What Drives Stochastic Risk Aversion? (original) (raw)

Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model

1989

When tastes are represented by a class of generalized preferences which-unlike traditional Von-Neumann preferencesdo not confuse behavior towards risk with attitudes towards intertemporal substitution, the true beta of an asset is, in general, an average of its consumption and market betas. We show that the two parameters measuring risk aversion and intertemporal substitution affect consumption and portfolio allocation decisions in symmetrical ways. A unit elasticity of intertemporal substitution gives rise to myopia in consumption-savings decisions (the future does not affect the optimal consumption plan), while a unit coefficient of relative risk aversion gives rise to myopia in portfolio allocation (the future does not affect optimal portfolio allocation). The empirical evidence is consistent with the behavior of intertemporal maximizers who have a unit coefficient of relative risk aversion and an elasticity of intertemporal substitution different from 1.

Essays in Empirical Asset Pricing

Thesis Columbia University 2007, 2007

This dissertation consists of two chapters, all of which attempt to shed some light on what constitutes the time-varying risk premia in financial markets. The first chapter demonstrates that monetary policy shocks identified from New-Keynesian dynamic stochastic general equilibrium(DSGE) models explain the risk premia in stock markets. Indeed, the implied ICAPMs explain the value and the industry premia for the periods of 1980 to 2004. In particular, the permanent monetary policy shocks to inflation target capture the value premium and part of industry risk premium once I account for the capital market imperfection endogenously in New-Keynesian models. The shocks to investment technology, as a main determinant of the external finance premium, are also important for understanding the value premium. The second chapter examines determinants of stochastic relative risk aversion in conditional asset pricing models by utilizing nonlinear state space model with GARCH specification. After imposing general version of the conditional CAPM or ICAPM, I develop non-ad-hoc empirical models and search for valid specifications of relative risk aversion along with appropriate hedging components. I discover that the surplus consumption ratio implied by the external habit formation model is the most important determinant of time varying relative risk aversion. The CAY of Lettau and Ludvigson (2001a) without a lookahead bias also captures part of relative risk aversion. The short term interest rate(RREL) has explanatory power for hedging components. I use the implied conditional asset pricing models in explaining the cross-section of average returns on either the Fama-French 25 size and book-to-market sorted portfolios alone or with 30 industry portfolios. I find that the chosen conditional CAPM and ICAPM with time-varying relative risk aversion and a hedging component are at least comparable to or better than the Fama-French three-factor model for the sample periods 1957 to 2005.

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 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

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.

Risk Preferences Heterogeneity: Evidence from Asset Markets

Review of Finance, 2002

Using asset market data, as well as theoretical relations between investors' preferences, option-implied, risk-neutral, probability distribution functions (PDFs,) and index-implied, actual, PDFs, this paper extracts a time-series of investors' relative risk aversion (RRA) functions. Based on results recently derived by Benninga and Mayshar (2000), these functions are used to recover the evolution of risk preferences heterogeneity. Applying non-parametric estimation on European call options written on the S&P500 index, we find that: (i) the RRA functions are decreasing; and (ii) the constructed risk preferences heterogeneity series is positively correlated in a static, as well as a dynamic, setup with a prevalent proxy for investors heterogeneity, namely, the spread between auction-and market-yields of Treasury bills.

Countercyclical and Time-Varying Risk Aversion and Equity Premium

SSRN Electronic Journal, 2016

This paper tests the counter-cyclicality of aggregate risk aversion and price of market risk using a novel testing approach introduced in Antell and Vaihekoski (2015) for conditional asset pricing models. Cohen et al. (2015) report experimental evidence that the risk aversion is countercyclical, although empirical support from financial studies is at best inconclusive. This paper applies the new testing approach for the Merton (1973, 1980) model. The testable implications link the realized equity premium to, among others, changes in conditional variance, its long-term persistence, and changes in the time-varying risk aversion. Empirically, the testing is conducted using monthly US stock market data from 1928 to 2013, and GARCH models to estimate time-varying variance. Various methods to model economic expectations are compared. Unlike the traditional estimation approach, the results from the new estimation approach give clear support for time-varying and countercyclical risk aversion.

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.

Substitution and Risk Aversion: Is Risk Aversion Important for Understanding Asset Prices?

2004

This paper uses a recursive time-non-separable expected utility function to separate between the intertemporal elasticity of substitution (IES) and a measure of relative risk aversion to bets in terms of money (RAM). Risk premium does not require risk aversion. Changes in IES have large effects on asset prices but changes in risk aversion have only a small effect on asset

RISK AVERSION AND THE EFFICIENT MARKETS MODEL FOR STOCK PRICES

The statistical and economic importance of the efficient markets model with varying discount factors is tested on monthly data from the Athens Stock Exchange over the period 198 1-1993. The time-series properties of the relevant information variables are determined by means of formal statistical tests and the relationship between stock price volatility and risk aversion is studied for admissible values of the Arrow-Pratt measure of relative risk aversion. In sharp contrast with existing evidence from well-organized markets, the results show a remarkably accurate fit of the model. The present value model for stock prices is among those simple stochastic dynamic models that have several important features. It is well-grounded on economic theory, it assumes that investors act in a rational manner, and it can be tested by means of alternative econometric techniques. However, there is considerable