Equity return dispersion is measured as the standard deviation of returns across different stocks or portfolios. Unlike volatility it can be measured even for a single relevant period and, thus, can record changing market conditions fast. Academic literature has shown a clear positive relation between return dispersion, volatility and economic conditions. New empirical research suggests that return dispersion can predict both future equity return volatility and equity premia. The predictive relation has been non-linear, suggesting that it is the large changes in dispersion that matter.

Demirer, Riza, Rangan Gupta, Zhihui Lv and Wing-Keung Wong (2018), “Equity Return Dispersion and Stock Market Volatility: Evidence from Multivariate Linear and Nonlinear Causality Tests”, University of Pretoria, Working paper, 2018-46.

The post ties in with SRSV’s summary lecture on macro information efficiency.
The below are quotes from the paper. Emphasis and cursive text have been added. Formulas have been replaced by text.

What is return dispersion and why does it matter?

“Equity return dispersion is expressed as the cross-sectional standard deviation of daily stock returns…[and] calculated as the square root of a (potentially weighted) average of squared daily stock return deviations from the market’s mean return…Equity return dispersion…can be regarded as a measure of directional similarity in stock returns for a given day…Unlike traditional measures of correlation and volatility, return dispersion provides an aggregate measure of co-movement in a portfolio for a given time period [and can be calculated even for a single day]. “

“Equity return dispersion…either at the individual stock or disaggregate portfolio level, carries reliable information regarding the state of the economy and future stock market volatility.”

“The [academic] literature provides ample evidence that associates equity return dispersion with different aspects of risk…Studies…associate return dispersion with economic expansions and recessions, documenting asymmetries in the cross-sectional dispersion of stock returns with respect to stock market movements and business cycles…[Academic research also] supports the role of return dispersion as a systematic risk factor [related to] accrual and investment anomalies, associating high level of return dispersion exposure with conditions that are not conducive to growth and investment…We find significant causality from business conditions to return dispersion… Expansionary market states are associated with low level of equity return dispersion.”

“Earlier studies…[1] show that return dispersion possesses incremental information regarding idiosyncratic as well as aggregate stock market volatility…[2] show that return dispersion reliably predicts the time-variation in stock market returns, volatility as well as the value and momentum premia.”

Empirical analysis

“We compute the cross-sectional standard deviation of daily returns on 100 portfolios sorted on size and book-to-market ratios…the use of portfolios in the computation of return dispersion mitigates estimation errors due to the presence of illiquid and small stocks in the cross-section of individual stocks. “

“[The figure below] presents the time series plots for daily equity return dispersion and stock market volatility during the sample period. Not surprisingly, we observe several notable spikes in both series particularly during the Asian crisis period in the late 1990s and the global financial crisis periods… return dispersion values also exhibit similar spikes during these periods…[suggesting] that these two series are possibly driven by a common fundamental factor.”

Multivariate causality tests that control for business cycles in the causal relationship between return dispersion and stock market volatility allows us to explore whether return dispersion possesses any incremental information regarding stock market return dynamics…We supplement our multivariate causality tests with the Aruoba-Diebold-Scotti Business Conditions Index (ADS) in order to account for economic conditions…The ADS index measures economic activity at high frequency using a dynamic factor model that includes a number of economic variables…[and is available on]  the Philadelphia Fed’s website.”

“Both bivariate and multivariate nonlinear causality tests yield significant evidence of causality from return dispersion to both stock market volatility and equity premium, even after controlling for the state of the economy…via a business conditions index…Overall, our findings suggest that both return dispersion and business conditions are valid joint forecasters of both the stock market volatility and excess market return…Return dispersion possesses incremental information regarding future stock return dynamics beyond which can be explained by the state of the economy.”

Linear causality tests generally fail to detect causal effects from return dispersion to excess market returns and volatility…when we control for the business conditions via the Aruoba-Diebold-Scotti business conditions index…Summary statistics reveal…significant skewness for both return dispersion and stock market volatility, suggesting greater likelihood of experiencing large values for these variables…Tests indicate significant evidence of nonlinearity in all time series at the highest significance level, justifying the use of subsequent nonlinear causality tests.