We study a number of large international military conflicts since World War II where we establish a news analysis as a proxy for the estimated likelihood that the conflict will result in a war. We find that in cases when there is a pre-war phase, an increase in the war likelihood tends to decrease stock prices, but the ultimate outbreak of a war increases them. In cases when a war starts as a surprise, the outbreak of a war decreases stock prices. We show that this paradox cannot be explained by uncertainty about investment decisions, nor by the expectation about a quick end of the war or ambiguity aversion. A connection of this puzzling phenomenon to mean-variance preferences of investors is suggested.