Equilibration Under Competition in Smalls : Theory and Experimental Evidence

Many real-world markets are competitive only in smalls, taken to mean that price taking applies only to small orders. Starting from this observation, a theory of equilibration is derived where orders are optimal merely in a local sense. Prices are assumed to adjust in the direction of the order imbalance. In the context of financial markets populated with mean-variance optimizing agents, the theory predicts that a security's price will correlate with excess demands in other securities, and the sign of this correlation is the same as that of the covariance of the final payoffs. In the short run, prices tend to a local equilibrium where the risk-aversion weighted endowment portfolio (RAWE) is mean-variance optimal. Relative to the market portfolio, RAWE overweighs securities that are held disproportionally by more risk averse agents; RAWE puts less weight on securities that are held primarily by more risk tolerant agents. Throughout equilibration, portfolio separation is violated generically, and violations are more extreme when payoff covariances are positive. For a variety of patterns of initial allocations (including identical initial holdings), the equity premium is larger at the outset than at (CAPM) equilibrium. All these implications are confirmed in experiments