Transaction costs, market depth, and short-term return predictability.

Abstract

Short-term stock returns, especially portfolio returns, are surprisingly predictable. The explanation presented here is that departures from random walk are due to the presence of transaction costs combined with a particular market microstructure. Specifically, I introduce a model in which an uninformed market maker quotes prices and trades with informed agents and strategic liquidity traders. The market maker is constrained to (a) make zero profits, and (b) offer as flat a price-quantity schedule as possible (i.e., the market is as deep as possible). These constraints imply that price changes are small following large orders. To prevent manipulation by strategic liquidity traders, market maker quote changes following small orders must be proportionately smaller as well. I also show that market makers use only the order flow in their own security to determine price, optimally ignoring marketwide information. This, combined with the fact that informed traders submit small orders in this continuous-time market, yields the main result: the quote midpoint generally does not equal the market maker's conditional expectation of the asset's intrinsic value. Since the bid and the ask continually lag changes in intrinsic value, there is short-term predictability in stock returns, which are represented in closed form using the mathematics of instantaneously controlled Brownian motion. The degree of predictability depends on only one input: the ratio of the proportional bid-ask spread to the standard deviation of changes in the asset's intrinsic value. Specifically, the model predicts high portfolio autocorrelations for firms with large relative bid-ask spreads, and it predicts that small-spread stocks will lead large-spread stocks. In addition, the model implies positive autocorrelation in individual security returns, a return distribution peaked at zero, as well as the potential for volatility persistence; the model's predictions are confirmed by the data. Using reasonable parameter values, simulations and closed-form results demonstrate that predicted return moments calibrate closely to observed NASDAQ-NMS stock returns. I also find that, as predicted by the model, cross-sectional differences in return autocorrelations and the likelihood of zero returns are closely related to the relative bid-ask spread rather than the size of the firm.