Cladistic Asset Pricing

Abstract

In most contexts in which agents possess long-lived private information about a firm's value, they will also have repeated access to new information over time. We develop a method for analyzing informed trade in such environments. We exploit the stationary structure of the economy to map informed agents' optimization problems in the time domain - maximize discounted expected trading profits - into the frequency domain. We then use control-theoretic arguments to solve for equilibrium trading strategies, pricing, profits and the information content of prices. We derive explicit characterizations of equilibrium outcomes - trading strategies, pricing, profits and information transmission - when informed agents see distinct AR(1) innovations to the asset value each period. We characterize analytically how equilibrium outcomes are affected by the amounts of private information or noise trade. Finally, we provide a practical method to approximate equilibrium trading strategies. We prove that the approximation converges to the true equilibrium, and then use it to characterize the equilibrium quantitatively to derive the impact of persistence in firm value and the degree of competition among informed agents on equilibrium outcomes.