Capital asset market equilibrium with liquidity risk, portfolio constraints, and asset price bubbles

Abstract

This paper derives an equilibrium asset pricing model with endogenous liquidity risk, portfolio constraints, and asset price bubbles. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Asset price bubbles are generated by the existence of portfolio constraints, e.g. short sale prohibitions and margin requirements. Under a restrictive set of assumptions, we prove a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including both liquidity risk and asset price bubbles. This yields a generalized intertemporal and consumption CAPM for our economy. In contrast to the traditional models without liquidity risk or asset price bubbles, there are additional systematic liquidity risk and asset price bubble factors which are related to the stock return’s covariation with liquidity risk and asset price bubbles.