Narrow Results

To investigate the effect of short-selling constraints on investor behavior, we formulate an optimal stopping model in which the decision to cover a short position is affected by two short sale-specific frictions — margin risk and recall risk. Margin risk is introduced by assuming that a short seller is forced to close out their position involuntarily if they cannot fund margin calls (since short sales are collateralized transactions). Recall risk is introduced by permitting the lender to recall borrowed stock at any time, once again triggering an involuntary close-out. Examining the effect of these frictions on the optimal close-out strategy and associated value function, we finding that the optimal behavior can be qualitatively different in their presence. Moreover, these frictions lead to a substantial loss in value, relative to the first-best situation without them (a reduction of approximately 17% for our conservative base-case parameters). This significant effect has important implications for many familiar no-arbitrage identities, which are predicated on the assumption of unfettered short selling.

We formulate a short-selling strategy of a stock and seek the optimal timing of short covering in the presence of a random recall and a loan fee rate in an illiquid stock loan market. The aim is to study how the optimal trading strategy of the short-seller is influenced by the relevant features of the stock loan market. We consider a regime-switching stock price model that captures the transition in between the bull and the bear markets. The solution to the optimal stopping problem is obtained in closed-form based on the techniques in Guo and Zhang (2005). We provide the numerical example to illustrate of importance of a regime-dependent stopping rule for the short-seller's problem.