Asymmetric volatility and risk in equity markets

It appears that volatility in equity markets is asymmetric: returns and conditional volatility are negatively correlated. We provide a unified framework to simultaneously investigate asymmetric volatility at the firm and the market level and to examine two potential explanations of the asymmetry: leverage effects and volatility feedback. Our empirical application uses the market portfolio and portfolios with different leverage constructed from Nikkei 225 stocks. We reject the pure leverage model of Christie (1982) and find support for a volatility feedback story. Volatility feedback at the firm level is enhanced by strong asymmetries in conditional covariances. Conditional betas do not show significant asymmetries, We document the risk premium implications of these findings.