We propose a theory of large movements in stock market activity. Our theory is motivated by growing empirical evidence on the power-law tailed nature of distributions that characterize large movements of distinct variables describing stock market activity such as returns, volumes, number of trades, and order flow. Remarkably, the exponents that characterize these power laws are similar for different countries, for different types and sizes of markets, and for different market trends, suggesting that a generic theoretical basis may underlie these regularities. Our theory provides a unified way to understand the power-law tailed distributions of these variables, their apparently universal nature, and the precise values of exponents. It links large movements in market activity to the power-law distribution of the size of large financial institutions. The trades made by large financial institutions create large fluctuations in volume and returns. We show that optimal trading by such large institutions generate power-law tailed distributions for market variables with exponents that agree with those found in empirical data. Furthermore, our model also makes a large number of testable out-of-sample predictions. Keywords: stock market crashes, power law, tail behavior, Levy distribution, market microstructure, behavioral finance, scaling, volume, excess volatility, price pressure. JEL Classification: G1, G12.