This paper documents that daily stock returns of both firms and industries are more dispersed when the overall stock market rises than when it falls. This positive relation is conceptually distinct from - and appears unrelated to - asymmetric return correlations. I argue that the source of the relation is positive skewness in sector-specific return shocks. I use this asymmetric behavior to explain a previously-observed puzzle: aggregate trading volume tends to be higher on days when the stock market rises than when it falls. The idea proposed here is that trading is more active on days when the market rises because on those days there is more non-market news on which to trade. I find that empirically, the bulk of the relation between volume and the signed market return is explained by variations in non-market volatility.