Miller (1977) demonstrated that if investors have heterogeneous beliefs and short sales are restricted, trade of a security will disproportionately reflect positive information, generating a price bubble. As this intuition applies most relevantly to short intervals of trade, a question arises as to the longevity of such a bubble. In this paper, I argue that a bubble effected by short-sale constraints persists only if agents cannot distinguish between order flow caused by positive information or order flow caused by the constraints. If the constraint is common knowledge, it should have no effect on the long-term pricing of the stock. If, however, the constraint is random and unknown, a price bubble may form.

The effectiveness of any sanction depends on the costs of avoiding its restrictions. We examine whether bearish option strategies were substitutes for short sales during the September 2008 short-sale ban. We find a significant diminution in option volumes and a significant increase in option bid-ask spreads for banned stock relative to unbanned stock during the ban period. Apparent violations of the put-call parity bound became significantly more frequent for banned stocks during the ban period. We conclude that the ban acted as an effective restriction on trading in options.