A theory of price variability and trading volume: The case of odd-lot trading.

Abstract

This paper develops and tests a partially-revealing rational expectations theory of the joint behavior of price variability and trading volume in the stock market. The model is able to explain many of the previously documented empirical observations. The key elements in the model are (i) the presence of liquidity (noise) trading, (ii) a random information arrival process, and (iii) investor revaluations that have a component of concordance and a component of discordance among investors. Prices reflect the concordance and volume of trade the discordance among investors. Both prices and volume are affected by noise trading. This gives rise to testable implications for the univariate and bivariate time-series behavior of price variability and trading volume. The model is tested using aggregate data on odd-lot trading activity, NYSE trading volume, returns on CRSP value-weighted index, and returns on a small-stock portfolio of firms. Empirical results support the theory in the paper. In the case of aggregate NYSE data, the strength of the price variability-volume relation can be predicted using odd-lot data. In the case of small-stocks, the profusion of liquidity trading at the turn of the year provides a unique opportunity to test the model. Consistent with the theory presented here, it is found that, in the case of small-stock portfolio, the widely-documented positive correlation between price variability and volume is exclusively a turn-of-the-year phenomenon. Furthermore, new empirical results about the time-series behavior of bid-ask spreads are also documented. It is shown that the spread size varies inversely with the level of uninformed trading. It is argued that the size of the wedge between bid prices and ask prices is a good indication of the level of noise trading in the market.