We use a threshold VAR model to capture the connectedness of the equity returns of the G7 in a regime-contingent manner as defined by low- and high-geopolitical risks (GPR). We find that connectedness is statistically stronger when GPR is at its higher rather than lower regime, but more importantly, this observation can be associated with the threat of adverse geopolitical events, rather than with their actual realization. To explain our empirical observations we employ a model of international trade in assets and international relative asset prices. We introduce uncertainty in future dividend payments combined with agents' ambiguity aversion to changes in the expected dividends. This allows us to model a geopolitical threat as a shock that affects the level of ambiguity about future dividends. At the same time, a geopolitical act is defined as a shock to the current period endowment of a given country, with limited effects on asset prices and returns. Our obtained results have important portfolio allocation implications for investors.