Asset pricing models have relied on the idea that a representative agent chooses consumption and a portfolio of assets in order to maximize her expected utility. However, this paradigm has led to a great literature describing such pricing anomalies as the equity premium puzzle, the risk-free rate puzzle, variability, predictability, small firm mispricing, weekend and January effects and so on. New assumptions and features have been added to the models in attempt to explain these anomalies. Few papers, in comparison, have taken a step back to the most fundamental initial assumptions of the models to determine the validity of these initial assumptions. Researchers have held tightly to the assumption that utility functions are time separable and that investor risk preferences are constant.
Further, these two assumptions imply that the elasticity of intertemporal substitution is constant and is the inverse of risk aversion. Constantinides (2002) argues that “relaxing the assumption of convenience that preferences are time separable drives a wedge between the preference properties of risk aversion and intertemporal substitution, within the class of von Neumann-Morgenstern preferences. Further work along these lines may enhance our understanding of the price behavior along the business cycle with credibly low risk-aversion coefficient.” Before we completely label the representative-agent paradigm as a failure, we must first better understand the limitations of the traditional assumptions regarding investor preferences.
An agent’s utility function describes how the agent makes decisions. Two important parameters within the utility function are the agent’s level of risk aversion and the agent’s coefficient of intertemporal substitution. An agent is risk averse if for any arbitrary gamble a certain amount with payoff equal to the expected value of the gamble is always preferred to taking the gamble. This is an immediately resolved decision. Either the investor chooses the certain amount or chooses the gamble.
The elasticity of intertemporal substitution describes the expected change in consumption growth as a function of expected changes in the return of an investment. This parameter describes an intertemporal decision. The investor chooses how his consumption changes in the future. These two parameters clearly describe two different affects yet the commonly used time separable utility functions force the two parameters to be inversely related when there is no a priori reason to believe this to be true. Further, there is no consensus as to the values of the two parameters and we have little knowledge of how they change through time.
We shed light on these issues by using options and the Epstein-Zin utility function to simultaneously estimate the representative agent’s coefficient of relative risk aversion (RA) and elasticity of intertemporal substitution (EIS). Epstein and Zin (1989) develop a class of utility functions that breaks the functional relationship between RA and EIS that is inherent in time separable utility functions. The cost is a more complicated function describing agent preferences. However, time-separability is a special case of the Epstein-Zin function. When RA is the inverse of EIS then the function reduces to the power utility function.
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