.

Risk aversion, risk premia, and the labor margin with generalized recursive preferences

2012

A flexible labor margin allows households to absorb shocks to asset values with changes in hours worked as well as changes in consumption. This ability to absorb shocks along both margins greatly alters the household's attitudes toward risk, as shown by Swanson (2012). The present paper extends that analysis to the case of generalized recursive preferences, as in Epstein and Zin (1989) and Weil (1989), including multiplier preferences, as in Hansen and Sargent (2001). Understanding risk aversion for these preferences is especially important because they are the primary mechanism being used to bring macroeconomic models into closer agreement with asset pricing facts. Measures of risk aversion commonly used in the literature-including traditional, fixed-labor measures and Cobb-Douglas composite-good measures-show no stable relationship to the equity premium in a standard macroeconomic model, while the closed-form expressions derived in this paper match the equity premium closely. Thus, measuring risk aversion correctly-taking into account the household's labor margin-is necessary for risk aversion to correspond to asset prices in the model.

Implications of Labor Market Frictions for Risk Aversion and Risk Premia

A flexible labor margin allows households to absorb shocks to asset values with changes in hours worked as well as changes in consumption. This ability to absorb shocks along both margins can greatly alter the household's attitudes toward risk, as shown by Swanson (2012a). The present paper analyzes how those results are affected by labor market frictions and shows that: 1) risk aversion is higher in recessions, 2) risk aversion is higher in more frictional labor markets, and 3) risk aversion is higher for households that are less employable. Quantitatively, labor market flow rates in the U.S. and other OECD countries are large relative to the discount rate, implying that the cost of labor market frictions is small because frictions only delay adjustment. Thus, the frictionless formulas in Swanson (2012a,b) appear to be very good approximations in frictional labor markets as well.

Risk aversion in securities markets

Journal of Banking & Finance, 1988

This study extends the theoretical analysis and empirical research of risk aversion in securities markets. The analysis of the determinants of the market price of risk, part of an equilibrium modei of asset pricing, involves relative risk aversion and is carried out for the continuous time case. Micro relationships which are equilibrium demand functions of individual investors are derived; on the macro level the determinants of the market price of risk are determined. The analysis is carried out first assuming that a!! assets are marketable; then this assumption is relaxed and non-marketable assets (human-capital) are considered. Finally, we consider explicitly the effects of uncertain inflation on risk aversion. The major empirical results are: the assumption of constant relative risk seems to be a reasonable approximation of the market; secondly, the coefficient of relative risk aversion seems to be greater than unity; thirdly, for the first time trends in risk aversion were estimated. where r. is the return on an asset uncorrelated with the market return (a zero-beta asset), and Yk is the ratio of the kth individual wealth (wk) to total wealth W A specific form of the assumption of an infinitesimal planning horizon and no finite changes in value in an infinitesimal period, would imply for a finite interval a log normal distribution of returns.* If we assume that all wealth is invested in risky assets, i.e. W= K we get here an identical expression to the discrete case, except that y. is substituted for rf. It should be noted that the measure of absolute risk aversioa in the discrete case is replaced here by the relative measure, i.e. wkak =ck. Parallel to Friend and Blume (1975) we apply the continuous time solution to the situation in which not all wealth is invested in risky assets, but rather as in the discrete case, part of the wealth is invested in risk-free asset with a certain rate of return. *See Merton (19?3), I! Landskroner, Risk aversion in securities markets 133 We assume in common to all studies cited above homogenous expectations for all individuals. In the literature we find models focusing on differences in expectations or on differences in attitudes towards risk. The reason that different models focus on one or the other is that to understand how each of them works they are best studied in isolation-in our study, to understand the effects of differences in attitudes towards risk on portfolio allocation we assume that individuals have the same expectations.* We can write the wealth dynamics for individual k in stochastic difference equation form and then, by taking limits, in stochastic differential equation form. Thus for individual k, f&t +dr) = Wkr[ 1 + (1-ak)rf dt + a&, dt], (4) where LI indicates a random variable; t a point in time; ak the proportion invested in risky assets (the existence of 'many risky assets does not pose a problem where the separation theorem holds). First assume that the market rate of return ?,,,, il generated by a continuous Gaussian (Wiener) process:3

1SUBSTITUTION and Risk Aversion: Is Risk Aversion Important for Understanding Asset PRICES?1

2005

The log utility function is widely used to explain asset prices. It assumes that both the elasticity of substitution and relative risk aversion are equal to one. Here I show that much of the same predictions about asset prices can be derived from a time-non-separable expected utility function that assumes an elasticity of substitution close to unity but does not impose restrictions on risk aversion to bets in terms of money. 1 I would like to thank Jeff Campbell and Greg Huffman for useful comments on an earlier draft.

Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies

2001

In this article, we show how to analyze analytically the equilibrium policies and prices in an economy with a stochastic investment opportunity set and incomplete financial markets, when agents have power utility over both intermediate consumption and terminal wealth, and face portfolio constraints. The exact local comparative statics and approximate but analytical expression for the portfolio policy and asset prices are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility. We then use this method to study a general equilibrium exchange economy with multiple agents who differ in their degree of risk aversion and face borrowing constraints. We characterize explicitly the consumption and portfolio policies and also the properties of asset returns. We find that the volatility of stock returns increases with the cross-sectional dispersion of risk aversion, with the cross-sectional dispersion in portfolio holdings, and with the relaxation of the constraint on borrowing. Moreover, tightening the borrowing constraint lowers the riskfree interest rate and raises the equity premium in equilibrium.

Asset Pricing with Endogenous State-Dependent Risk Aversion

Social Science Research Network, 2020

We present an economy where aggregate risk aversion is stochastic and state-dependent in response to information about the wider economy. A factor model is used to link aggregate risk aversion to the business cycle and to handle high-dimensionality of the information about the economy. Our estimated aggregate risk aversion is counter-cyclical and varies with news about economic booms and busts. We find new evidence of volatility clustering of risk aversion around recessions. In addition to the price of consumption risk associated with consumption risk, time variation in risk aversion introduces risk preferences as a new component of the risk premium.

Preferences, consumption smoothing, and risk premia

1997

Risk premia in the consumption capital asset pricing model depend on preferences and dividend. We develop a decomposition which allows a separate treatment of both components. We show that preferences alone determine the risk-return tradeoff measured by the Sharpe-ratio. In general, the risk-return trade-off implied by preferences depends on the elasticity of a preference-based stochastic discount factor for pricing assets with respect to the consumption innovation. Depending on the particular specification of preferences, the absolute value of this elasticity can coincide to the inverse of the elasticity of intertemporal substitution (e.g. for habit formation preferences) or the coefficient of relative risk-aversion (e.g. for Epstein-Zin preferences). We demonstrate that preferences based on a small elasticity of intertemporal substitution, such as habit formation, produce small risk premia once agents are allowed to save. Departing from the complete markets framework, we show that uninsurable risk can only increase the Sharpe-ratio and risk premia if dividends are correlated with individual consumption.

Substitution, Risk Aversion and Asset Prices: An Expected Utility Approach

The standard power utility function is widely used to explain asset prices. It assumes that the coefficient of relative risk aversion is the inverse of the elasticity of substitution. Here I use the Kihlstrom and Mirman (1974) expected utility approach to relax this assumption. I use time consistent preferences that lead to time consistent plans. In our examples, the past does not matter much for current portfolio decisions. The risk aversion parameter can be inferred from experiments and introspections about bets in terms of permanent consumption (wealth). Evidence about the change in the attitude towards bets over the life cycle may also restrict the value of the risk aversion parameter. Monotonic transformations of the standard power utility function do not change the predictions about asset prices by much. Both the elasticity of substitution and risk aversion play a role in determining the equity premium.

Standard Risk Aversion and the Demand for Risky Assets in the Presence of Background Risk

2000

We consider the demand for state contingent claims in the presence of a zero-mean, nonhedgeable background risk. An agent is defined to be generalized risk averse if he/she reacts to an increase in background risk by choosing a demand function for contingent claims with a smaller slope. We show that the conditions for standard risk aversion: positive, declining absolute risk aversion and prudence are necessary and sufficient for generalized risk aversion. We also derive anecessary and suÆcient condition for the agent's derived risk aversion to increase with a simple increase in background risk.