We examine pairs of large, 'Siamese twin' companies whose stocks are traded around the world but have different trading and ownership habitats. Twins pool their cash flows, so, with integrated markets, twin stocks should move together. However, the difference between the prices of twin stocks appears to be correlated with the markets on which they are traded most, i.e., a twin's relative price rises when the market on which it is traded relatively intensively rises. We examine several explanations of this phenomenon including: the discretionary use of dividend income by parent companies: differences in parent expenditures; voting rights; currency fluctuations; ex-dividend date timing issues; and tax-induced investor heterogeneity. Only the last hypothesis can explain some, but not all, of the empirical facts. We conjecture that: (a) country-specific sentiment shocks might affect share intensity, (b) investors are rational, but markets are segmented by frictions other than international transactions costs, such as agency problems. (C) 1999 Elsevier Science S.A. All rights reserved.