We train a machine learning method on a class of informed trades to develop a new measure of informed trading, the Informed Trading Intensity (``ITI''). ITI increases before earnings, M&A, and news announcements, and has implications for return reversal and asset pricing. ITI is effective...

We document a transaction level invariance relation among concurrent activity variables in the S&P 500 futures market: return volatility per transaction is proportional to the inverse of the squared expected trade size. It captures the time series behavior extremely well. Even more strikingly,...