We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive the optimal trading behavior of thse investors, which allows us to provide a unified explanation for apparently disconnected empirical regularities in returns, trading volume and investor size. Keywords: stock market crashes, power law, tail behavior, Levy distribution, market microstructure, behavioral finance, scaling, volume, excess volatility, price pressure. JEL Classifications: G10, E44.