We study the aftermarket for 72 initial public offerings (IPOs) using comprehensive trade and quote-change data from every market maker for the first three days of trading. Underwriters quote higher bid prices than other market makers for issues that commence trading at or below the offer price. Underwriters repurchase large quantities of stock in the aftermarket without risk by overselling the issue by the amount of the overallotment option. If the IPO is hot, the overallotment option is exercised. If not, the short position is covered with aftermarket selling. We discuss several reasons for underwriter support.

SOES bandits are individual investors who use Nasdaq's Small Order Execution System (SOES) for day trading. Their average profit per trade is small, but they trade dozens or hundreds of times per week. Bandits usually establish a position before most market-makers have updated their quotes, and lay off the position at favorable prices through Instinet or SelectNet. It is noteworthy that they trade profitably with market-makers despite having less information. Bandits keep the profits and bear the losses from their trades. Thus they have greater incentives to trade well than the employees of market-making firms.

Nasdaq's Small Order Execution System (SOES) allows orders to be submitted by computer, thereby assuring rapid execution at quoted prices. We examine trading in the 20 largest Nasdaq stocks around the time of a rule change that reduced the largest SOES trades from 1000 to 500 shares. We show that SOES trades contain information about short-term price movements and that SOES trading declined dramatically with the rule change. However, quoted and effective spreads were unaffected by the rule change.