Short Selling, Unwinding, and Mispricing

The paper is concerned with the influence of index arbitrage trading on the mispricing process in the presence of market frictions. Specifically, it highlights the as yet ignored impact of short selling restrictions in the spot market and early unwinding opportunities on the mispricing process. A multiperiod equilibrium model of the mispricing between a stock index and index futures is developed to study the impact of optimal arbitrage trading on the mispricing. The model leads to the following main results. First, the mean reversion of the mispricing is arbitrage induced. Second, arbitrage trading and mean reversion of the mispricing depend on the behavior of the mispricing in the past. Third, the impact of arbitrage trading on the mispricing increases with a decreasing time to maturity of the futures contract. Finally, arbitrage trading keeps the mispricing away from zero in certain cases. This suggests that mispricing may not exist despite arbitrage trading but exist due to arbitrage trading. The hypotheses derived from the theoretical model are tested using intraday data for the German stock index DAX and DAX futures. Results concerning the level, the mean reversion and the path dependence of the mispricing are provided. They support the hypotheses stated above. Overall, the empirical evidence suggests that short selling restrictions and early unwinding opportunities are very influential factors for the behavior of the mispricing.