The generality of spurious predictability

Previous empirical work has documented significant predictability (non-zero cross autocorrelations) in short-term security returns. Extant theoretical papers have shown that these cross autocorrelations can arise due to partial impounding of information in securities whose returns are driven by a common factor. In this paper, we show that non-zero cross autocorrelation in security returns can arise under weaker conditions than is generally known. We demonstrate that the existence of cross autocorrelations crucially depends on the information structure of informed traders. Thus, a common factor in security returns is neither sufficient nor necessary. Any one of the following conditions on the information structure can generate non-zero cross autocorrelations:

(1) existence of an informed trader with information relevant to two securities;

(2) correlation in the signal of informed traders with information relevant to different securities; or

(3) correlation in uninformed trading.

These cross autocorrelations are then shown to be spurious. That is, traders without any private information cannot make positive trading profit by exploiting cross autocorrelations.