Well-known empirical puzzles in international macroeconomics concern the large divergence of equilibrium outcomes for consumption across countries from the predictions of models with full risk sharing. It is commonly believed that these risk-sharing puzzles are related to another empirical puzzle-the home-bias in equity puzzle. However, we show in a series of dynamic models that the full risk sharing equilibrium may not require much diversification of equity portfolios when there is price stickiness of the degree typically calibrated in macroeconomic models. This conclusion holds under a range of assumptions about home bias in preferences, price setting as PCP or LCP, and with or without nominal wage stickiness as long as there is some price rigidity.