We analyse spillovers from European Central Bank (ECB) policy surprises to asset markets outside the euro area using Switzerland as a case study. Our results suggest that Swiss asset price responses to ECB policy surprises are significant. They depend on the type and nature of the surprise and change over time. Decomposing bond yields into expected short-term interest rates and the term premium reveals that both signalling and portfolio rebalancing effects explain the responses of bond yields of various maturities to surprises resulting from scheduled ECB policy decisions. ECB policy surprises are more important to Swiss government bond yields than Swiss stock prices.