Geopolitical events are widely reported in the press and may influence the risk premium demanded by investors in addition to demand and supply of energy resources. Using the daily geopolitical risk index of Caldara and Iacoviello (2018), we demonstrate that geopolitical risk plays an important role in determining both oil price volatility and (to a lesser extent) stock market volatility. An increase in geopolitical risk is associated with positive (negative) oil (stock) returns and is consistent with geopolitical risk been linked more closely to supply disruption. The impact of geopolitical risk is greater for oil prices and this may be related to the localised nature of some geopolitical events (e.g. terror attacks in oil fields) that directly affect oil production but receive limited global press coverage. A dynamic conditional correlation (DCC) model is preferred given the dynamic nature of the magnitude of the geopolitical risk effect and oil-stock return correlation. This model shows short- and long-term volatility persistence for oil and stock prices, together with spillover effects that run from oil to stock returns. Understanding the impact of geopolitical events on volatility is important given the significant role it plays in investment decisions and policy-making, and allows us to assess the systemic nature of geopolitical risk. Our results suggest that oil futures may be a useful hedge against geopolitical risk for stock investors.