On the (Market Microstructure) Origins of the Return Distribution 

Abstract

We propose a reduced-form microstructure model of price formation in an order-driven market. In this framework, the shape of the return distribution over a given interval is determined jointly by the distribution of market orders and the average shape of the limit order book over the same interval. We derive the closed form solutions for the first four central moments of the return distribution as functions of the mean and variance of the market order distribution and slopes, imbalance and convexity of the bid and ask sides of the limit order book. For a symmetric market order distribution, (1) the mean and skewness of the return distribution are increasing functions of the LOB imbalance (the ratio of the slopes of the ask and bid sides); (2) the return variance is a decreasing function of the LOB convexity (the ratio of the slopes of the higher and lower levels); (3) the return kurtosis is an increasing function of the LOB convexity. We test and provide empirical support for the predictions of our model using comprehensive ultra-high-frequency limit order book data for a sample of NYSE stocks from 2002 to 2012. We establish the causal effect of the shape of the limit order book on the distribution of stock returns using RegSHO as an exogenous shock to the shape of the limit order book.

Keywords: Limit Order Book, Imbalance, Convexity, Skewness, Kurtosis, Quantiles, Market Order Distribution

JEL Classification: G18