Geopolitical events can impact volatilities of all assets, asset classes, sectors and countries. It is shown that innovations to volatilities are correlated across assets and therefore can be used to measure and hedge geopolitical risk. We introduce a definition of geopolitical risk which is based on volatility shocks to a wide range of financial market prices. To measure geopolitical risk, we propose a statistical model for the magnitude of the common volatility shocks. Accordingly, a test and estimation methods are developed and studied using both empirical and simulated data. We provide a novel explanation for why idiosyncratic volatilities comove based on a new way to formulate multiplicative factors. Finally, we propose a new criterion for portfolio optimality which is intended to reduce the exposure to geopolitical risk.