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This paper documents that even naïve cross-market diversification strategies lead to substantial improvements of risk-return relations of government bond portfolios. Motivated by this finding, we derive a global stochastic discount factor, which prices excess returns of individual bond markets and international bond portfolio strategies. The SDF is supported by standard validation tests, but the fraction of unpriced components of bond returns is high, at around 50%. Hedging internationally diversified bond portfolios against these unpriced risks improves portfolio performance substantially. The performance improvements are robust, even when conservative bounds on individual market weights are imposed. We find that the SDF cannot be explained by the principal components derived from bond returns.