Introducing a New Form of Volatility Index: the Cross-Sectional Volatility Index

We introduce a new form of volatility index, the cross-sectional volatility index. Through formal central limit arguments, we show that the cross-sectional dispersion of stock returns can be regarded as an efficient estimator for the average idiosyncratic volatility of stocks within the universe under consideration. Amongst the key advantages of the cross-sectional volatility measure over currently available measures are its observability at any frequency, its model-free nature, and its availability for every region, sector and style of the world equity markets, without the need to resort to any auxiliary option market. We also provide some interpretation of the cross-sectional volatility index as a proxy for aggregate economic uncertainty, which suggests that the cross-sectional volatility index should be intimately related to option-based implied volatility measures. We confirm this intuition by reporting a high correlation level between the VIX index and the corresponding cross-sectional volatility index based on the S&P500 universe. We also find the high correlation between the two volatility measures to be robust with respect to changes in sample period, changes in market conditions, and changes in the region under consideration. Overall, these results suggest that the cross-sectional volatility index is closely related to other volatility measures where and when such measures are available, and that it can be used as a reliable proxy for volatility when such measures are not available.