Uses daily data for market returns as well as for the cross-listed securities on the three main stock exchanges in the Caribbean - Barbados, Jamaica and Trinidad and Tobago - to examine the beta-convergence and sigma-convergence of the markets. Suggests that with respect to sigma-convergence, while the markets are becoming increasingly integrated, the convergence of the returns of the cross-listed securities is debatable, indicating some degree of information asymmetry. Implies that the speed of convergence is still rather slow in comparison to other markets throughout the world.