Back, Kerry and Kevin Crotty (forthcoming), "The Informational Role of Stock and Bond Volume." Review of Financial Studies.

In a Kyle (1985} model, the sign of the correlation between a firm's debt and equity returns is the same as the sign of the cross-market Kyle's lambda.  The sign is positive (negative) if private information concerns the mean (risk) of the firm's assets.   We show empirically that information conveyed by order flows is primarily about asset means.  The cross-market lambdas are quite large; consequently, the portions of bond and stock returns explained by order flows are highly correlated, even though the order flows themselves are virtually uncorrelated.