Belief-dependent Utilities, Aversion to State-uncertainty and Asset Prices
This Paper reinterprets standard axioms in choice theory to introduce the concepts of ‘belief dependent’ utility functions and aversion to ‘state-uncertainty’. It shows that this type of preference helps to explain the various stylized facts of asset returns, including a high equity risk premium, a low risk-free rate, a high return volatility, stock return predictability and volatility clustering. In one particular specification consistent with habit formation preferences, I also argue that ‘aversion to state-uncertainty’ gives rise to ‘aversion to long-run risk’, that is, to the uncertainty surrounding the long-run average of future consumption. In order to solve for asset prices and returns under general conditions about the hidden state variable, the Paper also develops a discretization methodology to obtain approximate analytical solutions. In a parsimonious parametrization, I then show that the model calibrated to real consumption generates unconditional moments for asset returns that closely match the empirical ones. Finally, due to the estimated time-variation in the dispersion of the conditional distribution on the drift rate of consumption, the model also generates a time series of conditional return volatility in line with the ex-post integrated volatility of stock returns.
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agents approximation asset prices assume assumption aversion to state-uncertainty Axiom belief belief-dependent utility functions Campbell and Cochrane conditional price-dividend ratios conditional probability constant consumption data consumption growth Corollary defined denote dependent utility function dispersion displays aversion drift rate e.g. Campbell E\dR Economics eigenvalues elasticity of intertemporal equity premium expected returns formulas given habit formation model Hence high equity implies inequality interest rate intertemporal substitution investors Ito's lemma Kalman filter Kitagawa Knightian uncertainty long-run risk lotteries marginal utility matrix mean P/D Mean Square Error obtain Ornstein-Uhlenbeck process Panel paper parameters posterior distribution Prediction Error preferences probability distribution Proof of Proposition pure jump model pure jump process rate of consumption real consumption relative risk aversion return volatility risk premium risk-free rate RMSE Root Mean Square stochastic stochastic volatility stock prices stock returns structural breaks Theorem time-varying uncertainty utility of consumption vector Veronesi Wiener process yields