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Margins on short sales and equilibrium price indeterminacy. (English) Zbl 1388.91140

Summary: This paper studies the price and trading impact of margin rules for short selling within the context of H. Markowitz [“Portfolio selection”, J. Finance 7, 97–112 (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 E. M. Miller’s [“Risk, uncertainty, and divergence of opinion”, J. Finance 32, No. 4, 1151–1168 (1977; doi:10.1111/j.1540-6261.1977.tb03317.x)] prediction to a multi-asset context.

MSC:

91G10 Portfolio theory
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