This paper investigates asymmetric volatility and risk in equity markets, focusing on both firm-level and market-level volatility. The authors propose a unified framework to examine the two potential explanations for asymmetric volatility: leverage effects and time-varying risk premiums. Using data from the Nikkei 225 index, they find that volatility asymmetry is present and significant at both the market and portfolio levels, but its source differs across portfolios. They find that including leverage ratios in the volatility dynamics is important, although their economic effects are often dwarfed by the volatility feedback mechanism. Volatility feedback is enhanced by a phenomenon called covariance asymmetry, where conditional covariances with the market increase only significantly following negative market news. The authors also find no significant asymmetries in conditional betas. The paper develops a general empirical framework to examine volatility asymmetry at the market level and at the firm or portfolio level simultaneously and to differentiate between the two competing explanations. They also document a new phenomenon called covariance asymmetry, which helps explain volatility asymmetry at the firm level. They find evidence of such covariance asymmetry in their data. The authors also re-examine potential size effects in the asymmetry relation and find that volatility asymmetry is stronger for small firms. Finally, they hope that their analysis will contribute to a more widespread use of asymmetric volatility in financial modelling. The paper also discusses the implications of their findings for asset pricing models and the use of asymmetric volatility in financial modelling.This paper investigates asymmetric volatility and risk in equity markets, focusing on both firm-level and market-level volatility. The authors propose a unified framework to examine the two potential explanations for asymmetric volatility: leverage effects and time-varying risk premiums. Using data from the Nikkei 225 index, they find that volatility asymmetry is present and significant at both the market and portfolio levels, but its source differs across portfolios. They find that including leverage ratios in the volatility dynamics is important, although their economic effects are often dwarfed by the volatility feedback mechanism. Volatility feedback is enhanced by a phenomenon called covariance asymmetry, where conditional covariances with the market increase only significantly following negative market news. The authors also find no significant asymmetries in conditional betas. The paper develops a general empirical framework to examine volatility asymmetry at the market level and at the firm or portfolio level simultaneously and to differentiate between the two competing explanations. They also document a new phenomenon called covariance asymmetry, which helps explain volatility asymmetry at the firm level. They find evidence of such covariance asymmetry in their data. The authors also re-examine potential size effects in the asymmetry relation and find that volatility asymmetry is stronger for small firms. Finally, they hope that their analysis will contribute to a more widespread use of asymmetric volatility in financial modelling. The paper also discusses the implications of their findings for asset pricing models and the use of asymmetric volatility in financial modelling.