## Equilibrium asset pricing with time-varying pessimism

### Sbuelz, Alessandro ; Trojani, Fabio

We present a flexible analytical framework that incorporates the equilibrium impact of a (possibly state dependent) sentiment for pessimism in continuous time intertemporal asset pricing. State dependent pessimism comes from a state dependent confidence in the reference belief on equity returns dynamics and implies conservative optimal policies precisely in states where such confidence is low. In... Plus

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- We present a flexible analytical framework that incorporates the equilibrium impact of a (possibly state dependent) sentiment for pessimism in continuous time intertemporal asset pricing. State dependent pessimism comes from a state dependent confidence in the reference belief on equity returns dynamics and implies conservative optimal policies precisely in states where such confidence is low. In the setting of an homogeneous exchange economy we characterize the impact of pessimism on key equilibrium quantities, including the implied equity dynamics, the equilibrium interest rate and the corresponding equity premia and worst case equity premia. Due to the complexity of the implied optimization problems we adopt a perturbative approach to compute finite order approximations for these quantities. We find that pessimism induces directly lower equilibrium interest rates and higher equity premia, while it impacts only indirectly - through the interplay of risk and model uncertainty aversion - the expected returns on equity, their variances and covariances with the opportunity set process and the implied worst case equity premia. Thus, to first order these latter variables are fully determined by the standard risk aversion parameter. We compute some higher order asymptotics attempting to quantify the direct and indirect impacts of pessimism in equilibrium for several examples of a pessimistic exchange economy with intermediate consumption and stochastic opportunity set. For all these examples we find that the indirect impact of pessimism on equity dynamics and worst case equity premia is negligible, while the influence on equity premia and interest rates can be significant already for moderate amounts of pessimism.. This confirms the results implied by a pure first order analysis. Therefore, in the setting of a representative agent exchange economy a pessimistic concern for model uncertainty can help explaining part of the equity premium puzzle, while maintaining low interest rates and leaving virtually unaffected some target parameters in the equilibrium equity dynamics.