We propose an estimation methodology tailored for large unbalanced panels of individual stock returns to study the factor structure and expected returns in international stock markets. We show that the local market is necessary to capture the factor structure in both developed and emerging markets. Neither the presence of multiple world risk factors, regional risk factors, systematic currency risk factors, nor a country-specific currency subsumes the importance of the local market factor. All factors, including the local market, carry significant risk premia across a large proportion of countries. The contribution of pricing errors to total expected returns is large and time-varying.