| This dissertation studies the underlying microeconomic forces driving market volatility and risk premium in financial markets. In a non-stationary economy, agents do not know how the probability distribution of returns may change over time. This naturally leads to diversity of opinions among investors. Subjective beliefs are represented by Ito processes and the Rational Beliefs Theory (Kurz [1994], [1997]) is extended from discrete to continuous-time. Agents are assumed to use the data to learn the empirical distribution of the observables and individual beliefs are constrained to be compatible with it. A general algorithm to enforce such rationality condition is introduced, based on the Efficient Method of Moments (Gallant and Tauchen [1996], Gallant and Long [1997]). As an application to this methodology, we present the two assets case. Agents form subjective beliefs about the future expected risk-premium. Optimistic (or pessimistic) agents believe that the premium during a given period of time will be larger (or smaller) than the long-run average, which typically leads the optimistic agents to buy the stock and pessimistic agents to sell. As a result, agents' beliefs affect prices. Two forces play a central role in the model: forces of agreement versus forces of disagreement among agents. The correlation structure among beliefs balances both forces and plays a central role in determining equilibrium prices which satisfy the agents' rationality conditions, which make the beliefs of every agent compatible with the empirical distribution generated by the equilibrium prices. The model is fitted to U.S. data and matches a large set of moments that capture persistence in volatility and mean, as well as the shape of the joint distribution of observables (including for instance asymmetric fat tails in the distribution of stock returns). A central result of this study is that heterogeneous beliefs are necessary in order to match the empirical record. Indeed, asymmetry in the distribution of the states of beliefs is essential for the equilibrium to match the data. Additional analysis of the equilibrium dynamics of the states of beliefs yields deep insights into the underlying forces generating market volatility. Potential further applications to other markets are discussed. |
