This paper analyzes to what extent international and domestic asset pricing models lead to a different estimate of the cost of capital for an individual firm under the maintained assumption of perfect international financial integration. We distinguish between (i) the multifactor Solnik-Sercu ICAPM including both the global market portfolio and exchange rate risk premia, and (ii) the single factor domestic CAPM. We use a sample of 3,293 stocks from nine countries in the period 1980-1999. The domestic CAPM yields a significantly different estimate of the cost of capital from the multifactor ICAPM for only five percent of the firms in our sample. We attribute the close correspondence between local and global pricing to strong country factors in individual stock returns, which are probably due to lack of real integration. Our results reinforce the home bias puzzle.