In a world with multiplicative production uncertainty and implicit labor contracts, we show that the Rybczynski theorem retains its validity; therefore the quantity version of the Heckscher-Ohlin theorem survives as well. We also show that the Stolper-Samuelson theorem may not hold. A small increase in the price of the capital-intensive good may benefit labor. We derive a strong version of the factor price equalization theorem that shows free trade tends to equalize sector-specific unemployment rates and sector-specific factor prices across countries. Finally, we relate trade patterns to international differences in the degree of risk aversion.