Margins on short sales and equilibrium price indeterminacy

This paper studies the price and trading impact of margin rules for short selling within the context of Markowitz (1952). Our analysis is based on a newly obtained analytic solution for optimal portfolio holding under arbitrary margin rules. It is shown that heterogeneity in margins may have pricing effects and lead to price indeterminacy, particularly in the presence of derivative trading. Existence of equilibrium, along with a characterization theorem on the equilibrium outcome, is proved when investors have heterogeneous beliefs and different margins. Partial equilibrium analyses were carried out for the special case where investors agree on the volatility structure, but may hold different beliefs on expected payoffs. Upward deviations from the CAPM were discovered, extending Miller (1977)'s prediction to a multi-asset context.