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.

We document strong time-series momentum effects in individual stocks in the US markets from 1927 to 2017. Time-series momentum is not specific to sub-periods, firm sizes, formation- and holding-period lengths, or geographic markets. The effects persist after controlling for standard risk factors. Time-series momentum effects are conditional on the market state, the information discreteness of the constituent stocks and investor sentiment. We propose two alternative implementations, revised time-series momentum and dual momentum, which generate even higher profits than standard time-series momentum.

We use a simple two-stage dividend growth model to connect profitability growth and firm scale to stock returns. In this framework, both the magnitude and the length of the first-stage growth play a key role in determining returns. Using current profitability growth to estimate magnitude and firm scale as inverse proxy for length, we predict that future returns should increase with current profitability growth but, crucially, the effect should diminish with firm scale. Across a range of empirical tests, we find strong evidence in support of our model determinants and predictions. Our findings are not explained by an array of associated, potentially confounding variables.