The Relation between Aggregate Earnings and Security Returns over Long Windows

This paper derives theoretical explanations for the increase in the returns-earnings R2 as earnings are aggregated over longer windows. Consistent with our intuition, the model shows that aggregation is useful because accounting lags cancel out over time, thus improving the returns-earnings correlation. Interestingly, the model reveals an additional reason for high R2 over long windows: aggregating earnings over longer windows increases the positive covariance between current and future earnings, which further increases the R2. As a consequence of this, the magnitude of market response to a dollar of earnings can be greater than one over some time range. This is consistent with prior empirical findings that over the ten-year window the regression slope coefficient is greater than one (around 1.7). In fact, a re- examination of the empirical results shows that a slope coefficient greater than one is the major contributor to the high R2 over the ten-year window. The theoretical explanation offered by this paper may have implications for studies which use long aggregation windows as a research design to test other empirical accounting issues.