Lead-Lag Effects When Prices Reveal Cross-Security Information

This paper introduces and analyses a model of cross-security information aggregation in a rational expectations equilibrium (REE). The model predicts a well-defined lead-lag structure between securities returns as a result of Bayesian information extraction from realised securities prices. Both leads and lags will be strongest between securities with highly correlated return processes, but only weakly correlated return innovations. Securities whose prices reveal highly precise signals will tend to lead other securities. The model has important implications for empirical testing of lead-lag effects between financial markets and instruments. As an application of the model, it is demonstrated that stock option returns will tend to lag the corresponding stock prices. Direct empirical tests of the lead-lag effects between individual stocks on the Paris Bourse provided strong support for the model. In addition to confirming the predicted pattern of leads and lags, the paper demonstrates that the cross-security correlation is higher for short-term returns than for long-term returns for about a third of securities pairs traded on the Paris Bourse. This result is interpreted as strong cross-security correlation of revealed information, which gives the model strong support over alternative specifications of multi-asset securities markets, such as the nonsynchronous trading hypothesis or the Chan (1993) model.