Despite the liberalization of international capital flows during the last decades, typical investors continue to hold most of their wealth in domestic assets. International RBC models can explain that 'portfolio home bias', if consumption home bias is incorporated, i.e. the fact that the bulk of consumption consists of locally produced goods (Obstfeld (2006)). However RBC models fail to explain the high volatility of equity returns and real exchange rates, and predict excessive cross-country risk sharing. This paper develops a model that simultaneously generates realistic portfolio holdings and return volatilities, and imperfect risk pooling. In the structure here, there are supply shocks, aggregate demand shocks (variations in government purchases, taste shocks), and exogenous shocks to equity risk premia. There is trade in domestic and foreign stocks and bonds. Demand shocks and risk premium shocks generate realistic return volatility, and create a strong bias towards holding local equity. Intuitively, a country-specific demand increase raises the relative price of the locally produced good, if there is consumption home bias, and it thus raises the relative return on local equity; local equity thus has a high return, in states of the world in which the household wishes to consume a lot. By biasing their portfolios toward local equity, countries can also insulate their net foreign assets and consumption spending, from exogenous risk premium shocks. When taste shocks follow random walks, there are sunspot equilibria characterized by sizable departures from full risk sharing.