A Dynamic Analysis of Bid-Ask Spreads with Multiple Trade Sizes

This paper studies how the trade size and the historical sequence of trades affect bid-ask spreads, investors’ trading strategies, and the market maker’s learning process in a multi-period economy. First, we show that there is a nonzero cut-off size below which informed traders never buy or sell, and that larger trade sizes have positive bid-ask spreads, while smaller sizes do not. Then, we prove that the cut-off size decreases stochastically . We also derive the functional relationship between bid-ask spreads and trade sizes and show that bid- ask spreads are monotonically increasing in trade sizes. Moreover, we prove that when additional trade sizes are introduced to the market, the market maker’s learning process can be impaired and the bid-ask spreads for the previously existing trade sizes can vanish under a mild condition. We prove that the smaller trade sizes that do not have a positive bid-ask spread result in zero price change, while for larger trade sizes the rate at which price change increases is a decreasing function of the trade size in all trading periods. Most of our results are broadly consistent with the empirical findings.