THE SHARPE RATIO AND PREFERENCES: A PARAMETRIC APPROACH (original) (raw)
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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.
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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.
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SSRN Electronic Journal, 2000
We analyze consumption and asset pricing with recursive preferences given by Kreps-Porteus stochastic differential utility (K-P SDU). We show that utility depends on two state variables: current consumption and a second variable (related to the wealth-consumption ratio) that captures all information about future opportunities. This representation of utility reduces the internal consistency condition for K-P SDU to a restriction on the second variable in terms of the dynamics of a forcing process (consumption, the state-price deflator, or the return on the market portfolio). Solving the model for (i) optimal consumption, (ii) the optimal portfolio, and (iii) asset prices in general equilibrium amounts to finding the process for the second variable that satisfies this restriction. We show that the wealth-consumption ratio is the value of an annuity when the numeraire is changed from units of the consumption good to units of the consumption process, and we characterize certain features of the solution in a non-Markovian setting. In a Markovian setting, we provide a solution method that it quite general and can be used to produce fast, accurate numerical solutions that converge to the Taylor expansion.
Substitution, risk aversion, taste shocks and equity premia
Journal of Applied Econometrics, 1998
Zin for allowing us access to the returns data. We are also indebted to Stephen Gordon for useful discussions and comments. Normandin acknowledges nancial support from Social Sciences and Humanities Research Council of Canada. St-Amour acknowledges support from Universit e L a v al. We retain full responsibility for any errors.
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.
Substitution and Risk Aversion: Is Risk Aversion Important for Understanding Asset Prices?
Vanderbilt University Department of Economics Working Papers, 2004
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 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.
The Term Structure of Risk Premia with Heterogeneous Recursive Preferences and Beliefs
SSRN Electronic Journal, 2017
I investigate the effect of preference and belief heterogeneity on the term structure of risk premia in a continuous-time time economy with Epstein-Zin-Weil preferences. The slope of the term structure of equity risk premia is driven by heterogeneity in the agents' own prices of risk and the sensitivity of the equity market valuation to the changes in economic conditions. As a result, the slope can switch its sign in response to a significant shock to the aggregate consumption. Significant negative shocks shift the consumption and wealth toward the more "pessimistic" agent i.e. the agent with a higher risk aversion or more pessimistic beliefs. As a result, the equity market valuation changes from being pro-cyclical to counter-cyclical, which inverts the term structure. Thus, the model can generate a switch in the sign of the slope of the term structure of the dividend strip risk premia after the 2008-2009 global financial crisis, a result consistent with recent empirical studies and my own calibration based on a proprietary dataset of dividend swap prices.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights a b s t r a c t This paper explores the implications of a novel class of preferences for the behavior of asset prices. Following a suggestion by Marshall (1920), we entertain the possibility that people derive utility not only from consumption, but also from the very act of saving. These ''saving-based'' preferences are related to models of habit formation and the spirit of capitalism, but incorporate the feature that people have anticipatory habits because they care about the future accumulation of wealth. We derive the Euler equations for these preferences and estimate them with GMM. Our estimates suggest that the preference for saving is economically significant.