Limited Arbitrage and Short Sales Restrictions: Evidence from the Options Markets

Abstract

In this paper, we investigate empirically the well-known put-call parity no-arbitrage relation in the presence of short sale restrictions. We use a new and comprehensive sample of options on individual stocks in combination with a measure of the cost and difficulty of short selling, specifically the spread between the rate a short-seller earns on the proceeds from the sale relative to the normal rate (the rebate rate spread). We find statistically and economically significant violations of put-call parity that are strongly related to the rebate rate spread. Stocks with negative rebate rate spreads exhibit prices in the stock market that are up to 7.5% greater than those implied in the options market (for the extreme 1% tail). Even after accounting for transaction costs in the options markets, these violations persist and their magnitude appears to be related to the general level of valuations in the stock market. Moreover, the extent of violations of put-call parity and the rebate rate spread for individual stocks are significant predictors of future stock returns. For example, cumulative abnormal returns, net of borrowing costs, over a 2½-year sample period can exceed 70%. It is difficult to reconcile these results with rational models of investor behavior, and, in fact, they are consistent with the presence of over-optimistic irrational investors in the markets for some individual securities.